1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="m1" class="ltx_Math" alttext="m" display="inline">
<semantics>
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci>m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="m1" class="ltx_Math" alttext="m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
- <ci>m</ci>
+ <ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="m2" class="ltx_Math" alttext="t" display="inline">
<semantics>
<mi>t</mi>
<annotation-xml encoding="MathML-Content">
<ci>t</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">t</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>t</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">t</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>t</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">t</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="m2" class="ltx_Math" alttext="t" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>t</mi>
<annotation-xml encoding="MathML-Content">
- <ci>t</ci>
+ <ci encoding="">t</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok>t</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">t</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="m3" class="ltx_Math" alttext="|n^{2}+n-m|" display="inline">
<semantics>
<mrow>
<mo fence="true">|</mo>
<mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>n</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
<mo fence="true">|</mo>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<abs/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>n</ci>
<cn type="integer">2</cn>
</apply>
<ci>n</ci>
</apply>
<ci>m</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
<XMApp>
<XMTok meaning="minus" role="ADDOP">-</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post3"/>
<XMTok role="UNKNOWN" font="italic">n</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">n</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">|n^{2}+n-m|</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mo>|</mo>
<mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>n</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
<mo>|</mo>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<abs/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">n</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<ci encoding="">n</ci>
</apply>
<ci encoding="">m</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMApp>
<XMTok>-</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok/>
<XMTok>n</XMTok>
<XMTok>2</XMTok>
</XMApp>
<XMTok>n</XMTok>
</XMApp>
<XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">|n^{2}+n-m|</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 | @@ -1,58 +1,58 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="m3" class="ltx_Math" alttext="|n^{2}+n-m|" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
- <mo fence="true">|</mo>
+ <mo>|</mo>
<mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>n</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
- <mo fence="true">|</mo>
+ <mo>|</mo>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<abs/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>n</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">n</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
- <ci>n</ci>
+ <ci encoding="">n</ci>
</apply>
- <ci>m</ci>
+ <ci encoding="">m</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="minus" role="ADDOP">-</XMTok>
+ <XMTok>-</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post3"/>
- <XMTok role="UNKNOWN" font="italic">n</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>n</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">n</XMTok>
+ <XMTok>n</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">|n^{2}+n-m|</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="m4" class="ltx_Math" alttext="n\in[t+1,t+\sqrt{m}]" display="inline">
<semantics>
<mrow>
<mi>n</mi>
<mo>∈</mo>
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>,</mo>
<mrow>
<mi>t</mi>
<mo>+</mo>
<msqrt>
<mi>m</mi>
</msqrt>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<in/>
<ci>n</ci>
<apply>
<interval closure="closed"/>
<apply>
<plus/>
<ci>t</ci>
<cn type="integer">1</cn>
</apply>
<apply>
<plus/>
<ci>t</ci>
<apply>
<root/>
<ci>m</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="element-of" name="in" role="RELOP">∈</XMTok>
<XMTok role="UNKNOWN" font="italic">n</XMTok>
<XMApp>
<XMTok argclose="]" argopen="[" meaning="closed-interval" role="FENCED" separators=","/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMApp>
<XMTok meaning="square-root"/>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n\in[t+1,t+\sqrt{m}]</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>n</mi>
<mo>∈</mo>
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>,</mo>
<mrow>
<mi>t</mi>
<mo>+</mo>
<msqrt>
<mi>m</mi>
</msqrt>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<in/>
<ci encoding="">n</ci>
<apply>
<interval closure="closed"/>
<apply>
<plus/>
<ci encoding="">t</ci>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
<apply>
<plus/>
<ci encoding="">t</ci>
<apply>
<root/>
<ci encoding="">m</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>∈</XMTok>
<XMTok>n</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMTok>t</XMTok>
<XMTok>1</XMTok>
</XMApp>
<XMApp>
<XMTok>+</XMTok>
<XMTok>t</XMTok>
<XMApp>
<XMTok/>
<XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n\in[t+1,t+\sqrt{m}]</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 | @@ -1,75 +1,75 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="m4" class="ltx_Math" alttext="n\in[t+1,t+\sqrt{m}]" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>n</mi>
<mo>∈</mo>
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>,</mo>
<mrow>
<mi>t</mi>
<mo>+</mo>
<msqrt>
<mi>m</mi>
</msqrt>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<in/>
- <ci>n</ci>
+ <ci encoding="">n</ci>
<apply>
<interval closure="closed"/>
<apply>
<plus/>
- <ci>t</ci>
- <cn type="integer">1</cn>
+ <ci encoding="">t</ci>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
<apply>
<plus/>
- <ci>t</ci>
+ <ci encoding="">t</ci>
<apply>
<root/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="element-of" name="in" role="RELOP">∈</XMTok>
- <XMTok role="UNKNOWN" font="italic">n</XMTok>
+ <XMTok>∈</XMTok>
+ <XMTok>n</XMTok>
<XMApp>
- <XMTok argclose="]" argopen="[" meaning="closed-interval" role="FENCED" separators=","/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>+</XMTok>
+ <XMTok>t</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok>+</XMTok>
+ <XMTok>t</XMTok>
<XMApp>
- <XMTok meaning="square-root"/>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n\in[t+1,t+\sqrt{m}]</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m1" class="ltx_Math" alttext="m" display="inline">
<semantics>
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci>m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m1" class="ltx_Math" alttext="m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
- <ci>m</ci>
+ <ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m2" class="ltx_Math" alttext="4m-1" display="inline">
<semantics>
<mrow>
<mrow>
<mn>4</mn>
<mo></mo>
<mi>m</mi>
</mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<minus/>
<apply>
<times/>
<cn type="integer">4</cn>
<ci>m</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="minus" role="ADDOP">-</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m-1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mn>4</mn>
<mi>m</mi>
</mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<minus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">m</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>-</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m-1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,39 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m2" class="ltx_Math" alttext="4m-1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mn>4</mn>
- <mo></mo>
<mi>m</mi>
</mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<minus/>
<apply>
<times/>
- <cn type="integer">4</cn>
- <ci>m</ci>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">m</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="minus" role="ADDOP">-</XMTok>
+ <XMTok>-</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m-1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m3" class="ltx_Math" alttext="\mathbb{Q}(\sqrt{1-4m})" display="inline">
<semantics>
<mrow>
<mi>ℚ</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<msqrt>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mrow>
<mn>4</mn>
<mo></mo>
<mi>m</mi>
</mrow>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
<ci>ℚ</ci>
<apply>
<root/>
<apply>
<minus/>
<cn type="integer">1</cn>
<apply>
<times/>
<cn type="integer">4</cn>
<ci>m</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
<XMApp close=")" open="(">
<XMTok meaning="square-root"/>
<XMApp>
<XMTok meaning="minus" role="ADDOP">-</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{1-4m})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mn>1</mn>
<mo>-</mo>
<mrow>
<mn>4</mn>
<mi>m</mi>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
<ci encoding="">Q</ci>
<apply>
<root/>
<apply>
<minus/>
<cn encoding="" base="10" type="integer">1</cn>
<apply>
<times/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">m</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok></XMTok>
<XMTok>Q</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>-</XMTok>
<XMTok>1</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{1-4m})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 | @@ -1,63 +1,59 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m3" class="ltx_Math" alttext="\mathbb{Q}(\sqrt{1-4m})" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
- <mi>ℚ</mi>
- <mo></mo>
+ <mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
+ <mn>1</mn>
+ <mo>-</mo>
<mrow>
- <mn>1</mn>
- <mo>-</mo>
- <mrow>
- <mn>4</mn>
- <mo></mo>
- <mi>m</mi>
- </mrow>
+ <mn>4</mn>
+ <mi>m</mi>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
- <ci>ℚ</ci>
+ <ci encoding="">Q</ci>
<apply>
<root/>
<apply>
<minus/>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
<apply>
<times/>
- <cn type="integer">4</cn>
- <ci>m</ci>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">m</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
- <XMApp close=")" open="(">
- <XMTok meaning="square-root"/>
+ <XMTok></XMTok>
+ <XMTok>Q</XMTok>
+ <XMApp>
+ <XMTok/>
<XMApp>
- <XMTok meaning="minus" role="ADDOP">-</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>-</XMTok>
+ <XMTok>1</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{1-4m})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m4" class="ltx_Math" alttext="n^{2}+n+m" display="inline">
<semantics>
<mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>n</mi>
<mo>+</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>n</ci>
<cn type="integer">2</cn>
</apply>
<ci>n</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">n</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">n</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n^{2}+n+m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>n</mi>
<mo>+</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">n</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<ci encoding="">n</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok/>
<XMTok>n</XMTok>
<XMTok>2</XMTok>
</XMApp>
<XMTok>n</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n^{2}+n+m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 | @@ -1,42 +1,42 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m4" class="ltx_Math" alttext="n^{2}+n+m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>n</mi>
<mo>+</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>n</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">n</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
- <ci>n</ci>
- <ci>m</ci>
+ <ci encoding="">n</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">n</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>n</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">n</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>n</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n^{2}+n+m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m5" class="ltx_Math" alttext="0\leq n\leq m-3" display="inline">
<semantics>
<mrow>
<mn>0</mn>
<mo>≤</mo>
<mi>n</mi>
<mo>≤</mo>
<mrow>
<mi>m</mi>
<mo>-</mo>
<mn>3</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<leq/>
<cn type="integer">0</cn>
<ci xml:id="p2.m5.sh1.cmml">n</ci>
</apply>
<apply>
<leq/>
<share href="#p2.m5.sh1.cmml"/>
<apply xml:id="p2.m5.sh2c.cmml">
<minus xml:id="p2.m5.sh2.cmml"/>
<ci xml:id="p2.m5.sh2a.cmml">m</ci>
<cn type="integer" xml:id="p2.m5.sh2b.cmml">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="multirelation"/>
<XMTok meaning="0" role="NUMBER">0</XMTok>
<XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
<XMTok role="UNKNOWN" font="italic" xml:id="p2.m5.sh1.xm" fragid="p2.m5.sh1.xm">n</XMTok>
<XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
<XMApp xml:id="p2.m5.sh2.xm" fragid="p2.m5.sh2.xm">
<XMTok meaning="minus" role="ADDOP">-</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMTok meaning="3" role="NUMBER">3</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">0\leq n\leq m-3</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mn>0</mn>
<mo>≤</mo>
<mi>n</mi>
<mo>≤</mo>
<mrow>
<mi>m</mi>
<mo>-</mo>
<mn>3</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<leq/>
<cn encoding="" base="10" type="integer">0</cn>
<ci encoding="">n</ci>
</apply>
<apply>
<leq/>
<share/>
<apply>
<minus encoding=""/>
<ci encoding="">m</ci>
<cn encoding="" base="10" type="integer">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>0</XMTok>
<XMTok>≤</XMTok>
<XMTok>n</XMTok>
<XMTok>≤</XMTok>
<XMApp>
<XMTok>-</XMTok>
<XMTok>m</XMTok>
<XMTok>3</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">0\leq n\leq m-3</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 | @@ -1,52 +1,52 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m5" class="ltx_Math" alttext="0\leq n\leq m-3" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mn>0</mn>
<mo>≤</mo>
<mi>n</mi>
<mo>≤</mo>
<mrow>
<mi>m</mi>
<mo>-</mo>
<mn>3</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<leq/>
- <cn type="integer">0</cn>
- <ci xml:id="p2.m5.sh1.cmml">n</ci>
+ <cn encoding="" base="10" type="integer">0</cn>
+ <ci encoding="">n</ci>
</apply>
<apply>
<leq/>
- <share href="#p2.m5.sh1.cmml"/>
- <apply xml:id="p2.m5.sh2c.cmml">
- <minus xml:id="p2.m5.sh2.cmml"/>
- <ci xml:id="p2.m5.sh2a.cmml">m</ci>
- <cn type="integer" xml:id="p2.m5.sh2b.cmml">3</cn>
+ <share/>
+ <apply>
+ <minus encoding=""/>
+ <ci encoding="">m</ci>
+ <cn encoding="" base="10" type="integer">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="multirelation"/>
- <XMTok meaning="0" role="NUMBER">0</XMTok>
- <XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
- <XMTok role="UNKNOWN" font="italic" xml:id="p2.m5.sh1.xm" fragid="p2.m5.sh1.xm">n</XMTok>
- <XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
- <XMApp xml:id="p2.m5.sh2.xm" fragid="p2.m5.sh2.xm">
- <XMTok meaning="minus" role="ADDOP">-</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
- <XMTok meaning="3" role="NUMBER">3</XMTok>
+ <XMTok/>
+ <XMTok>0</XMTok>
+ <XMTok>≤</XMTok>
+ <XMTok>n</XMTok>
+ <XMTok>≤</XMTok>
+ <XMApp>
+ <XMTok>-</XMTok>
+ <XMTok>m</XMTok>
+ <XMTok>3</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">0\leq n\leq m-3</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m6" class="ltx_Math" alttext="f_{m}(x)=x^{2}+x-m" display="inline">
<semantics>
<mrow>
<mrow>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<mo></mo>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>x</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
<ci>x</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>x</ci>
<cn type="integer">2</cn>
</apply>
<ci>x</ci>
</apply>
<ci>m</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok possibleFunction="yes" role="UNKNOWN" font="italic">f</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok close=")" open="(" role="UNKNOWN" font="italic">x</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="minus" role="ADDOP">-</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">x</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">x</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}(x)=x^{2}+x-m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>x</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
<ci encoding="">x</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">x</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<ci encoding="">x</ci>
</apply>
<ci encoding="">m</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMApp>
<XMTok></XMTok>
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>x</XMTok>
</XMApp>
<XMApp>
<XMTok>-</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok/>
<XMTok>x</XMTok>
<XMTok>2</XMTok>
</XMApp>
<XMTok>x</XMTok>
</XMApp>
<XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}(x)=x^{2}+x-m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 | @@ -1,87 +1,86 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m6" class="ltx_Math" alttext="f_{m}(x)=x^{2}+x-m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
- <mo></mo>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>x</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
- <ci>x</ci>
+ <ci encoding="">x</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>x</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">x</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
- <ci>x</ci>
+ <ci encoding="">x</ci>
</apply>
- <ci>m</ci>
+ <ci encoding="">m</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
+ <XMTok>=</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
+ <XMTok></XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="italic">f</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok close=")" open="(" role="UNKNOWN" font="italic">x</XMTok>
+ <XMTok>x</XMTok>
</XMApp>
<XMApp>
- <XMTok meaning="minus" role="ADDOP">-</XMTok>
+ <XMTok>-</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">x</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>x</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">x</XMTok>
+ <XMTok>x</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}(x)=x^{2}+x-m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m7" class="ltx_Math" alttext="t" display="inline">
<semantics>
<mi>t</mi>
<annotation-xml encoding="MathML-Content">
<ci>t</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">t</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>t</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">t</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>t</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">t</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m7" class="ltx_Math" alttext="t" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>t</mi>
<annotation-xml encoding="MathML-Content">
- <ci>t</ci>
+ <ci encoding="">t</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok>t</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">t</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m8" class="ltx_Math" alttext="|f_{m}(n)|" display="inline">
<semantics>
<mrow>
<mo fence="true">|</mo>
<mrow>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<mo></mo>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo fence="true">|</mo>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<abs/>
<apply>
<times/>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
<ci>n</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok possibleFunction="yes" role="UNKNOWN" font="italic">f</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok close=")" open="(" role="UNKNOWN" font="italic">n</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">|f_{m}(n)|</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mo>|</mo>
<mrow>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>|</mo>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<abs/>
<apply>
<times/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
<ci encoding="">n</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMApp>
<XMTok></XMTok>
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>n</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">|f_{m}(n)|</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 | @@ -1,52 +1,51 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m8" class="ltx_Math" alttext="|f_{m}(n)|" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
- <mo fence="true">|</mo>
+ <mo>|</mo>
<mrow>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
- <mo></mo>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
</mrow>
- <mo fence="true">|</mo>
+ <mo>|</mo>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<abs/>
<apply>
<times/>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
- <ci>n</ci>
+ <ci encoding="">n</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
+ <XMTok></XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="italic">f</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok close=")" open="(" role="UNKNOWN" font="italic">n</XMTok>
+ <XMTok>n</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">|f_{m}(n)|</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m9" class="ltx_Math" alttext="n\in[t+1,t+\sqrt{m}]" display="inline">
<semantics>
<mrow>
<mi>n</mi>
<mo>∈</mo>
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>,</mo>
<mrow>
<mi>t</mi>
<mo>+</mo>
<msqrt>
<mi>m</mi>
</msqrt>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<in/>
<ci>n</ci>
<apply>
<interval closure="closed"/>
<apply>
<plus/>
<ci>t</ci>
<cn type="integer">1</cn>
</apply>
<apply>
<plus/>
<ci>t</ci>
<apply>
<root/>
<ci>m</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="element-of" name="in" role="RELOP">∈</XMTok>
<XMTok role="UNKNOWN" font="italic">n</XMTok>
<XMApp>
<XMTok argclose="]" argopen="[" meaning="closed-interval" role="FENCED" separators=","/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMApp>
<XMTok meaning="square-root"/>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n\in[t+1,t+\sqrt{m}]</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>n</mi>
<mo>∈</mo>
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>,</mo>
<mrow>
<mi>t</mi>
<mo>+</mo>
<msqrt>
<mi>m</mi>
</msqrt>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<in/>
<ci encoding="">n</ci>
<apply>
<interval closure="closed"/>
<apply>
<plus/>
<ci encoding="">t</ci>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
<apply>
<plus/>
<ci encoding="">t</ci>
<apply>
<root/>
<ci encoding="">m</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>∈</XMTok>
<XMTok>n</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMTok>t</XMTok>
<XMTok>1</XMTok>
</XMApp>
<XMApp>
<XMTok>+</XMTok>
<XMTok>t</XMTok>
<XMApp>
<XMTok/>
<XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n\in[t+1,t+\sqrt{m}]</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 | @@ -1,75 +1,75 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p2.m9" class="ltx_Math" alttext="n\in[t+1,t+\sqrt{m}]" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>n</mi>
<mo>∈</mo>
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>,</mo>
<mrow>
<mi>t</mi>
<mo>+</mo>
<msqrt>
<mi>m</mi>
</msqrt>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<in/>
- <ci>n</ci>
+ <ci encoding="">n</ci>
<apply>
<interval closure="closed"/>
<apply>
<plus/>
- <ci>t</ci>
- <cn type="integer">1</cn>
+ <ci encoding="">t</ci>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
<apply>
<plus/>
- <ci>t</ci>
+ <ci encoding="">t</ci>
<apply>
<root/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="element-of" name="in" role="RELOP">∈</XMTok>
- <XMTok role="UNKNOWN" font="italic">n</XMTok>
+ <XMTok>∈</XMTok>
+ <XMTok>n</XMTok>
<XMApp>
- <XMTok argclose="]" argopen="[" meaning="closed-interval" role="FENCED" separators=","/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>+</XMTok>
+ <XMTok>t</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok>+</XMTok>
+ <XMTok>t</XMTok>
<XMApp>
- <XMTok meaning="square-root"/>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n\in[t+1,t+\sqrt{m}]</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m1" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post4"/>
<XMTok role="UNKNOWN" font="italic">f</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m1" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post4"/>
- <XMTok role="UNKNOWN" font="italic">f</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m2" class="ltx_Math" alttext="m=1" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>m</ci>
<cn type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">m</ci>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>m</XMTok>
<XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,27 +1,27 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m2" class="ltx_Math" alttext="m=1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>m</ci>
- <cn type="integer">1</cn>
+ <ci encoding="">m</ci>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>m</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m3" class="ltx_Math" alttext="m=2" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>m</ci>
<cn type="integer">2</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">m</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>m</XMTok>
<XMTok>2</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,27 +1,27 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m3" class="ltx_Math" alttext="m=2" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>m</ci>
- <cn type="integer">2</cn>
+ <ci encoding="">m</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>m</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m4" class="ltx_Math" alttext="m=p^{2}" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>=</mo>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>m</ci>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>p</ci>
<cn type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post4"/>
<XMTok role="UNKNOWN" font="italic">p</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=p^{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">m</ci>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">p</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>m</XMTok>
<XMApp>
<XMTok/>
<XMTok>p</XMTok>
<XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=p^{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,38 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m4" class="ltx_Math" alttext="m=p^{2}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<msup>
<mi>p</mi>
<mn>2</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>p</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">p</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post4"/>
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>p</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=p^{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m5" class="ltx_Math" alttext="p" display="inline">
<semantics>
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci>p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m5" class="ltx_Math" alttext="p" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
- <ci>p</ci>
+ <ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
+ <XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m6" class="ltx_Math" alttext="m=t^{2}+t\pm 1" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
<mn>1</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>m</ci>
<apply>
<csymbol cd="latexml">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>t</ci>
<cn type="integer">2</cn>
</apply>
<ci>t</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post4"/>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=t^{2}+t\pm 1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
<mn>1</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">m</ci>
<apply>
<csymbol encoding="">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">t</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<ci encoding="">t</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>m</XMTok>
<XMApp>
<XMTok>±</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok/>
<XMTok>t</XMTok>
<XMTok>2</XMTok>
</XMApp>
<XMTok>t</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=t^{2}+t\pm 1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 | @@ -1,60 +1,60 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m6" class="ltx_Math" alttext="m=t^{2}+t\pm 1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
<mn>1</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
<apply>
- <csymbol cd="latexml">plus-or-minus</csymbol>
+ <csymbol encoding="">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>t</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
- <ci>t</ci>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
+ <XMTok>±</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post4"/>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>t</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=t^{2}+t\pm 1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m7" class="ltx_Math" alttext="m=t^{2}+t\pm\frac{2t+1}{3}" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
<mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>m</ci>
<apply>
<csymbol cd="latexml">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>t</ci>
<cn type="integer">2</cn>
</apply>
<ci>t</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">2</cn>
<ci>t</ci>
</apply>
<cn type="integer">1</cn>
</apply>
<cn type="integer">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post4"/>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMApp>
<XMTok mathstyle="text" meaning="divide" role="MULOP"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
<XMTok meaning="3" role="NUMBER">3</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=t^{2}+t\pm\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">m</ci>
<apply>
<csymbol encoding="">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">t</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<ci encoding="">t</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">2</cn>
<ci encoding="">t</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
<cn encoding="" base="10" type="integer">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>m</XMTok>
<XMApp>
<XMTok>±</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok/>
<XMTok>t</XMTok>
<XMTok>2</XMTok>
</XMApp>
<XMTok>t</XMTok>
</XMApp>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>2</XMTok>
<XMTok>t</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
<XMTok>3</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=t^{2}+t\pm\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 | @@ -1,95 +1,94 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m7" class="ltx_Math" alttext="m=t^{2}+t\pm\frac{2t+1}{3}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
- <mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
<apply>
- <csymbol cd="latexml">plus-or-minus</csymbol>
+ <csymbol encoding="">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>t</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
- <ci>t</ci>
+ <ci encoding="">t</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">2</cn>
- <ci>t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
- <cn type="integer">3</cn>
+ <cn encoding="" base="10" type="integer">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
+ <XMTok>±</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post4"/>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>t</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
<XMApp>
- <XMTok mathstyle="text" meaning="divide" role="MULOP"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>2</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
- <XMTok meaning="3" role="NUMBER">3</XMTok>
+ <XMTok>3</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=t^{2}+t\pm\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m8" class="ltx_Math" alttext="\frac{2t+1}{3}" display="inline">
<semantics>
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
<mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>3</mn>
</mfrac>
<annotation-xml encoding="MathML-Content">
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">2</cn>
<ci>t</ci>
</apply>
<cn type="integer">1</cn>
</apply>
<cn type="integer">3</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok mathstyle="text" meaning="divide" role="MULOP"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
<XMTok meaning="3" role="NUMBER">3</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>3</mn>
</mfrac>
<annotation-xml encoding="MathML-Content">
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">2</cn>
<ci encoding="">t</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
<cn encoding="" base="10" type="integer">3</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>2</XMTok>
<XMTok>t</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
<XMTok>3</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 | @@ -1,50 +1,49 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i1.p1.m8" class="ltx_Math" alttext="\frac{2t+1}{3}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
- <mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>3</mn>
</mfrac>
<annotation-xml encoding="MathML-Content">
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">2</cn>
- <ci>t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
- <cn type="integer">3</cn>
+ <cn encoding="" base="10" type="integer">3</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok mathstyle="text" meaning="divide" role="MULOP"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>2</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
- <XMTok meaning="3" role="NUMBER">3</XMTok>
+ <XMTok>3</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i2.p1.m1" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post4"/>
<XMTok role="UNKNOWN" font="italic">f</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i2.p1.m1" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post4"/>
- <XMTok role="UNKNOWN" font="italic">f</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i2.p1.m2" class="ltx_Math" alttext="\mathbb{Q}(\sqrt{4m+1})" display="inline">
<semantics>
<mrow>
<mi>ℚ</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<msqrt>
<mrow>
<mrow>
<mn>4</mn>
<mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
<ci>ℚ</ci>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">4</cn>
<ci>m</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
<XMApp close=")" open="(">
<XMTok meaning="square-root"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{4m+1})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mrow>
<mn>4</mn>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
<ci encoding="">Q</ci>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">m</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok></XMTok>
<XMTok>Q</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{4m+1})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 | @@ -1,63 +1,59 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i2.p1.m2" class="ltx_Math" alttext="\mathbb{Q}(\sqrt{4m+1})" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
- <mi>ℚ</mi>
- <mo></mo>
+ <mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mrow>
- <mrow>
- <mn>4</mn>
- <mo></mo>
- <mi>m</mi>
- </mrow>
- <mo>+</mo>
- <mn>1</mn>
+ <mn>4</mn>
+ <mi>m</mi>
</mrow>
+ <mo>+</mo>
+ <mn>1</mn>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
- <ci>ℚ</ci>
+ <ci encoding="">Q</ci>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">4</cn>
- <ci>m</ci>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">m</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
- <XMApp close=")" open="(">
- <XMTok meaning="square-root"/>
+ <XMTok></XMTok>
+ <XMTok>Q</XMTok>
+ <XMApp>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{4m+1})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i2.p1.m3" class="ltx_Math" alttext="1" display="inline">
<semantics>
<mn>1</mn>
<annotation-xml encoding="MathML-Content">
<cn type="integer">1</cn>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mn>1</mn>
<annotation-xml encoding="MathML-Content">
<cn encoding="" base="10" type="integer">1</cn>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>1</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i2.p1.m3" class="ltx_Math" alttext="1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mn>1</mn>
<annotation-xml encoding="MathML-Content">
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i3.p1.m1" class="ltx_Math" alttext="m" display="inline">
<semantics>
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci>m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i3.p1.m1" class="ltx_Math" alttext="m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
- <ci>m</ci>
+ <ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i3.p1.m2" class="ltx_Math" alttext="4m+1" display="inline">
<semantics>
<mrow>
<mrow>
<mn>4</mn>
<mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">4</cn>
<ci>m</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mn>4</mn>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">m</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,39 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i3.p1.m2" class="ltx_Math" alttext="4m+1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mn>4</mn>
- <mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">4</cn>
- <ci>m</ci>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">m</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i3.p1.m3" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post4"/>
<XMTok role="UNKNOWN" font="italic">f</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="I1.i3.p1.m3" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post4"/>
- <XMTok role="UNKNOWN" font="italic">f</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p3.m1" class="ltx_Math" alttext="m" display="inline">
<semantics>
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci>m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p3.m1" class="ltx_Math" alttext="m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
- <ci>m</ci>
+ <ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p3.m2" class="ltx_Math" alttext="4m+1" display="inline">
<semantics>
<mrow>
<mrow>
<mn>4</mn>
<mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">4</cn>
<ci>m</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mn>4</mn>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">m</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,39 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p3.m2" class="ltx_Math" alttext="4m+1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mn>4</mn>
- <mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">4</cn>
- <ci>m</ci>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">m</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmTheo2.p1.m1" class="ltx_Math" alttext="m\geq 0" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo mathvariant="normal">≥</mo>
<mn mathvariant="normal">0</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<geq/>
<ci>m</ci>
<cn type="integer">0</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="greater-than-or-equals" name="geq" role="RELOP" font="upright">≥</XMTok>
<XMTok role="UNKNOWN">m</XMTok>
<XMTok meaning="0" role="NUMBER" font="upright">0</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m\geq 0</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo mathvariant="normal">≥</mo>
<mn mathvariant="normal">0</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<geq/>
<ci encoding="">m</ci>
<cn encoding="" base="10" type="integer">0</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>≥</XMTok>
<XMTok>m</XMTok>
<XMTok>0</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m\geq 0</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,27 +1,27 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmTheo2.p1.m1" class="ltx_Math" alttext="m\geq 0" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo mathvariant="normal">≥</mo>
<mn mathvariant="normal">0</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<geq/>
- <ci>m</ci>
- <cn type="integer">0</cn>
+ <ci encoding="">m</ci>
+ <cn encoding="" base="10" type="integer">0</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="greater-than-or-equals" name="geq" role="RELOP" font="upright">≥</XMTok>
- <XMTok role="UNKNOWN">m</XMTok>
- <XMTok meaning="0" role="NUMBER" font="upright">0</XMTok>
+ <XMTok>≥</XMTok>
+ <XMTok>m</XMTok>
+ <XMTok>0</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m\geq 0</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmTheo2.p1.m2" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post3"/>
<XMTok role="UNKNOWN">f</XMTok>
<XMTok role="UNKNOWN">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmTheo2.p1.m2" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post3"/>
- <XMTok role="UNKNOWN">f</XMTok>
- <XMTok role="UNKNOWN">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m1" class="ltx_Math" alttext="4m+1=u^{2}D" display="inline">
<semantics>
<mrow>
<mrow>
<mrow>
<mn>4</mn>
<mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
<mo></mo>
<mi>D</mi>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">4</cn>
<ci>m</ci>
</apply>
<cn type="integer">1</cn>
</apply>
<apply>
<times/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>u</ci>
<cn type="integer">2</cn>
</apply>
<ci>D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">u</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1=u^{2}D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mrow>
<mn>4</mn>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
<mi>D</mi>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">m</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
<apply>
<times/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">u</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<ci encoding="">D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
<XMApp>
<XMTok></XMTok>
<XMApp>
<XMTok/>
<XMTok>u</XMTok>
<XMTok>2</XMTok>
</XMApp>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1=u^{2}D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 | @@ -1,74 +1,72 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m1" class="ltx_Math" alttext="4m+1=u^{2}D" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mrow>
<mn>4</mn>
- <mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
- <mo></mo>
<mi>D</mi>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">4</cn>
- <ci>m</ci>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">m</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
<apply>
<times/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>u</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">u</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
- <ci>D</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
+ <XMTok>=</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
+ <XMTok></XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">u</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>u</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1=u^{2}D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m2" class="ltx_Math" alttext="D" display="inline">
<semantics>
<mi>D</mi>
<annotation-xml encoding="MathML-Content">
<ci>D</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>D</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">D</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>D</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m2" class="ltx_Math" alttext="D" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>D</mi>
<annotation-xml encoding="MathML-Content">
- <ci>D</ci>
+ <ci encoding="">D</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok>D</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m3" class="ltx_Math" alttext="u" display="inline">
<semantics>
<mi>u</mi>
<annotation-xml encoding="MathML-Content">
<ci>u</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">u</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">u</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>u</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">u</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>u</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">u</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m3" class="ltx_Math" alttext="u" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>u</mi>
<annotation-xml encoding="MathML-Content">
- <ci>u</ci>
+ <ci encoding="">u</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">u</XMTok>
+ <XMTok>u</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">u</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m4" class="ltx_Math" alttext="D=1" display="inline">
<semantics>
<mrow>
<mi>D</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>D</ci>
<cn type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>D</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">D</ci>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>D</XMTok>
<XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,27 +1,27 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m4" class="ltx_Math" alttext="D=1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>D</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>D</ci>
- <cn type="integer">1</cn>
+ <ci encoding="">D</ci>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>D</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m5" class="ltx_Math" alttext="1<D<m^{1/12}" display="inline">
<semantics>
<mrow>
<mn>1</mn>
<mo><</mo>
<mi>D</mi>
<mo><</mo>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
<cn type="integer">1</cn>
<ci xml:id="p4.m5.sh1.cmml">D</ci>
</apply>
<apply>
<lt/>
<share href="#p4.m5.sh1.cmml"/>
<apply xml:id="p4.m5.sh2f.cmml">
<csymbol cd="ambiguous" xml:id="p4.m5.sh2.cmml">superscript</csymbol>
<ci xml:id="p4.m5.sh2a.cmml">m</ci>
<apply xml:id="p4.m5.sh2e.cmml">
<divide xml:id="p4.m5.sh2b.cmml"/>
<cn type="integer" xml:id="p4.m5.sh2c.cmml">1</cn>
<cn type="integer" xml:id="p4.m5.sh2d.cmml">12</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="multirelation"/>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMTok meaning="less-than" role="RELOP"><</XMTok>
<XMTok role="UNKNOWN" font="italic" xml:id="p4.m5.sh1.xm" fragid="p4.m5.sh1.xm">D</XMTok>
<XMTok meaning="less-than" role="RELOP"><</XMTok>
<XMApp xml:id="p4.m5.sh2.xm" fragid="p4.m5.sh2.xm">
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMTok meaning="12" role="NUMBER">12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1<D<m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mn>1</mn>
<mo><</mo>
<mi>D</mi>
<mo><</mo>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
<cn encoding="" base="10" type="integer">1</cn>
<ci encoding="">D</ci>
</apply>
<apply>
<lt/>
<share/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">m</ci>
<apply>
<divide encoding=""/>
<cn encoding="" base="10" type="integer">1</cn>
<cn encoding="" base="10" type="integer">12</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>1</XMTok>
<XMTok><</XMTok>
<XMTok>D</XMTok>
<XMTok><</XMTok>
<XMApp>
<XMTok/>
<XMTok>m</XMTok>
<XMApp>
<XMTok>/</XMTok>
<XMTok>1</XMTok>
<XMTok>12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1<D<m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 | @@ -1,63 +1,63 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m5" class="ltx_Math" alttext="1<D<m^{1/12}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mn>1</mn>
<mo><</mo>
<mi>D</mi>
<mo><</mo>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
- <cn type="integer">1</cn>
- <ci xml:id="p4.m5.sh1.cmml">D</ci>
+ <cn encoding="" base="10" type="integer">1</cn>
+ <ci encoding="">D</ci>
</apply>
<apply>
<lt/>
- <share href="#p4.m5.sh1.cmml"/>
- <apply xml:id="p4.m5.sh2f.cmml">
- <csymbol cd="ambiguous" xml:id="p4.m5.sh2.cmml">superscript</csymbol>
- <ci xml:id="p4.m5.sh2a.cmml">m</ci>
- <apply xml:id="p4.m5.sh2e.cmml">
- <divide xml:id="p4.m5.sh2b.cmml"/>
- <cn type="integer" xml:id="p4.m5.sh2c.cmml">1</cn>
- <cn type="integer" xml:id="p4.m5.sh2d.cmml">12</cn>
+ <share/>
+ <apply>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">m</ci>
+ <apply>
+ <divide encoding=""/>
+ <cn encoding="" base="10" type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">12</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="multirelation"/>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
- <XMTok meaning="less-than" role="RELOP"><</XMTok>
- <XMTok role="UNKNOWN" font="italic" xml:id="p4.m5.sh1.xm" fragid="p4.m5.sh1.xm">D</XMTok>
- <XMTok meaning="less-than" role="RELOP"><</XMTok>
- <XMApp xml:id="p4.m5.sh2.xm" fragid="p4.m5.sh2.xm">
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>1</XMTok>
+ <XMTok><</XMTok>
+ <XMTok>D</XMTok>
+ <XMTok><</XMTok>
+ <XMApp>
+ <XMTok/>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
- <XMTok meaning="12" role="NUMBER">12</XMTok>
+ <XMTok>/</XMTok>
+ <XMTok>1</XMTok>
+ <XMTok>12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1<D<m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m6" class="ltx_Math" alttext="D\geq m^{1/12}" display="inline">
<semantics>
<mrow>
<mi>D</mi>
<mo>≥</mo>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<geq/>
<ci>D</ci>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>m</ci>
<apply>
<divide/>
<cn type="integer">1</cn>
<cn type="integer">12</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="greater-than-or-equals" name="geq" role="RELOP">≥</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMTok meaning="12" role="NUMBER">12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D\geq m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>D</mi>
<mo>≥</mo>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<geq/>
<ci encoding="">D</ci>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">m</ci>
<apply>
<divide/>
<cn encoding="" base="10" type="integer">1</cn>
<cn encoding="" base="10" type="integer">12</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>≥</XMTok>
<XMTok>D</XMTok>
<XMApp>
<XMTok/>
<XMTok>m</XMTok>
<XMApp>
<XMTok>/</XMTok>
<XMTok>1</XMTok>
<XMTok>12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D\geq m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 | @@ -1,50 +1,50 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m6" class="ltx_Math" alttext="D\geq m^{1/12}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>D</mi>
<mo>≥</mo>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<geq/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>m</ci>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">m</ci>
<apply>
<divide/>
- <cn type="integer">1</cn>
- <cn type="integer">12</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">12</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="greater-than-or-equals" name="geq" role="RELOP">≥</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok>≥</XMTok>
+ <XMTok>D</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
- <XMTok meaning="12" role="NUMBER">12</XMTok>
+ <XMTok>/</XMTok>
+ <XMTok>1</XMTok>
+ <XMTok>12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D\geq m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m7" class="ltx_Math" alttext="4m+1" display="inline">
<semantics>
<mrow>
<mrow>
<mn>4</mn>
<mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">4</cn>
<ci>m</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mn>4</mn>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">m</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,39 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p4.m7" class="ltx_Math" alttext="4m+1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mn>4</mn>
- <mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">4</cn>
- <ci>m</ci>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">m</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4m+1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem1.p1.m1" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post3"/>
<XMTok role="UNKNOWN">f</XMTok>
<XMTok role="UNKNOWN">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem1.p1.m1" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post3"/>
- <XMTok role="UNKNOWN">f</XMTok>
- <XMTok role="UNKNOWN">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem1.p1.m2" class="ltx_Math" alttext="D=1" display="inline">
<semantics>
<mrow>
<mi>D</mi>
<mo mathvariant="normal">=</mo>
<mn mathvariant="normal">1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>D</ci>
<cn type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP" font="upright">=</XMTok>
<XMTok role="UNKNOWN">D</XMTok>
<XMTok meaning="1" role="NUMBER" font="upright">1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>D</mi>
<mo mathvariant="normal">=</mo>
<mn mathvariant="normal">1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">D</ci>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>D</XMTok>
<XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,27 +1,27 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem1.p1.m2" class="ltx_Math" alttext="D=1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>D</mi>
<mo mathvariant="normal">=</mo>
<mn mathvariant="normal">1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>D</ci>
- <cn type="integer">1</cn>
+ <ci encoding="">D</ci>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP" font="upright">=</XMTok>
- <XMTok role="UNKNOWN">D</XMTok>
- <XMTok meaning="1" role="NUMBER" font="upright">1</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>D</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem1.p1.m3" class="ltx_Math" alttext="m=2" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo mathvariant="normal">=</mo>
<mn mathvariant="normal">2</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>m</ci>
<cn type="integer">2</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP" font="upright">=</XMTok>
<XMTok role="UNKNOWN">m</XMTok>
<XMTok meaning="2" role="NUMBER" font="upright">2</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo mathvariant="normal">=</mo>
<mn mathvariant="normal">2</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">m</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>m</XMTok>
<XMTok>2</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,27 +1,27 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem1.p1.m3" class="ltx_Math" alttext="m=2" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo mathvariant="normal">=</mo>
<mn mathvariant="normal">2</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>m</ci>
- <cn type="integer">2</cn>
+ <ci encoding="">m</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP" font="upright">=</XMTok>
- <XMTok role="UNKNOWN">m</XMTok>
- <XMTok meaning="2" role="NUMBER" font="upright">2</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>m</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m1" class="ltx_Math" alttext="m=t^{2}+t+\frac{2t+1}{3}" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
<mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>m</ci>
<apply>
<plus/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>t</ci>
<cn type="integer">2</cn>
</apply>
<ci>t</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">2</cn>
<ci>t</ci>
</apply>
<cn type="integer">1</cn>
</apply>
<cn type="integer">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMApp>
<XMTok mathstyle="text" meaning="divide" role="MULOP"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
<XMTok meaning="3" role="NUMBER">3</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=t^{2}+t+\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">m</ci>
<apply>
<plus/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">t</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<ci encoding="">t</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">2</cn>
<ci encoding="">t</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
<cn encoding="" base="10" type="integer">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>m</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok/>
<XMTok>t</XMTok>
<XMTok>2</XMTok>
</XMApp>
<XMTok>t</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>2</XMTok>
<XMTok>t</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
<XMTok>3</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=t^{2}+t+\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 | @@ -1,89 +1,88 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m1" class="ltx_Math" alttext="m=t^{2}+t+\frac{2t+1}{3}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
- <mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
<apply>
<plus/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>t</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
- <ci>t</ci>
+ <ci encoding="">t</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">2</cn>
- <ci>t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
- <cn type="integer">3</cn>
+ <cn encoding="" base="10" type="integer">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>t</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok>t</XMTok>
<XMApp>
- <XMTok mathstyle="text" meaning="divide" role="MULOP"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>2</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
- <XMTok meaning="3" role="NUMBER">3</XMTok>
+ <XMTok>3</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=t^{2}+t+\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m2" class="ltx_Math" alttext="D=1" display="inline">
<semantics>
<mrow>
<mi>D</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>D</ci>
<cn type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>D</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">D</ci>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>D</XMTok>
<XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,27 +1,27 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m2" class="ltx_Math" alttext="D=1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>D</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>D</ci>
- <cn type="integer">1</cn>
+ <ci encoding="">D</ci>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>D</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m3" class="ltx_Math" alttext="4t^{2}+\frac{20t}{3}+\frac{7}{3}=u^{2}" display="inline">
<semantics>
<mrow>
<mrow>
<mrow>
<mn>4</mn>
<mo></mo>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>20</mn>
<mo></mo>
<mi>t</mi>
</mrow>
<mn>3</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>7</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>=</mo>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">4</cn>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>t</ci>
<cn type="integer">2</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn type="integer">20</cn>
<ci>t</ci>
</apply>
<cn type="integer">3</cn>
</apply>
<apply>
<divide/>
<cn type="integer">7</cn>
<cn type="integer">3</cn>
</apply>
</apply>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>u</ci>
<cn type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok mathstyle="text" meaning="divide" role="MULOP"/>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="20" role="NUMBER">20</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMTok meaning="3" role="NUMBER">3</XMTok>
</XMApp>
<XMApp>
<XMTok mathstyle="text" meaning="divide" role="MULOP"/>
<XMTok meaning="7" role="NUMBER">7</XMTok>
<XMTok meaning="3" role="NUMBER">3</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">u</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4t^{2}+\frac{20t}{3}+\frac{7}{3}=u^{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mrow>
<mn>4</mn>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>20</mn>
<mi>t</mi>
</mrow>
<mn>3</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>7</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>=</mo>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">4</cn>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">t</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">20</cn>
<ci encoding="">t</ci>
</apply>
<cn encoding="" base="10" type="integer">3</cn>
</apply>
<apply>
<divide/>
<cn encoding="" base="10" type="integer">7</cn>
<cn encoding="" base="10" type="integer">3</cn>
</apply>
</apply>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">u</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMApp>
<XMTok/>
<XMTok>t</XMTok>
<XMTok>2</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok/>
<XMApp>
<XMTok></XMTok>
<XMTok>20</XMTok>
<XMTok>t</XMTok>
</XMApp>
<XMTok>3</XMTok>
</XMApp>
<XMApp>
<XMTok/>
<XMTok>7</XMTok>
<XMTok>3</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok/>
<XMTok>u</XMTok>
<XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4t^{2}+\frac{20t}{3}+\frac{7}{3}=u^{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 | @@ -1,111 +1,109 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m3" class="ltx_Math" alttext="4t^{2}+\frac{20t}{3}+\frac{7}{3}=u^{2}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mrow>
<mn>4</mn>
- <mo></mo>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>20</mn>
- <mo></mo>
<mi>t</mi>
</mrow>
<mn>3</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>7</mn>
<mn>3</mn>
</mfrac>
</mrow>
<mo>=</mo>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">4</cn>
+ <cn encoding="" base="10" type="integer">4</cn>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>t</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
- <cn type="integer">20</cn>
- <ci>t</ci>
+ <cn encoding="" base="10" type="integer">20</cn>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer">3</cn>
+ <cn encoding="" base="10" type="integer">3</cn>
</apply>
<apply>
<divide/>
- <cn type="integer">7</cn>
- <cn type="integer">3</cn>
+ <cn encoding="" base="10" type="integer">7</cn>
+ <cn encoding="" base="10" type="integer">3</cn>
</apply>
</apply>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>u</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">u</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
+ <XMTok>=</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>t</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
<XMApp>
- <XMTok mathstyle="text" meaning="divide" role="MULOP"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="20" role="NUMBER">20</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>20</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="3" role="NUMBER">3</XMTok>
+ <XMTok>3</XMTok>
</XMApp>
<XMApp>
- <XMTok mathstyle="text" meaning="divide" role="MULOP"/>
- <XMTok meaning="7" role="NUMBER">7</XMTok>
- <XMTok meaning="3" role="NUMBER">3</XMTok>
+ <XMTok/>
+ <XMTok>7</XMTok>
+ <XMTok>3</XMTok>
</XMApp>
</XMApp>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">u</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>u</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4t^{2}+\frac{20t}{3}+\frac{7}{3}=u^{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex1.m1" class="ltx_Math" alttext="4t^{2}+4t+1<4t^{2}+\frac{20t}{3}+\frac{7}{3}<4t^{2}+8t+4" display="block">
<semantics>
<mrow>
<mrow>
<mrow>
<mn>4</mn>
<mo></mo>
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|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<apply>
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<lt/>
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<apply>
<csymbol encoding="">superscript</csymbol>
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<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
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<XMTok/>
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|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 | @@ -1,215 +1,209 @@
<?xml version="1.0" encoding="UTF-8"?>
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- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mrow>
<mn>4</mn>
- <mo></mo>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<mn>4</mn>
- <mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
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</mrow>
<mo><</mo>
<mrow>
<mrow>
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- <mo></mo>
<msup>
<mi>t</mi>
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</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>20</mn>
- <mo></mo>
<mi>t</mi>
</mrow>
<mn>3</mn>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>7</mn>
<mn>3</mn>
</mfrac>
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<mo><</mo>
<mrow>
<mrow>
<mn>4</mn>
- <mo></mo>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<mn>8</mn>
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<mi>t</mi>
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<mo>+</mo>
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<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">4</cn>
+ <cn encoding="" base="10" type="integer">4</cn>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>t</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
<apply>
<times/>
- <cn type="integer">4</cn>
- <ci>t</ci>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer">1</cn>
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+ <apply>
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- <cn type="integer" xml:id="S0.Ex1.m1.sh1j.cmml">20</cn>
- <ci xml:id="S0.Ex1.m1.sh1k.cmml">t</ci>
+ <apply>
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+ <ci encoding="">t</ci>
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- <cn type="integer" xml:id="S0.Ex1.m1.sh1m.cmml">3</cn>
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+ <share/>
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+ <apply>
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+ <apply>
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+ <ci encoding="">t</ci>
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<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
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<XMApp>
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+ <XMTok/>
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- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
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<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
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+ <XMTok>4</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>t</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
<XMApp>
- <XMTok mathstyle="display" meaning="divide" role="MULOP"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="20" role="NUMBER">20</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>20</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="3" role="NUMBER">3</XMTok>
+ <XMTok>3</XMTok>
</XMApp>
<XMApp>
- <XMTok mathstyle="display" meaning="divide" role="MULOP"/>
- <XMTok meaning="7" role="NUMBER">7</XMTok>
- <XMTok meaning="3" role="NUMBER">3</XMTok>
+ <XMTok/>
+ <XMTok>7</XMTok>
+ <XMTok>3</XMTok>
</XMApp>
</XMApp>
- <XMTok meaning="less-than" role="RELOP"><</XMTok>
- <XMApp xml:id="S0.Ex1.m1.sh2.xm" fragid="S0.Ex1.m1.sh2.xm">
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok><</XMTok>
+ <XMApp>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>t</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="8" role="NUMBER">8</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>8</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
+ <XMTok>4</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">4t^{2}+4t+1<4t^{2}+\frac{20t}{3}+\frac{7}{3}<4t^{2}+8t+4</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m4" class="ltx_Math" alttext="2t+1<u<2t+2" display="inline">
<semantics>
<mrow>
<mrow>
<mrow>
<mn>2</mn>
<mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo><</mo>
<mi>u</mi>
<mo><</mo>
<mrow>
<mrow>
<mn>2</mn>
<mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">2</cn>
<ci>t</ci>
</apply>
<cn type="integer">1</cn>
</apply>
<ci xml:id="p5.m4.sh1.cmml">u</ci>
</apply>
<apply>
<lt/>
<share href="#p5.m4.sh1.cmml"/>
<apply xml:id="p5.m4.sh2f.cmml">
<plus xml:id="p5.m4.sh2.cmml"/>
<apply xml:id="p5.m4.sh2d.cmml">
<times xml:id="p5.m4.sh2a.cmml"/>
<cn type="integer" xml:id="p5.m4.sh2b.cmml">2</cn>
<ci xml:id="p5.m4.sh2c.cmml">t</ci>
</apply>
<cn type="integer" xml:id="p5.m4.sh2e.cmml">2</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="multirelation"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
<XMTok meaning="less-than" role="RELOP"><</XMTok>
<XMTok role="UNKNOWN" font="italic" xml:id="p5.m4.sh1.xm" fragid="p5.m4.sh1.xm">u</XMTok>
<XMTok meaning="less-than" role="RELOP"><</XMTok>
<XMApp xml:id="p5.m4.sh2.xm" fragid="p5.m4.sh2.xm">
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">2t+1<u<2t+2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mrow>
<mn>2</mn>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo><</mo>
<mi>u</mi>
<mo><</mo>
<mrow>
<mrow>
<mn>2</mn>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">2</cn>
<ci encoding="">t</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
<ci encoding="">u</ci>
</apply>
<apply>
<lt/>
<share/>
<apply>
<plus encoding=""/>
<apply>
<times encoding=""/>
<cn encoding="" base="10" type="integer">2</cn>
<ci encoding="">t</ci>
</apply>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>2</XMTok>
<XMTok>t</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
<XMTok><</XMTok>
<XMTok>u</XMTok>
<XMTok><</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>2</XMTok>
<XMTok>t</XMTok>
</XMApp>
<XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">2t+1<u<2t+2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 | @@ -1,88 +1,86 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m4" class="ltx_Math" alttext="2t+1<u<2t+2" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mrow>
<mn>2</mn>
- <mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo><</mo>
<mi>u</mi>
<mo><</mo>
<mrow>
<mrow>
<mn>2</mn>
- <mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">2</cn>
- <ci>t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
- <ci xml:id="p5.m4.sh1.cmml">u</ci>
+ <ci encoding="">u</ci>
</apply>
<apply>
<lt/>
- <share href="#p5.m4.sh1.cmml"/>
- <apply xml:id="p5.m4.sh2f.cmml">
- <plus xml:id="p5.m4.sh2.cmml"/>
- <apply xml:id="p5.m4.sh2d.cmml">
- <times xml:id="p5.m4.sh2a.cmml"/>
- <cn type="integer" xml:id="p5.m4.sh2b.cmml">2</cn>
- <ci xml:id="p5.m4.sh2c.cmml">t</ci>
+ <share/>
+ <apply>
+ <plus encoding=""/>
+ <apply>
+ <times encoding=""/>
+ <cn encoding="" base="10" type="integer">2</cn>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer" xml:id="p5.m4.sh2e.cmml">2</cn>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="multirelation"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>2</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
- <XMTok meaning="less-than" role="RELOP"><</XMTok>
- <XMTok role="UNKNOWN" font="italic" xml:id="p5.m4.sh1.xm" fragid="p5.m4.sh1.xm">u</XMTok>
- <XMTok meaning="less-than" role="RELOP"><</XMTok>
- <XMApp xml:id="p5.m4.sh2.xm" fragid="p5.m4.sh2.xm">
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok><</XMTok>
+ <XMTok>u</XMTok>
+ <XMTok><</XMTok>
+ <XMApp>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>2</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">2t+1<u<2t+2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m5" class="ltx_Math" alttext="t" display="inline">
<semantics>
<mi>t</mi>
<annotation-xml encoding="MathML-Content">
<ci>t</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">t</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>t</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">t</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>t</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">t</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m5" class="ltx_Math" alttext="t" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>t</mi>
<annotation-xml encoding="MathML-Content">
- <ci>t</ci>
+ <ci encoding="">t</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok>t</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">t</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m6" class="ltx_Math" alttext="u" display="inline">
<semantics>
<mi>u</mi>
<annotation-xml encoding="MathML-Content">
<ci>u</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">u</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">u</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>u</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">u</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>u</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">u</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p5.m6" class="ltx_Math" alttext="u" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>u</mi>
<annotation-xml encoding="MathML-Content">
- <ci>u</ci>
+ <ci encoding="">u</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">u</XMTok>
+ <XMTok>u</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">u</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem2.p1.m1" class="ltx_Math" alttext="m" display="inline">
<semantics>
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci>m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN">m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem2.p1.m1" class="ltx_Math" alttext="m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
- <ci>m</ci>
+ <ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN">m</XMTok>
+ <XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem2.p1.m2" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post3"/>
<XMTok role="UNKNOWN">f</XMTok>
<XMTok role="UNKNOWN">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem2.p1.m2" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post3"/>
- <XMTok role="UNKNOWN">f</XMTok>
- <XMTok role="UNKNOWN">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem2.p1.m3" class="ltx_Math" alttext="1<D<m^{1/12}" display="inline">
<semantics>
<mrow>
<mn mathvariant="normal">1</mn>
<mo mathvariant="normal"><</mo>
<mi>D</mi>
<mo mathvariant="normal"><</mo>
<msup>
<mi>m</mi>
<mrow>
<mn mathvariant="normal">1</mn>
<mo mathvariant="normal">/</mo>
<mn mathvariant="normal">12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
<cn type="integer">1</cn>
<ci xml:id="ThmLem2.p1.m3.sh1.cmml">D</ci>
</apply>
<apply>
<lt/>
<share href="#ThmLem2.p1.m3.sh1.cmml"/>
<apply xml:id="ThmLem2.p1.m3.sh2f.cmml">
<csymbol cd="ambiguous" xml:id="ThmLem2.p1.m3.sh2.cmml">superscript</csymbol>
<ci xml:id="ThmLem2.p1.m3.sh2a.cmml">m</ci>
<apply xml:id="ThmLem2.p1.m3.sh2e.cmml">
<divide xml:id="ThmLem2.p1.m3.sh2b.cmml"/>
<cn type="integer" xml:id="ThmLem2.p1.m3.sh2c.cmml">1</cn>
<cn type="integer" xml:id="ThmLem2.p1.m3.sh2d.cmml">12</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="multirelation"/>
<XMTok meaning="1" role="NUMBER" font="upright">1</XMTok>
<XMTok meaning="less-than" role="RELOP" font="upright"><</XMTok>
<XMTok role="UNKNOWN" xml:id="ThmLem2.p1.m3.sh1.xm" fragid="ThmLem2.p1.m3.sh1.xm">D</XMTok>
<XMTok meaning="less-than" role="RELOP" font="upright"><</XMTok>
<XMApp xml:id="ThmLem2.p1.m3.sh2.xm" fragid="ThmLem2.p1.m3.sh2.xm">
<XMTok role="SUPERSCRIPTOP" scriptpos="post3"/>
<XMTok role="UNKNOWN">m</XMTok>
<XMApp>
<XMTok mathstyle="inline" meaning="divide" role="MULOP" font="upright">/</XMTok>
<XMTok meaning="1" role="NUMBER" font="upright">1</XMTok>
<XMTok meaning="12" role="NUMBER" font="upright">12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1<D<m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mn mathvariant="normal">1</mn>
<mo mathvariant="normal"><</mo>
<mi>D</mi>
<mo mathvariant="normal"><</mo>
<msup>
<mi>m</mi>
<mrow>
<mn mathvariant="normal">1</mn>
<mo mathvariant="normal">/</mo>
<mn mathvariant="normal">12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
<cn encoding="" base="10" type="integer">1</cn>
<ci encoding="">D</ci>
</apply>
<apply>
<lt/>
<share/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">m</ci>
<apply>
<divide encoding=""/>
<cn encoding="" base="10" type="integer">1</cn>
<cn encoding="" base="10" type="integer">12</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>1</XMTok>
<XMTok><</XMTok>
<XMTok>D</XMTok>
<XMTok><</XMTok>
<XMApp>
<XMTok/>
<XMTok>m</XMTok>
<XMApp>
<XMTok>/</XMTok>
<XMTok>1</XMTok>
<XMTok>12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1<D<m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 | @@ -1,63 +1,63 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem2.p1.m3" class="ltx_Math" alttext="1<D<m^{1/12}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mn mathvariant="normal">1</mn>
<mo mathvariant="normal"><</mo>
<mi>D</mi>
<mo mathvariant="normal"><</mo>
<msup>
<mi>m</mi>
<mrow>
<mn mathvariant="normal">1</mn>
<mo mathvariant="normal">/</mo>
<mn mathvariant="normal">12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
- <cn type="integer">1</cn>
- <ci xml:id="ThmLem2.p1.m3.sh1.cmml">D</ci>
+ <cn encoding="" base="10" type="integer">1</cn>
+ <ci encoding="">D</ci>
</apply>
<apply>
<lt/>
- <share href="#ThmLem2.p1.m3.sh1.cmml"/>
- <apply xml:id="ThmLem2.p1.m3.sh2f.cmml">
- <csymbol cd="ambiguous" xml:id="ThmLem2.p1.m3.sh2.cmml">superscript</csymbol>
- <ci xml:id="ThmLem2.p1.m3.sh2a.cmml">m</ci>
- <apply xml:id="ThmLem2.p1.m3.sh2e.cmml">
- <divide xml:id="ThmLem2.p1.m3.sh2b.cmml"/>
- <cn type="integer" xml:id="ThmLem2.p1.m3.sh2c.cmml">1</cn>
- <cn type="integer" xml:id="ThmLem2.p1.m3.sh2d.cmml">12</cn>
+ <share/>
+ <apply>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">m</ci>
+ <apply>
+ <divide encoding=""/>
+ <cn encoding="" base="10" type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">12</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="multirelation"/>
- <XMTok meaning="1" role="NUMBER" font="upright">1</XMTok>
- <XMTok meaning="less-than" role="RELOP" font="upright"><</XMTok>
- <XMTok role="UNKNOWN" xml:id="ThmLem2.p1.m3.sh1.xm" fragid="ThmLem2.p1.m3.sh1.xm">D</XMTok>
- <XMTok meaning="less-than" role="RELOP" font="upright"><</XMTok>
- <XMApp xml:id="ThmLem2.p1.m3.sh2.xm" fragid="ThmLem2.p1.m3.sh2.xm">
- <XMTok role="SUPERSCRIPTOP" scriptpos="post3"/>
- <XMTok role="UNKNOWN">m</XMTok>
+ <XMTok/>
+ <XMTok>1</XMTok>
+ <XMTok><</XMTok>
+ <XMTok>D</XMTok>
+ <XMTok><</XMTok>
+ <XMApp>
+ <XMTok/>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok mathstyle="inline" meaning="divide" role="MULOP" font="upright">/</XMTok>
- <XMTok meaning="1" role="NUMBER" font="upright">1</XMTok>
- <XMTok meaning="12" role="NUMBER" font="upright">12</XMTok>
+ <XMTok>/</XMTok>
+ <XMTok>1</XMTok>
+ <XMTok>12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1<D<m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m1" class="ltx_Math" alttext="p" display="inline">
<semantics>
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci>p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m1" class="ltx_Math" alttext="p" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
- <ci>p</ci>
+ <ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
+ <XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m2" class="ltx_Math" alttext="p\equiv 1\;\;(\mathop{{\rm mod}}4D)" display="inline">
<semantics>
<mrow>
<mi>p</mi>
<mo>≡</mo>
<mrow>
<mn>1</mn>
<mspace width="veryverythickmathspace"/>
<mrow>
<mo>(</mo>
<mrow>
<mo>mod</mo>
<mrow xml:id="p6.m2.xm1c" xref="p6.m2.xm1.cmml">
<mn xml:id="p6.m2.xm1" xref="p6.m2.xm1.cmml">4</mn>
<mo xml:id="p6.m2.xm1a" xref="p6.m2.xm1.cmml"></mo>
<mi xml:id="p6.m2.xm1b" xref="p6.m2.xm1.cmml">D</mi>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<equivalent/>
<ci>p</ci>
<apply>
<csymbol cd="latexml">annotated</csymbol>
<cn type="integer">1</cn>
<apply>
<ci>pmod</ci>
<apply xml:id="p6.m2.xm1c.cmml" xref="p6.m2.xm1">
<times xml:id="p6.m2.xm1.cmml" xref="p6.m2.xm1"/>
<cn type="integer" xml:id="p6.m2.xm1a.cmml" xref="p6.m2.xm1">4</cn>
<ci xml:id="p6.m2.xm1b.cmml" xref="p6.m2.xm1">D</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equivalent-to" name="equiv" role="RELOP">≡</XMTok>
<XMTok role="UNKNOWN" font="italic">p</XMTok>
<XMApp>
<XMTok meaning="annotated"/>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMDual role="MODIFIER">
<XMApp role="MODIFIER">
<XMTok name="pmod" role="UNKNOWN"/>
<XMApp xml:id="p6.m2.xm1.xm" fragid="p6.m2.xm1.xm">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
<XMApp close=")" open="(">
<XMTok role="BIGOP">mod</XMTok>
<XMRef idref="p6.m2.xm1.xm"/>
</XMApp>
</XMDual>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p\equiv 1\;\;(\mathop{{\rm mod}}4D)</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>p</mi>
<mo>≡</mo>
<mrow>
<mn>1</mn>
<mrow>
<mo>(</mo>
<mrow>
<mo>mod</mo>
<mrow>
<mn>4</mn>
<mi>D</mi>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<equivalent/>
<ci encoding="">p</ci>
<apply>
<csymbol encoding="">annotated</csymbol>
<cn encoding="" base="10" type="integer">1</cn>
<apply>
<ci encoding="">pmod</ci>
<apply>
<times encoding=""/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">D</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>≡</XMTok>
<XMTok>p</XMTok>
<XMApp>
<XMTok/>
<XMTok>1</XMTok>
<XMDual>
<XMApp>
<XMTok/>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok>mod</XMTok>
<XMRef/>
</XMApp>
</XMDual>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p\equiv 1\;\;(\mathop{{\rm mod}}4D)</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 | @@ -1,70 +1,68 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m2" class="ltx_Math" alttext="p\equiv 1\;\;(\mathop{{\rm mod}}4D)" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>p</mi>
<mo>≡</mo>
<mrow>
<mn>1</mn>
- <mspace width="veryverythickmathspace"/>
<mrow>
<mo>(</mo>
<mrow>
<mo>mod</mo>
- <mrow xml:id="p6.m2.xm1c" xref="p6.m2.xm1.cmml">
- <mn xml:id="p6.m2.xm1" xref="p6.m2.xm1.cmml">4</mn>
- <mo xml:id="p6.m2.xm1a" xref="p6.m2.xm1.cmml"></mo>
- <mi xml:id="p6.m2.xm1b" xref="p6.m2.xm1.cmml">D</mi>
+ <mrow>
+ <mn>4</mn>
+ <mi>D</mi>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<equivalent/>
- <ci>p</ci>
+ <ci encoding="">p</ci>
<apply>
- <csymbol cd="latexml">annotated</csymbol>
- <cn type="integer">1</cn>
+ <csymbol encoding="">annotated</csymbol>
+ <cn encoding="" base="10" type="integer">1</cn>
<apply>
- <ci>pmod</ci>
- <apply xml:id="p6.m2.xm1c.cmml" xref="p6.m2.xm1">
- <times xml:id="p6.m2.xm1.cmml" xref="p6.m2.xm1"/>
- <cn type="integer" xml:id="p6.m2.xm1a.cmml" xref="p6.m2.xm1">4</cn>
- <ci xml:id="p6.m2.xm1b.cmml" xref="p6.m2.xm1">D</ci>
+ <ci encoding="">pmod</ci>
+ <apply>
+ <times encoding=""/>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">D</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equivalent-to" name="equiv" role="RELOP">≡</XMTok>
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
+ <XMTok>≡</XMTok>
+ <XMTok>p</XMTok>
<XMApp>
- <XMTok meaning="annotated"/>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
- <XMDual role="MODIFIER">
- <XMApp role="MODIFIER">
- <XMTok name="pmod" role="UNKNOWN"/>
- <XMApp xml:id="p6.m2.xm1.xm" fragid="p6.m2.xm1.xm">
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>1</XMTok>
+ <XMDual>
+ <XMApp>
+ <XMTok/>
+ <XMApp>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
- <XMApp close=")" open="(">
- <XMTok role="BIGOP">mod</XMTok>
- <XMRef idref="p6.m2.xm1.xm"/>
+ <XMApp>
+ <XMTok>mod</XMTok>
+ <XMRef/>
</XMApp>
</XMDual>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p\equiv 1\;\;(\mathop{{\rm mod}}4D)</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m3" class="ltx_Math" alttext="(p,m)=1" display="inline">
<semantics>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>m</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<interval closure="open"/>
<ci>p</ci>
<ci>m</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMTok argclose=")" argopen="(" meaning="open-interval" role="FENCED" separators=","/>
<XMTok role="UNKNOWN" font="italic">p</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">(p,m)=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>m</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<interval closure="open"/>
<ci encoding="">p</ci>
<ci encoding="">m</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMApp>
<XMTok/>
<XMTok>p</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">(p,m)=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | @@ -1,43 +1,43 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m3" class="ltx_Math" alttext="(p,m)=1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>m</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<interval closure="open"/>
- <ci>p</ci>
- <ci>m</ci>
+ <ci encoding="">p</ci>
+ <ci encoding="">m</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
+ <XMTok>=</XMTok>
<XMApp>
- <XMTok argclose=")" argopen="(" meaning="open-interval" role="FENCED" separators=","/>
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>p</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">(p,m)=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m4" class="ltx_Math" alttext="p<D^{C}" display="inline">
<semantics>
<mrow>
<mi>p</mi>
<mo><</mo>
<msup>
<mi>D</mi>
<mi>C</mi>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
<ci>p</ci>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>D</ci>
<ci>C</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="less-than" role="RELOP"><</XMTok>
<XMTok role="UNKNOWN" font="italic">p</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
<XMTok role="UNKNOWN" font="italic">C</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p<D^{C}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>p</mi>
<mo><</mo>
<msup>
<mi>D</mi>
<mi>C</mi>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
<ci encoding="">p</ci>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">D</ci>
<ci encoding="">C</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok><</XMTok>
<XMTok>p</XMTok>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
<XMTok>C</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p<D^{C}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,38 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m4" class="ltx_Math" alttext="p<D^{C}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>p</mi>
<mo><</mo>
<msup>
<mi>D</mi>
<mi>C</mi>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
- <ci>p</ci>
+ <ci encoding="">p</ci>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>D</ci>
- <ci>C</ci>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">D</ci>
+ <ci encoding="">C</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="less-than" role="RELOP"><</XMTok>
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
+ <XMTok><</XMTok>
+ <XMTok>p</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
- <XMTok role="UNKNOWN" font="italic">C</XMTok>
+ <XMTok/>
+ <XMTok>D</XMTok>
+ <XMTok>C</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p<D^{C}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m5" class="ltx_Math" alttext="C" display="inline">
<semantics>
<mi>C</mi>
<annotation-xml encoding="MathML-Content">
<ci>C</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">C</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">C</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>C</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">C</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>C</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">C</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m5" class="ltx_Math" alttext="C" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>C</mi>
<annotation-xml encoding="MathML-Content">
- <ci>C</ci>
+ <ci encoding="">C</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">C</XMTok>
+ <XMTok>C</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">C</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m6" class="ltx_Math" alttext="D" display="inline">
<semantics>
<mi>D</mi>
<annotation-xml encoding="MathML-Content">
<ci>D</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>D</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">D</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>D</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m6" class="ltx_Math" alttext="D" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>D</mi>
<annotation-xml encoding="MathML-Content">
- <ci>D</ci>
+ <ci encoding="">D</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok>D</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m7" class="ltx_Math" alttext="C=5.5" display="inline">
<semantics>
<mrow>
<mi>C</mi>
<mo>=</mo>
<mn>5.5</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>C</ci>
<cn type="float">5.5</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">C</XMTok>
<XMTok meaning="5.5" role="NUMBER">5.5</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">C=5.5</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>C</mi>
<mo>=</mo>
<mn>5.5</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">C</ci>
<cn encoding="" base="10" type="float">5.5</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>C</XMTok>
<XMTok>5.5</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">C=5.5</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,27 +1,27 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m7" class="ltx_Math" alttext="C=5.5" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>C</mi>
<mo>=</mo>
<mn>5.5</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>C</ci>
- <cn type="float">5.5</cn>
+ <ci encoding="">C</ci>
+ <cn encoding="" base="10" type="float">5.5</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">C</XMTok>
- <XMTok meaning="5.5" role="NUMBER">5.5</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>C</XMTok>
+ <XMTok>5.5</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">C=5.5</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m8" class="ltx_Math" alttext="D_{0}" display="inline">
<semantics>
<msub>
<mi>D</mi>
<mn>0</mn>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>D</ci>
<cn type="integer">0</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
<XMTok meaning="0" role="NUMBER">0</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>D</mi>
<mn>0</mn>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">D</ci>
<cn encoding="" base="10" type="integer">0</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
<XMTok>0</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m8" class="ltx_Math" alttext="D_{0}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>D</mi>
<mn>0</mn>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>D</ci>
- <cn type="integer">0</cn>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">D</ci>
+ <cn encoding="" base="10" type="integer">0</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
- <XMTok meaning="0" role="NUMBER">0</XMTok>
+ <XMTok/>
+ <XMTok>D</XMTok>
+ <XMTok>0</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m9" class="ltx_Math" alttext="D>D_{0}" display="inline">
<semantics>
<mrow>
<mi>D</mi>
<mo>></mo>
<msub>
<mi>D</mi>
<mn>0</mn>
</msub>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<ci>D</ci>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>D</ci>
<cn type="integer">0</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="greater-than" role="RELOP">></XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
<XMTok meaning="0" role="NUMBER">0</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D>D_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>D</mi>
<mo>></mo>
<msub>
<mi>D</mi>
<mn>0</mn>
</msub>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<ci encoding="">D</ci>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">D</ci>
<cn encoding="" base="10" type="integer">0</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>></XMTok>
<XMTok>D</XMTok>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
<XMTok>0</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D>D_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,38 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m9" class="ltx_Math" alttext="D>D_{0}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>D</mi>
<mo>></mo>
<msub>
<mi>D</mi>
<mn>0</mn>
</msub>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>D</ci>
- <cn type="integer">0</cn>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">D</ci>
+ <cn encoding="" base="10" type="integer">0</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="greater-than" role="RELOP">></XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok>></XMTok>
+ <XMTok>D</XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
- <XMTok meaning="0" role="NUMBER">0</XMTok>
+ <XMTok/>
+ <XMTok>D</XMTok>
+ <XMTok>0</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D>D_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m10" class="ltx_Math" alttext="p<m^{1/2}/6" display="inline">
<semantics>
<mrow>
<mi>p</mi>
<mo><</mo>
<mrow>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mo>/</mo>
<mn>6</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
<ci>p</ci>
<apply>
<divide/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>m</ci>
<apply>
<divide/>
<cn type="integer">1</cn>
<cn type="integer">2</cn>
</apply>
</apply>
<cn type="integer">6</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="less-than" role="RELOP"><</XMTok>
<XMTok role="UNKNOWN" font="italic">p</XMTok>
<XMApp>
<XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
<XMTok meaning="6" role="NUMBER">6</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p<m^{1/2}/6</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>p</mi>
<mo><</mo>
<mrow>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mo>/</mo>
<mn>6</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
<ci encoding="">p</ci>
<apply>
<divide/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">m</ci>
<apply>
<divide/>
<cn encoding="" base="10" type="integer">1</cn>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
<cn encoding="" base="10" type="integer">6</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok><</XMTok>
<XMTok>p</XMTok>
<XMApp>
<XMTok>/</XMTok>
<XMApp>
<XMTok/>
<XMTok>m</XMTok>
<XMApp>
<XMTok>/</XMTok>
<XMTok>1</XMTok>
<XMTok>2</XMTok>
</XMApp>
</XMApp>
<XMTok>6</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p<m^{1/2}/6</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 | @@ -1,62 +1,62 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m10" class="ltx_Math" alttext="p<m^{1/2}/6" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>p</mi>
<mo><</mo>
<mrow>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mo>/</mo>
<mn>6</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
- <ci>p</ci>
+ <ci encoding="">p</ci>
<apply>
<divide/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>m</ci>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">m</ci>
<apply>
<divide/>
- <cn type="integer">1</cn>
- <cn type="integer">2</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
- <cn type="integer">6</cn>
+ <cn encoding="" base="10" type="integer">6</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="less-than" role="RELOP"><</XMTok>
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
+ <XMTok><</XMTok>
+ <XMTok>p</XMTok>
<XMApp>
- <XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
+ <XMTok>/</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok>/</XMTok>
+ <XMTok>1</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
- <XMTok meaning="6" role="NUMBER">6</XMTok>
+ <XMTok>6</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p<m^{1/2}/6</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m11" class="ltx_Math" alttext="p" display="inline">
<semantics>
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci>p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m11" class="ltx_Math" alttext="p" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
- <ci>p</ci>
+ <ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
+ <XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m12" class="ltx_Math" alttext="p" display="inline">
<semantics>
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci>p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m12" class="ltx_Math" alttext="p" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
- <ci>p</ci>
+ <ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
+ <XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m13" class="ltx_Math" alttext="n" display="inline">
<semantics>
<mi>n</mi>
<annotation-xml encoding="MathML-Content">
<ci>n</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">n</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>n</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">n</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>n</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m13" class="ltx_Math" alttext="n" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>n</mi>
<annotation-xml encoding="MathML-Content">
- <ci>n</ci>
+ <ci encoding="">n</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">n</XMTok>
+ <XMTok>n</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m14" class="ltx_Math" alttext="x-\frac{1+u\sqrt{D}}{2}" display="inline">
<semantics>
<mrow>
<mi>x</mi>
<mo>-</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mrow>
<mi>u</mi>
<mo></mo>
<msqrt>
<mi>D</mi>
</msqrt>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<minus/>
<ci>x</ci>
<apply>
<divide/>
<apply>
<plus/>
<cn type="integer">1</cn>
<apply>
<times/>
<ci>u</ci>
<apply>
<root/>
<ci>D</ci>
</apply>
</apply>
</apply>
<cn type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="minus" role="ADDOP">-</XMTok>
<XMTok role="UNKNOWN" font="italic">x</XMTok>
<XMApp>
<XMTok mathstyle="text" meaning="divide" role="MULOP"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok role="UNKNOWN" font="italic">u</XMTok>
<XMApp>
<XMTok meaning="square-root"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
</XMApp>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">x-\frac{1+u\sqrt{D}}{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>x</mi>
<mo>-</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mrow>
<mi>u</mi>
<msqrt>
<mi>D</mi>
</msqrt>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<minus/>
<ci encoding="">x</ci>
<apply>
<divide/>
<apply>
<plus/>
<cn encoding="" base="10" type="integer">1</cn>
<apply>
<times/>
<ci encoding="">u</ci>
<apply>
<root/>
<ci encoding="">D</ci>
</apply>
</apply>
</apply>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>-</XMTok>
<XMTok>x</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMTok>1</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>u</XMTok>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
<XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">x-\frac{1+u\sqrt{D}}{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 | @@ -1,70 +1,69 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m14" class="ltx_Math" alttext="x-\frac{1+u\sqrt{D}}{2}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>x</mi>
<mo>-</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mrow>
<mi>u</mi>
- <mo></mo>
<msqrt>
<mi>D</mi>
</msqrt>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<minus/>
- <ci>x</ci>
+ <ci encoding="">x</ci>
<apply>
<divide/>
<apply>
<plus/>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
<apply>
<times/>
- <ci>u</ci>
+ <ci encoding="">u</ci>
<apply>
<root/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
</apply>
- <cn type="integer">2</cn>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="minus" role="ADDOP">-</XMTok>
- <XMTok role="UNKNOWN" font="italic">x</XMTok>
+ <XMTok>-</XMTok>
+ <XMTok>x</XMTok>
<XMApp>
- <XMTok mathstyle="text" meaning="divide" role="MULOP"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>+</XMTok>
+ <XMTok>1</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok role="UNKNOWN" font="italic">u</XMTok>
+ <XMTok></XMTok>
+ <XMTok>u</XMTok>
<XMApp>
- <XMTok meaning="square-root"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">x-\frac{1+u\sqrt{D}}{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m15" class="ltx_Math" alttext="p" display="inline">
<semantics>
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci>p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m15" class="ltx_Math" alttext="p" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
- <ci>p</ci>
+ <ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
+ <XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m16" class="ltx_Math" alttext="p" display="inline">
<semantics>
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci>p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m16" class="ltx_Math" alttext="p" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>p</mi>
<annotation-xml encoding="MathML-Content">
- <ci>p</ci>
+ <ci encoding="">p</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
+ <XMTok>p</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m17" class="ltx_Math" alttext="n^{2}+n-m" display="inline">
<semantics>
<mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>n</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<minus/>
<apply>
<plus/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>n</ci>
<cn type="integer">2</cn>
</apply>
<ci>n</ci>
</apply>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="minus" role="ADDOP">-</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">n</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">n</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n^{2}+n-m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>n</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<minus/>
<apply>
<plus/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">n</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<ci encoding="">n</ci>
</apply>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>-</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok/>
<XMTok>n</XMTok>
<XMTok>2</XMTok>
</XMApp>
<XMTok>n</XMTok>
</XMApp>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n^{2}+n-m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | @@ -1,48 +1,48 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m17" class="ltx_Math" alttext="n^{2}+n-m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<msup>
<mi>n</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>n</mi>
<mo>-</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<minus/>
<apply>
<plus/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>n</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">n</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
- <ci>n</ci>
+ <ci encoding="">n</ci>
</apply>
- <ci>m</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="minus" role="ADDOP">-</XMTok>
+ <XMTok>-</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">n</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>n</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">n</XMTok>
+ <XMTok>n</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n^{2}+n-m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m18" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">f</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m18" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">f</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m19" class="ltx_Math" alttext="f_{m}(n)=\pm p" display="inline">
<semantics>
<mrow>
<mrow>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<mo></mo>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mrow>
<mo>±</mo>
<mi>p</mi>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
<ci>n</ci>
</apply>
<apply>
<csymbol cd="latexml">plus-or-minus</csymbol>
<ci>p</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok possibleFunction="yes" role="UNKNOWN" font="italic">f</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok close=")" open="(" role="UNKNOWN" font="italic">n</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
<XMTok role="UNKNOWN" font="italic">p</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}(n)=\pm p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mrow>
<mo>±</mo>
<mi>p</mi>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
<ci encoding="">n</ci>
</apply>
<apply>
<csymbol encoding="">plus-or-minus</csymbol>
<ci encoding="">p</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMApp>
<XMTok></XMTok>
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>n</XMTok>
</XMApp>
<XMApp>
<XMTok>±</XMTok>
<XMTok>p</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}(n)=\pm p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 | @@ -1,63 +1,62 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m19" class="ltx_Math" alttext="f_{m}(n)=\pm p" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
- <mo></mo>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mrow>
<mo>±</mo>
<mi>p</mi>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
- <ci>n</ci>
+ <ci encoding="">n</ci>
</apply>
<apply>
- <csymbol cd="latexml">plus-or-minus</csymbol>
- <ci>p</ci>
+ <csymbol encoding="">plus-or-minus</csymbol>
+ <ci encoding="">p</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
+ <XMTok>=</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
+ <XMTok></XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="italic">f</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok close=")" open="(" role="UNKNOWN" font="italic">n</XMTok>
+ <XMTok>n</XMTok>
</XMApp>
<XMApp>
- <XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
+ <XMTok>±</XMTok>
+ <XMTok>p</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}(n)=\pm p</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m20" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">f</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m20" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">f</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m21" class="ltx_Math" alttext="n" display="inline">
<semantics>
<mi>n</mi>
<annotation-xml encoding="MathML-Content">
<ci>n</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">n</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>n</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">n</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>n</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m21" class="ltx_Math" alttext="n" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>n</mi>
<annotation-xml encoding="MathML-Content">
- <ci>n</ci>
+ <ci encoding="">n</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">n</XMTok>
+ <XMTok>n</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m22" class="ltx_Math" alttext="p<m^{1/2}/6" display="inline">
<semantics>
<mrow>
<mi>p</mi>
<mo><</mo>
<mrow>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mo>/</mo>
<mn>6</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
<ci>p</ci>
<apply>
<divide/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>m</ci>
<apply>
<divide/>
<cn type="integer">1</cn>
<cn type="integer">2</cn>
</apply>
</apply>
<cn type="integer">6</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="less-than" role="RELOP"><</XMTok>
<XMTok role="UNKNOWN" font="italic">p</XMTok>
<XMApp>
<XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
<XMTok meaning="6" role="NUMBER">6</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p<m^{1/2}/6</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>p</mi>
<mo><</mo>
<mrow>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mo>/</mo>
<mn>6</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
<ci encoding="">p</ci>
<apply>
<divide/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">m</ci>
<apply>
<divide/>
<cn encoding="" base="10" type="integer">1</cn>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
<cn encoding="" base="10" type="integer">6</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok><</XMTok>
<XMTok>p</XMTok>
<XMApp>
<XMTok>/</XMTok>
<XMApp>
<XMTok/>
<XMTok>m</XMTok>
<XMApp>
<XMTok>/</XMTok>
<XMTok>1</XMTok>
<XMTok>2</XMTok>
</XMApp>
</XMApp>
<XMTok>6</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p<m^{1/2}/6</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 | @@ -1,62 +1,62 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m22" class="ltx_Math" alttext="p<m^{1/2}/6" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>p</mi>
<mo><</mo>
<mrow>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<mo>/</mo>
<mn>6</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
- <ci>p</ci>
+ <ci encoding="">p</ci>
<apply>
<divide/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>m</ci>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">m</ci>
<apply>
<divide/>
- <cn type="integer">1</cn>
- <cn type="integer">2</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
- <cn type="integer">6</cn>
+ <cn encoding="" base="10" type="integer">6</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="less-than" role="RELOP"><</XMTok>
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
+ <XMTok><</XMTok>
+ <XMTok>p</XMTok>
<XMApp>
- <XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
+ <XMTok>/</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok>/</XMTok>
+ <XMTok>1</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
- <XMTok meaning="6" role="NUMBER">6</XMTok>
+ <XMTok>6</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p<m^{1/2}/6</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m23" class="ltx_Math" alttext="m^{1/2}" display="inline">
<semantics>
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>m</ci>
<apply>
<divide/>
<cn type="integer">1</cn>
<cn type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m^{1/2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">m</ci>
<apply>
<divide/>
<cn encoding="" base="10" type="integer">1</cn>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>m</XMTok>
<XMApp>
<XMTok>/</XMTok>
<XMTok>1</XMTok>
<XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m^{1/2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,38 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m23" class="ltx_Math" alttext="m^{1/2}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msup>
<mi>m</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msup>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>m</ci>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">m</ci>
<apply>
<divide/>
- <cn type="integer">1</cn>
- <cn type="integer">2</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok>/</XMTok>
+ <XMTok>1</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m^{1/2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m24" class="ltx_Math" alttext="n" display="inline">
<semantics>
<mi>n</mi>
<annotation-xml encoding="MathML-Content">
<ci>n</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">n</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>n</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">n</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>n</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m24" class="ltx_Math" alttext="n" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>n</mi>
<annotation-xml encoding="MathML-Content">
- <ci>n</ci>
+ <ci encoding="">n</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">n</XMTok>
+ <XMTok>n</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">n</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m25" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">f</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p6.m25" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">f</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p7.m1" class="ltx_Math" alttext="p_{D}\equiv 1\;\;(\mathop{{\rm mod}}4D)" display="inline">
<semantics>
<mrow>
<msub>
<mi>p</mi>
<mi>D</mi>
</msub>
<mo>≡</mo>
<mrow>
<mn>1</mn>
<mspace width="veryverythickmathspace"/>
<mrow>
<mo>(</mo>
<mrow>
<mo>mod</mo>
<mrow xml:id="p7.m1.xm1c" xref="p7.m1.xm1.cmml">
<mn xml:id="p7.m1.xm1" xref="p7.m1.xm1.cmml">4</mn>
<mo xml:id="p7.m1.xm1a" xref="p7.m1.xm1.cmml"></mo>
<mi xml:id="p7.m1.xm1b" xref="p7.m1.xm1.cmml">D</mi>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<equivalent/>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>p</ci>
<ci>D</ci>
</apply>
<apply>
<csymbol cd="latexml">annotated</csymbol>
<cn type="integer">1</cn>
<apply>
<ci>pmod</ci>
<apply xml:id="p7.m1.xm1c.cmml" xref="p7.m1.xm1">
<times xml:id="p7.m1.xm1.cmml" xref="p7.m1.xm1"/>
<cn type="integer" xml:id="p7.m1.xm1a.cmml" xref="p7.m1.xm1">4</cn>
<ci xml:id="p7.m1.xm1b.cmml" xref="p7.m1.xm1">D</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equivalent-to" name="equiv" role="RELOP">≡</XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">p</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="annotated"/>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMDual role="MODIFIER">
<XMApp role="MODIFIER">
<XMTok name="pmod" role="UNKNOWN"/>
<XMApp xml:id="p7.m1.xm1.xm" fragid="p7.m1.xm1.xm">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
<XMApp close=")" open="(">
<XMTok role="BIGOP">mod</XMTok>
<XMRef idref="p7.m1.xm1.xm"/>
</XMApp>
</XMDual>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p_{D}\equiv 1\;\;(\mathop{{\rm mod}}4D)</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<msub>
<mi>p</mi>
<mi>D</mi>
</msub>
<mo>≡</mo>
<mrow>
<mn>1</mn>
<mrow>
<mo>(</mo>
<mrow>
<mo>mod</mo>
<mrow>
<mn>4</mn>
<mi>D</mi>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<equivalent/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">p</ci>
<ci encoding="">D</ci>
</apply>
<apply>
<csymbol encoding="">annotated</csymbol>
<cn encoding="" base="10" type="integer">1</cn>
<apply>
<ci encoding="">pmod</ci>
<apply>
<times encoding=""/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">D</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>≡</XMTok>
<XMApp>
<XMTok/>
<XMTok>p</XMTok>
<XMTok>D</XMTok>
</XMApp>
<XMApp>
<XMTok/>
<XMTok>1</XMTok>
<XMDual>
<XMApp>
<XMTok/>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok>mod</XMTok>
<XMRef/>
</XMApp>
</XMDual>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p_{D}\equiv 1\;\;(\mathop{{\rm mod}}4D)</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 | @@ -1,81 +1,79 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p7.m1" class="ltx_Math" alttext="p_{D}\equiv 1\;\;(\mathop{{\rm mod}}4D)" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<msub>
<mi>p</mi>
<mi>D</mi>
</msub>
<mo>≡</mo>
<mrow>
<mn>1</mn>
- <mspace width="veryverythickmathspace"/>
<mrow>
<mo>(</mo>
<mrow>
<mo>mod</mo>
- <mrow xml:id="p7.m1.xm1c" xref="p7.m1.xm1.cmml">
- <mn xml:id="p7.m1.xm1" xref="p7.m1.xm1.cmml">4</mn>
- <mo xml:id="p7.m1.xm1a" xref="p7.m1.xm1.cmml"></mo>
- <mi xml:id="p7.m1.xm1b" xref="p7.m1.xm1.cmml">D</mi>
+ <mrow>
+ <mn>4</mn>
+ <mi>D</mi>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<equivalent/>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>p</ci>
- <ci>D</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">p</ci>
+ <ci encoding="">D</ci>
</apply>
<apply>
- <csymbol cd="latexml">annotated</csymbol>
- <cn type="integer">1</cn>
+ <csymbol encoding="">annotated</csymbol>
+ <cn encoding="" base="10" type="integer">1</cn>
<apply>
- <ci>pmod</ci>
- <apply xml:id="p7.m1.xm1c.cmml" xref="p7.m1.xm1">
- <times xml:id="p7.m1.xm1.cmml" xref="p7.m1.xm1"/>
- <cn type="integer" xml:id="p7.m1.xm1a.cmml" xref="p7.m1.xm1">4</cn>
- <ci xml:id="p7.m1.xm1b.cmml" xref="p7.m1.xm1">D</ci>
+ <ci encoding="">pmod</ci>
+ <apply>
+ <times encoding=""/>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">D</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equivalent-to" name="equiv" role="RELOP">≡</XMTok>
+ <XMTok>≡</XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>p</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
<XMApp>
- <XMTok meaning="annotated"/>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
- <XMDual role="MODIFIER">
- <XMApp role="MODIFIER">
- <XMTok name="pmod" role="UNKNOWN"/>
- <XMApp xml:id="p7.m1.xm1.xm" fragid="p7.m1.xm1.xm">
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>1</XMTok>
+ <XMDual>
+ <XMApp>
+ <XMTok/>
+ <XMApp>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
- <XMApp close=")" open="(">
- <XMTok role="BIGOP">mod</XMTok>
- <XMRef idref="p7.m1.xm1.xm"/>
+ <XMApp>
+ <XMTok>mod</XMTok>
+ <XMRef/>
</XMApp>
</XMDual>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">p_{D}\equiv 1\;\;(\mathop{{\rm mod}}4D)</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p7.m2" class="ltx_Math" alttext="D\leq D_{0}" display="inline">
<semantics>
<mrow>
<mi>D</mi>
<mo>≤</mo>
<msub>
<mi>D</mi>
<mn>0</mn>
</msub>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<leq/>
<ci>D</ci>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>D</ci>
<cn type="integer">0</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
<XMTok meaning="0" role="NUMBER">0</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D\leq D_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>D</mi>
<mo>≤</mo>
<msub>
<mi>D</mi>
<mn>0</mn>
</msub>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<leq/>
<ci encoding="">D</ci>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">D</ci>
<cn encoding="" base="10" type="integer">0</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>≤</XMTok>
<XMTok>D</XMTok>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
<XMTok>0</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D\leq D_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,38 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p7.m2" class="ltx_Math" alttext="D\leq D_{0}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>D</mi>
<mo>≤</mo>
<msub>
<mi>D</mi>
<mn>0</mn>
</msub>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<leq/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>D</ci>
- <cn type="integer">0</cn>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">D</ci>
+ <cn encoding="" base="10" type="integer">0</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok>≤</XMTok>
+ <XMTok>D</XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
- <XMTok meaning="0" role="NUMBER">0</XMTok>
+ <XMTok/>
+ <XMTok>D</XMTok>
+ <XMTok>0</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D\leq D_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p7.m3" class="ltx_Math" alttext="m>6\max p_{D}" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>></mo>
<mrow>
<mn>6</mn>
<mo></mo>
<mrow>
<mo>max</mo>
<mo></mo>
<msub>
<mi>p</mi>
<mi>D</mi>
</msub>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<ci>m</ci>
<apply>
<times/>
<cn type="integer">6</cn>
<apply>
<max/>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>p</ci>
<ci>D</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="greater-than" role="RELOP">></XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="6" role="NUMBER">6</XMTok>
<XMApp>
<XMTok meaning="maximum" role="LIMITOP" scriptpos="post">max</XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">p</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m>6\max p_{D}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>></mo>
<mrow>
<mn>6</mn>
<mrow>
<mo>max</mo>
<mo></mo>
<msub>
<mi>p</mi>
<mi>D</mi>
</msub>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<ci encoding="">m</ci>
<apply>
<times/>
<cn encoding="" base="10" type="integer">6</cn>
<apply>
<max/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">p</ci>
<ci encoding="">D</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>></XMTok>
<XMTok>m</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>6</XMTok>
<XMApp>
<XMTok>max</XMTok>
<XMApp>
<XMTok/>
<XMTok>p</XMTok>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m>6\max p_{D}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 | @@ -1,60 +1,59 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p7.m3" class="ltx_Math" alttext="m>6\max p_{D}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>></mo>
<mrow>
<mn>6</mn>
- <mo></mo>
<mrow>
<mo>max</mo>
<mo></mo>
<msub>
<mi>p</mi>
<mi>D</mi>
</msub>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
<apply>
<times/>
- <cn type="integer">6</cn>
+ <cn encoding="" base="10" type="integer">6</cn>
<apply>
<max/>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>p</ci>
- <ci>D</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">p</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="greater-than" role="RELOP">></XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>></XMTok>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="6" role="NUMBER">6</XMTok>
+ <XMTok></XMTok>
+ <XMTok>6</XMTok>
<XMApp>
- <XMTok meaning="maximum" role="LIMITOP" scriptpos="post">max</XMTok>
+ <XMTok>max</XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">p</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>p</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m>6\max p_{D}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem3.p1.m1" class="ltx_Math" alttext="m" display="inline">
<semantics>
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci>m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN">m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem3.p1.m1" class="ltx_Math" alttext="m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
- <ci>m</ci>
+ <ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN">m</XMTok>
+ <XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem3.p1.m2" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post3"/>
<XMTok role="UNKNOWN">f</XMTok>
<XMTok role="UNKNOWN">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem3.p1.m2" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post3"/>
- <XMTok role="UNKNOWN">f</XMTok>
- <XMTok role="UNKNOWN">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem3.p1.m3" class="ltx_Math" alttext="D\geq m^{1/12}" display="inline">
<semantics>
<mrow>
<mi>D</mi>
<mo mathvariant="normal">≥</mo>
<msup>
<mi>m</mi>
<mrow>
<mn mathvariant="normal">1</mn>
<mo mathvariant="normal">/</mo>
<mn mathvariant="normal">12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<geq/>
<ci>D</ci>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>m</ci>
<apply>
<divide/>
<cn type="integer">1</cn>
<cn type="integer">12</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="greater-than-or-equals" name="geq" role="RELOP" font="upright">≥</XMTok>
<XMTok role="UNKNOWN">D</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post3"/>
<XMTok role="UNKNOWN">m</XMTok>
<XMApp>
<XMTok mathstyle="inline" meaning="divide" role="MULOP" font="upright">/</XMTok>
<XMTok meaning="1" role="NUMBER" font="upright">1</XMTok>
<XMTok meaning="12" role="NUMBER" font="upright">12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D\geq m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>D</mi>
<mo mathvariant="normal">≥</mo>
<msup>
<mi>m</mi>
<mrow>
<mn mathvariant="normal">1</mn>
<mo mathvariant="normal">/</mo>
<mn mathvariant="normal">12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<geq/>
<ci encoding="">D</ci>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">m</ci>
<apply>
<divide/>
<cn encoding="" base="10" type="integer">1</cn>
<cn encoding="" base="10" type="integer">12</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>≥</XMTok>
<XMTok>D</XMTok>
<XMApp>
<XMTok/>
<XMTok>m</XMTok>
<XMApp>
<XMTok>/</XMTok>
<XMTok>1</XMTok>
<XMTok>12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D\geq m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 | @@ -1,50 +1,50 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="ThmLem3.p1.m3" class="ltx_Math" alttext="D\geq m^{1/12}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>D</mi>
<mo mathvariant="normal">≥</mo>
<msup>
<mi>m</mi>
<mrow>
<mn mathvariant="normal">1</mn>
<mo mathvariant="normal">/</mo>
<mn mathvariant="normal">12</mn>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<geq/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>m</ci>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">m</ci>
<apply>
<divide/>
- <cn type="integer">1</cn>
- <cn type="integer">12</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">12</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="greater-than-or-equals" name="geq" role="RELOP" font="upright">≥</XMTok>
- <XMTok role="UNKNOWN">D</XMTok>
+ <XMTok>≥</XMTok>
+ <XMTok>D</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post3"/>
- <XMTok role="UNKNOWN">m</XMTok>
+ <XMTok/>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok mathstyle="inline" meaning="divide" role="MULOP" font="upright">/</XMTok>
- <XMTok meaning="1" role="NUMBER" font="upright">1</XMTok>
- <XMTok meaning="12" role="NUMBER" font="upright">12</XMTok>
+ <XMTok>/</XMTok>
+ <XMTok>1</XMTok>
+ <XMTok>12</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D\geq m^{1/12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m1" class="ltx_Math" alttext="m=2" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>m</ci>
<cn type="integer">2</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">m</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>m</XMTok>
<XMTok>2</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,27 +1,27 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m1" class="ltx_Math" alttext="m=2" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>2</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>m</ci>
- <cn type="integer">2</cn>
+ <ci encoding="">m</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>m</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m=2</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m2" class="ltx_Math" alttext="\epsilon_{m}" display="inline">
<semantics>
<msub>
<mi>ϵ</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>ϵ</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>ε</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m2" class="ltx_Math" alttext="\epsilon_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
- <mi>ϵ</mi>
+ <mi>ε</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>ϵ</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m3" class="ltx_Math" alttext="\mathbb{Q}(\sqrt{D})" display="inline">
<semantics>
<mrow>
<mi>ℚ</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
<ci>ℚ</ci>
<apply>
<root/>
<ci>D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
<XMApp close=")" open="(">
<XMTok meaning="square-root"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{D})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
<ci encoding="">Q</ci>
<apply>
<root/>
<ci encoding="">D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok></XMTok>
<XMTok>Q</XMTok>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{D})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,39 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m3" class="ltx_Math" alttext="\mathbb{Q}(\sqrt{D})" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
- <mi>ℚ</mi>
- <mo></mo>
+ <mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
- <ci>ℚ</ci>
+ <ci encoding="">Q</ci>
<apply>
<root/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
- <XMApp close=")" open="(">
- <XMTok meaning="square-root"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok></XMTok>
+ <XMTok>Q</XMTok>
+ <XMApp>
+ <XMTok/>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{D})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m4" class="ltx_Math" alttext="1<|\epsilon_{m}|\ll m" display="inline">
<semantics>
<mrow>
<mn>1</mn>
<mo><</mo>
<mrow>
<mo fence="true">|</mo>
<msub>
<mi>ϵ</mi>
<mi>m</mi>
</msub>
<mo fence="true">|</mo>
</mrow>
<mo>≪</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
<cn type="integer">1</cn>
<apply xml:id="p8.m4.sh1e.cmml">
<abs xml:id="p8.m4.sh1.cmml"/>
<apply xml:id="p8.m4.sh1d.cmml">
<csymbol cd="ambiguous" xml:id="p8.m4.sh1a.cmml">subscript</csymbol>
<ci xml:id="p8.m4.sh1b.cmml">ϵ</ci>
<ci xml:id="p8.m4.sh1c.cmml">m</ci>
</apply>
</apply>
</apply>
<apply>
<csymbol cd="latexml">much-less-than</csymbol>
<share href="#p8.m4.sh1.cmml"/>
<ci xml:id="p8.m4.sh2.cmml">m</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="multirelation"/>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMTok meaning="less-than" role="RELOP"><</XMTok>
<XMApp xml:id="p8.m4.sh1.xm" fragid="p8.m4.sh1.xm">
<XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMApp>
<XMTok meaning="much-less-than" name="ll" role="RELOP">≪</XMTok>
<XMTok role="UNKNOWN" font="italic" xml:id="p8.m4.sh2.xm" fragid="p8.m4.sh2.xm">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1<|\epsilon_{m}|\ll m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mn>1</mn>
<mo><</mo>
<mrow>
<mo>|</mo>
<msub>
<mi>ε</mi>
<mi>m</mi>
</msub>
<mo>|</mo>
</mrow>
<mo>≪</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
<cn encoding="" base="10" type="integer">1</cn>
<apply>
<abs encoding=""/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">m</ci>
</apply>
</apply>
</apply>
<apply>
<csymbol encoding="">much-less-than</csymbol>
<share/>
<ci encoding="">m</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>1</XMTok>
<XMTok><</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMApp>
<XMTok>≪</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1<|\epsilon_{m}|\ll m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 | @@ -1,61 +1,61 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m4" class="ltx_Math" alttext="1<|\epsilon_{m}|\ll m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mn>1</mn>
<mo><</mo>
<mrow>
- <mo fence="true">|</mo>
+ <mo>|</mo>
<msub>
- <mi>ϵ</mi>
+ <mi>ε</mi>
<mi>m</mi>
</msub>
- <mo fence="true">|</mo>
+ <mo>|</mo>
</mrow>
<mo>≪</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<lt/>
- <cn type="integer">1</cn>
- <apply xml:id="p8.m4.sh1e.cmml">
- <abs xml:id="p8.m4.sh1.cmml"/>
- <apply xml:id="p8.m4.sh1d.cmml">
- <csymbol cd="ambiguous" xml:id="p8.m4.sh1a.cmml">subscript</csymbol>
- <ci xml:id="p8.m4.sh1b.cmml">ϵ</ci>
- <ci xml:id="p8.m4.sh1c.cmml">m</ci>
+ <cn encoding="" base="10" type="integer">1</cn>
+ <apply>
+ <abs encoding=""/>
+ <apply>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">m</ci>
</apply>
</apply>
</apply>
<apply>
- <csymbol cd="latexml">much-less-than</csymbol>
- <share href="#p8.m4.sh1.cmml"/>
- <ci xml:id="p8.m4.sh2.cmml">m</ci>
+ <csymbol encoding="">much-less-than</csymbol>
+ <share/>
+ <ci encoding="">m</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="multirelation"/>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
- <XMTok meaning="less-than" role="RELOP"><</XMTok>
- <XMApp xml:id="p8.m4.sh1.xm" fragid="p8.m4.sh1.xm">
- <XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
+ <XMTok/>
+ <XMTok>1</XMTok>
+ <XMTok><</XMTok>
+ <XMApp>
+ <XMTok/>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMApp>
- <XMTok meaning="much-less-than" name="ll" role="RELOP">≪</XMTok>
- <XMTok role="UNKNOWN" font="italic" xml:id="p8.m4.sh2.xm" fragid="p8.m4.sh2.xm">m</XMTok>
+ <XMTok>≪</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">1<|\epsilon_{m}|\ll m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex2.m2" class="ltx_Math" alttext="\displaystyle m=t^{2}" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>=</mo>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>m</ci>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>t</ci>
<cn type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post7"/>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle m=t^{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">m</ci>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">t</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>m</XMTok>
<XMApp>
<XMTok/>
<XMTok>t</XMTok>
<XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle m=t^{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,38 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex2.m2" class="ltx_Math" alttext="\displaystyle m=t^{2}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>t</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post7"/>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>t</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle m=t^{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex2.m3" class="ltx_Math" alttext="\displaystyle:" display="inline">
<semantics>
<mo>:</mo>
<annotation-xml encoding="MathML-Content">
<ci>normal-:</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok name="colon" role="METARELOP">:</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle:</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mo>/</mo>
<annotation-xml encoding="MathML-Content">
<ci encoding="">normal-:</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>:</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle:</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex2.m3" class="ltx_Math" alttext="\displaystyle:" display="inline">
- <semantics>
- <mo>:</mo>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
+ <mo>/</mo>
<annotation-xml encoding="MathML-Content">
- <ci>normal-:</ci>
+ <ci encoding="">normal-:</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok name="colon" role="METARELOP">:</XMTok>
+ <XMTok>:</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle:</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex2.m4" class="ltx_Math" alttext="\displaystyle\quad\epsilon_{m}=2t+\sqrt{4m+1}" display="inline">
<semantics>
<mrow>
<mrow>
<mi mathvariant="normal"> </mi>
<mo></mo>
<msub>
<mi>ϵ</mi>
<mi>m</mi>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<mrow>
<mn>2</mn>
<mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<msqrt>
<mrow>
<mrow>
<mn>4</mn>
<mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msqrt>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<ci>normal- </ci>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>ϵ</ci>
<ci>m</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">2</cn>
<ci>t</ci>
</apply>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">4</cn>
<ci>m</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok role="UNKNOWN"> </XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post7"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="square-root"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle\quad\epsilon_{m}=2t+\sqrt{4m+1}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mi mathvariant="normal"> </mi>
<msub>
<mi>ε</mi>
<mi>m</mi>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<mrow>
<mn>2</mn>
<mi>t</mi>
</mrow>
<mo>+</mo>
<msqrt>
<mrow>
<mn>4</mn>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</msqrt>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<ci encoding="">normal- </ci>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">m</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">2</cn>
<ci encoding="">t</ci>
</apply>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">m</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok> </XMTok>
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>2</XMTok>
<XMTok>t</XMTok>
</XMApp>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle\quad\epsilon_{m}=2t+\sqrt{4m+1}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 | @@ -1,106 +1,101 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex2.m4" class="ltx_Math" alttext="\displaystyle\quad\epsilon_{m}=2t+\sqrt{4m+1}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
- <mi mathvariant="normal"> </mi>
- <mo></mo>
+ <mi mathvariant="normal"> </mi>
<msub>
- <mi>ϵ</mi>
+ <mi>ε</mi>
<mi>m</mi>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<mrow>
<mn>2</mn>
- <mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<msqrt>
<mrow>
- <mrow>
- <mn>4</mn>
- <mo></mo>
- <mi>m</mi>
- </mrow>
- <mo>+</mo>
- <mn>1</mn>
+ <mn>4</mn>
+ <mi>m</mi>
</mrow>
+ <mo>+</mo>
+ <mn>1</mn>
</msqrt>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
- <ci>normal- </ci>
+ <ci encoding="">normal- </ci>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>ϵ</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">m</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">2</cn>
- <ci>t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
+ <ci encoding="">t</ci>
</apply>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">4</cn>
- <ci>m</ci>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">m</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
+ <XMTok>=</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok role="UNKNOWN"> </XMTok>
+ <XMTok></XMTok>
+ <XMTok> </XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post7"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMApp>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>2</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
<XMApp>
- <XMTok meaning="square-root"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle\quad\epsilon_{m}=2t+\sqrt{4m+1}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex3.m2" class="ltx_Math" alttext="\displaystyle m=t^{2}+t\pm 1" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
<mn>1</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>m</ci>
<apply>
<csymbol cd="latexml">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>t</ci>
<cn type="integer">2</cn>
</apply>
<ci>t</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post7"/>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle m=t^{2}+t\pm 1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
<mn>1</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">m</ci>
<apply>
<csymbol encoding="">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">t</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<ci encoding="">t</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>m</XMTok>
<XMApp>
<XMTok>±</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok/>
<XMTok>t</XMTok>
<XMTok>2</XMTok>
</XMApp>
<XMTok>t</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle m=t^{2}+t\pm 1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 | @@ -1,60 +1,60 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex3.m2" class="ltx_Math" alttext="\displaystyle m=t^{2}+t\pm 1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
<mn>1</mn>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
<apply>
- <csymbol cd="latexml">plus-or-minus</csymbol>
+ <csymbol encoding="">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>t</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
- <ci>t</ci>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
+ <XMTok>±</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post7"/>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>t</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle m=t^{2}+t\pm 1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex3.m3" class="ltx_Math" alttext="\displaystyle:" display="inline">
<semantics>
<mo>:</mo>
<annotation-xml encoding="MathML-Content">
<ci>normal-:</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok name="colon" role="METARELOP">:</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle:</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mo>/</mo>
<annotation-xml encoding="MathML-Content">
<ci encoding="">normal-:</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>:</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle:</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex3.m3" class="ltx_Math" alttext="\displaystyle:" display="inline">
- <semantics>
- <mo>:</mo>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
+ <mo>/</mo>
<annotation-xml encoding="MathML-Content">
- <ci>normal-:</ci>
+ <ci encoding="">normal-:</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok name="colon" role="METARELOP">:</XMTok>
+ <XMTok>:</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle:</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex3.m4" class="ltx_Math" alttext="\displaystyle\quad\epsilon_{m}=\frac{2t+1+\sqrt{4m+1}}{2}" display="inline">
<semantics>
<mrow>
<mrow>
<mi mathvariant="normal"> </mi>
<mo></mo>
<msub>
<mi>ϵ</mi>
<mi>m</mi>
</msub>
</mrow>
<mo>=</mo>
<mstyle displaystyle="true">
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
<mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
<mo>+</mo>
<msqrt>
<mrow>
<mrow>
<mn>4</mn>
<mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msqrt>
</mrow>
<mn>2</mn>
</mfrac>
</mstyle>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<ci>normal- </ci>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>ϵ</ci>
<ci>m</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">2</cn>
<ci>t</ci>
</apply>
<cn type="integer">1</cn>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">4</cn>
<ci>m</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</apply>
</apply>
<cn type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok role="UNKNOWN"> </XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post7"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok mathstyle="display" meaning="divide" role="MULOP"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMApp>
<XMTok meaning="square-root"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMApp>
</XMApp>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle\quad\epsilon_{m}=\frac{2t+1+\sqrt{4m+1}}{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mi mathvariant="normal"> </mi>
<msub>
<mi>ε</mi>
<mi>m</mi>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
<mo>+</mo>
<msqrt>
<mrow>
<mn>4</mn>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</msqrt>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<ci encoding="">normal- </ci>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">m</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">2</cn>
<ci encoding="">t</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">m</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</apply>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok> </XMTok>
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>2</XMTok>
<XMTok>t</XMTok>
</XMApp>
<XMTok>1</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMApp>
<XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle\quad\epsilon_{m}=\frac{2t+1+\sqrt{4m+1}}{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 | @@ -1,123 +1,116 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex3.m4" class="ltx_Math" alttext="\displaystyle\quad\epsilon_{m}=\frac{2t+1+\sqrt{4m+1}}{2}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
- <mi mathvariant="normal"> </mi>
- <mo></mo>
+ <mi mathvariant="normal"> </mi>
<msub>
- <mi>ϵ</mi>
+ <mi>ε</mi>
<mi>m</mi>
</msub>
</mrow>
<mo>=</mo>
- <mstyle displaystyle="true">
- <mfrac>
+ <mfrac>
+ <mrow>
<mrow>
+ <mn>2</mn>
+ <mi>t</mi>
+ </mrow>
+ <mo>+</mo>
+ <mn>1</mn>
+ <mo>+</mo>
+ <msqrt>
<mrow>
- <mn>2</mn>
- <mo></mo>
- <mi>t</mi>
+ <mn>4</mn>
+ <mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
- <mo>+</mo>
- <msqrt>
- <mrow>
- <mrow>
- <mn>4</mn>
- <mo></mo>
- <mi>m</mi>
- </mrow>
- <mo>+</mo>
- <mn>1</mn>
- </mrow>
- </msqrt>
- </mrow>
- <mn>2</mn>
- </mfrac>
- </mstyle>
+ </msqrt>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
- <ci>normal- </ci>
+ <ci encoding="">normal- </ci>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>ϵ</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">m</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">2</cn>
- <ci>t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">4</cn>
- <ci>m</ci>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">m</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</apply>
- <cn type="integer">2</cn>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
+ <XMTok>=</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok role="UNKNOWN"> </XMTok>
+ <XMTok></XMTok>
+ <XMTok> </XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post7"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMApp>
<XMApp>
- <XMTok mathstyle="display" meaning="divide" role="MULOP"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>2</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
<XMApp>
- <XMTok meaning="square-root"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMApp>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle\quad\epsilon_{m}=\frac{2t+1+\sqrt{4m+1}}{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex4.m2" class="ltx_Math" alttext="\displaystyle m=t^{2}+t\pm\frac{2t+1}{3}" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
<mstyle displaystyle="true">
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
<mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mstyle>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci>m</ci>
<apply>
<csymbol cd="latexml">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>t</ci>
<cn type="integer">2</cn>
</apply>
<ci>t</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">2</cn>
<ci>t</ci>
</apply>
<cn type="integer">1</cn>
</apply>
<cn type="integer">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post7"/>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMApp>
<XMTok mathstyle="display" meaning="divide" role="MULOP"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
<XMTok meaning="3" role="NUMBER">3</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle m=t^{2}+t\pm\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
<mfrac>
<mrow>
<mrow>
<mn>2</mn>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<ci encoding="">m</ci>
<apply>
<csymbol encoding="">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">t</ci>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<ci encoding="">t</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">2</cn>
<ci encoding="">t</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
<cn encoding="" base="10" type="integer">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMTok>m</XMTok>
<XMApp>
<XMTok>±</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok/>
<XMTok>t</XMTok>
<XMTok>2</XMTok>
</XMApp>
<XMTok>t</XMTok>
</XMApp>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>2</XMTok>
<XMTok>t</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
<XMTok>3</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle m=t^{2}+t\pm\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 | @@ -1,97 +1,94 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex4.m2" class="ltx_Math" alttext="\displaystyle m=t^{2}+t\pm\frac{2t+1}{3}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>t</mi>
<mo>±</mo>
- <mstyle displaystyle="true">
- <mfrac>
+ <mfrac>
+ <mrow>
<mrow>
- <mrow>
- <mn>2</mn>
- <mo></mo>
- <mi>t</mi>
- </mrow>
- <mo>+</mo>
- <mn>1</mn>
+ <mn>2</mn>
+ <mi>t</mi>
</mrow>
- <mn>3</mn>
- </mfrac>
- </mstyle>
+ <mo>+</mo>
+ <mn>1</mn>
+ </mrow>
+ <mn>3</mn>
+ </mfrac>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
<apply>
- <csymbol cd="latexml">plus-or-minus</csymbol>
+ <csymbol encoding="">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>t</ci>
- <cn type="integer">2</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
- <ci>t</ci>
+ <ci encoding="">t</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">2</cn>
- <ci>t</ci>
+ <cn encoding="" base="10" type="integer">2</cn>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
- <cn type="integer">3</cn>
+ <cn encoding="" base="10" type="integer">3</cn>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>=</XMTok>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
+ <XMTok>±</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post7"/>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok/>
+ <XMTok>t</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
<XMApp>
- <XMTok mathstyle="display" meaning="divide" role="MULOP"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>2</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
- <XMTok meaning="3" role="NUMBER">3</XMTok>
+ <XMTok>3</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle m=t^{2}+t\pm\frac{2t+1}{3}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex4.m3" class="ltx_Math" alttext="\displaystyle:" display="inline">
<semantics>
<mo>:</mo>
<annotation-xml encoding="MathML-Content">
<ci>normal-:</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok name="colon" role="METARELOP">:</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle:</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mo>/</mo>
<annotation-xml encoding="MathML-Content">
<ci encoding="">normal-:</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>:</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle:</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex4.m3" class="ltx_Math" alttext="\displaystyle:" display="inline">
- <semantics>
- <mo>:</mo>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
+ <mo>/</mo>
<annotation-xml encoding="MathML-Content">
- <ci>normal-:</ci>
+ <ci encoding="">normal-:</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok name="colon" role="METARELOP">:</XMTok>
+ <XMTok>:</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle:</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex4.m4" class="ltx_Math" alttext="\displaystyle\quad\epsilon_{m}=\frac{6t+3\pm 2+3\sqrt{4m+1}}{2}" display="inline">
<semantics>
<mrow>
<mrow>
<mi mathvariant="normal"> </mi>
<mo></mo>
<msub>
<mi>ϵ</mi>
<mi>m</mi>
</msub>
</mrow>
<mo>=</mo>
<mstyle displaystyle="true">
<mfrac>
<mrow>
<mrow>
<mn>6</mn>
<mo></mo>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mo>±</mo>
<mn>2</mn>
<mo>+</mo>
<mrow>
<mn>3</mn>
<mo></mo>
<msqrt>
<mrow>
<mrow>
<mn>4</mn>
<mo></mo>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msqrt>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
</mstyle>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<ci>normal- </ci>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>ϵ</ci>
<ci>m</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<csymbol cd="latexml">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">6</cn>
<ci>t</ci>
</apply>
<cn type="integer">3</cn>
</apply>
<cn type="integer">2</cn>
</apply>
<apply>
<times/>
<cn type="integer">3</cn>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
<cn type="integer">4</cn>
<ci>m</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</apply>
</apply>
</apply>
<cn type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok role="UNKNOWN"> </XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post7"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok mathstyle="display" meaning="divide" role="MULOP"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="6" role="NUMBER">6</XMTok>
<XMTok role="UNKNOWN" font="italic">t</XMTok>
</XMApp>
<XMTok meaning="3" role="NUMBER">3</XMTok>
</XMApp>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="3" role="NUMBER">3</XMTok>
<XMApp>
<XMTok meaning="square-root"/>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="4" role="NUMBER">4</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle\quad\epsilon_{m}=\frac{6t+3\pm 2+3\sqrt{4m+1}}{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mi mathvariant="normal"> </mi>
<msub>
<mi>ε</mi>
<mi>m</mi>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mn>6</mn>
<mi>t</mi>
</mrow>
<mo>+</mo>
<mn>3</mn>
<mo>±</mo>
<mn>2</mn>
<mo>+</mo>
<mrow>
<mn>3</mn>
<msqrt>
<mrow>
<mn>4</mn>
<mi>m</mi>
</mrow>
<mo>+</mo>
<mn>1</mn>
</msqrt>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<ci encoding="">normal- </ci>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">m</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<csymbol encoding="">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">6</cn>
<ci encoding="">t</ci>
</apply>
<cn encoding="" base="10" type="integer">3</cn>
</apply>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<apply>
<times/>
<cn encoding="" base="10" type="integer">3</cn>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">4</cn>
<ci encoding="">m</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</apply>
</apply>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok> </XMTok>
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok>±</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>6</XMTok>
<XMTok>t</XMTok>
</XMApp>
<XMTok>3</XMTok>
</XMApp>
<XMTok>2</XMTok>
</XMApp>
<XMApp>
<XMTok></XMTok>
<XMTok>3</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>4</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
<XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle\quad\epsilon_{m}=\frac{6t+3\pm 2+3\sqrt{4m+1}}{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 | @@ -1,151 +1,143 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex4.m4" class="ltx_Math" alttext="\displaystyle\quad\epsilon_{m}=\frac{6t+3\pm 2+3\sqrt{4m+1}}{2}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
- <mi mathvariant="normal"> </mi>
- <mo></mo>
+ <mi mathvariant="normal"> </mi>
<msub>
- <mi>ϵ</mi>
+ <mi>ε</mi>
<mi>m</mi>
</msub>
</mrow>
<mo>=</mo>
- <mstyle displaystyle="true">
- <mfrac>
+ <mfrac>
+ <mrow>
<mrow>
- <mrow>
- <mn>6</mn>
- <mo></mo>
- <mi>t</mi>
- </mrow>
- <mo>+</mo>
- <mn>3</mn>
- <mo>±</mo>
- <mn>2</mn>
- <mo>+</mo>
- <mrow>
- <mn>3</mn>
- <mo></mo>
- <msqrt>
- <mrow>
- <mrow>
- <mn>4</mn>
- <mo></mo>
- <mi>m</mi>
- </mrow>
- <mo>+</mo>
- <mn>1</mn>
- </mrow>
- </msqrt>
- </mrow>
+ <mn>6</mn>
+ <mi>t</mi>
</mrow>
+ <mo>+</mo>
+ <mn>3</mn>
+ <mo>±</mo>
<mn>2</mn>
- </mfrac>
- </mstyle>
+ <mo>+</mo>
+ <mrow>
+ <mn>3</mn>
+ <msqrt>
+ <mrow>
+ <mn>4</mn>
+ <mi>m</mi>
+ </mrow>
+ <mo>+</mo>
+ <mn>1</mn>
+ </msqrt>
+ </mrow>
+ </mrow>
+ <mn>2</mn>
+ </mfrac>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
- <ci>normal- </ci>
+ <ci encoding="">normal- </ci>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>ϵ</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">m</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
- <csymbol cd="latexml">plus-or-minus</csymbol>
+ <csymbol encoding="">plus-or-minus</csymbol>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">6</cn>
- <ci>t</ci>
+ <cn encoding="" base="10" type="integer">6</cn>
+ <ci encoding="">t</ci>
</apply>
- <cn type="integer">3</cn>
+ <cn encoding="" base="10" type="integer">3</cn>
</apply>
- <cn type="integer">2</cn>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
<apply>
<times/>
- <cn type="integer">3</cn>
+ <cn encoding="" base="10" type="integer">3</cn>
<apply>
<root/>
<apply>
<plus/>
<apply>
<times/>
- <cn type="integer">4</cn>
- <ci>m</ci>
+ <cn encoding="" base="10" type="integer">4</cn>
+ <ci encoding="">m</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</apply>
</apply>
- <cn type="integer">2</cn>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
+ <XMTok>=</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok role="UNKNOWN"> </XMTok>
+ <XMTok></XMTok>
+ <XMTok> </XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post7"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMApp>
<XMApp>
- <XMTok mathstyle="display" meaning="divide" role="MULOP"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="plus-or-minus" name="pm" role="ADDOP">±</XMTok>
+ <XMTok>±</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="6" role="NUMBER">6</XMTok>
- <XMTok role="UNKNOWN" font="italic">t</XMTok>
+ <XMTok></XMTok>
+ <XMTok>6</XMTok>
+ <XMTok>t</XMTok>
</XMApp>
- <XMTok meaning="3" role="NUMBER">3</XMTok>
+ <XMTok>3</XMTok>
</XMApp>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="3" role="NUMBER">3</XMTok>
+ <XMTok></XMTok>
+ <XMTok>3</XMTok>
<XMApp>
- <XMTok meaning="square-root"/>
+ <XMTok/>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="4" role="NUMBER">4</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok></XMTok>
+ <XMTok>4</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\displaystyle\quad\epsilon_{m}=\frac{6t+3\pm 2+3\sqrt{4m+1}}{2}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m5" class="ltx_Math" alttext="\epsilon_{D}>1" display="inline">
<semantics>
<mrow>
<msub>
<mi>ϵ</mi>
<mi>D</mi>
</msub>
<mo>></mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>ϵ</ci>
<ci>D</ci>
</apply>
<cn type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="greater-than" role="RELOP">></XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{D}>1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<msub>
<mi>ε</mi>
<mi>D</mi>
</msub>
<mo>></mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">D</ci>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>></XMTok>
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>D</XMTok>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{D}>1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 | @@ -1,38 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m5" class="ltx_Math" alttext="\epsilon_{D}>1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<msub>
- <mi>ϵ</mi>
+ <mi>ε</mi>
<mi>D</mi>
</msub>
<mo>></mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>ϵ</ci>
- <ci>D</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">D</ci>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="greater-than" role="RELOP">></XMTok>
+ <XMTok>></XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{D}>1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m6" class="ltx_Math" alttext="\mathbb{Q}(\sqrt{D})" display="inline">
<semantics>
<mrow>
<mi>ℚ</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
<ci>ℚ</ci>
<apply>
<root/>
<ci>D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
<XMApp close=")" open="(">
<XMTok meaning="square-root"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{D})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
<ci encoding="">Q</ci>
<apply>
<root/>
<ci encoding="">D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok></XMTok>
<XMTok>Q</XMTok>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{D})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,39 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m6" class="ltx_Math" alttext="\mathbb{Q}(\sqrt{D})" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
- <mi>ℚ</mi>
- <mo></mo>
+ <mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
- <ci>ℚ</ci>
+ <ci encoding="">Q</ci>
<apply>
<root/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
- <XMApp close=")" open="(">
- <XMTok meaning="square-root"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok></XMTok>
+ <XMTok>Q</XMTok>
+ <XMApp>
+ <XMTok/>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{D})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m7" class="ltx_Math" alttext="\mathbb{Q}(\sqrt{D})" display="inline">
<semantics>
<mrow>
<mi>ℚ</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
<ci>ℚ</ci>
<apply>
<root/>
<ci>D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
<XMApp close=")" open="(">
<XMTok meaning="square-root"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{D})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
<ci encoding="">Q</ci>
<apply>
<root/>
<ci encoding="">D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok></XMTok>
<XMTok>Q</XMTok>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{D})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,39 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m7" class="ltx_Math" alttext="\mathbb{Q}(\sqrt{D})" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
- <mi>ℚ</mi>
- <mo></mo>
+ <mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<times/>
- <ci>ℚ</ci>
+ <ci encoding="">Q</ci>
<apply>
<root/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
- <XMApp close=")" open="(">
- <XMTok meaning="square-root"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok></XMTok>
+ <XMTok>Q</XMTok>
+ <XMApp>
+ <XMTok/>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\mathbb{Q}(\sqrt{D})</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m8" class="ltx_Math" alttext="k" display="inline">
<semantics>
<mi>k</mi>
<annotation-xml encoding="MathML-Content">
<ci>k</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">k</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">k</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>k</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">k</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>k</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">k</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m8" class="ltx_Math" alttext="k" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>k</mi>
<annotation-xml encoding="MathML-Content">
- <ci>k</ci>
+ <ci encoding="">k</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">k</XMTok>
+ <XMTok>k</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">k</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m9" class="ltx_Math" alttext="\epsilon_{m}=\epsilon_{D}^{k}" display="inline">
<semantics>
<mrow>
<msub>
<mi>ϵ</mi>
<mi>m</mi>
</msub>
<mo>=</mo>
<msubsup>
<mi>ϵ</mi>
<mi>D</mi>
<mi>k</mi>
</msubsup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>ϵ</ci>
<ci>m</ci>
</apply>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>ϵ</ci>
<ci>D</ci>
</apply>
<ci>k</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">k</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{m}=\epsilon_{D}^{k}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<msub>
<mi>ε</mi>
<mi>m</mi>
</msub>
<mo>=</mo>
<msup>
<msub>
<mi>ε</mi>
<mi>D</mi>
</msub>
<mi>k</mi>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">m</ci>
</apply>
<apply>
<csymbol encoding="">superscript</csymbol>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">D</ci>
</apply>
<ci encoding="">k</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMApp>
<XMTok/>
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>D</XMTok>
</XMApp>
<XMTok>k</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{m}=\epsilon_{D}^{k}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 | @@ -1,58 +1,60 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m9" class="ltx_Math" alttext="\epsilon_{m}=\epsilon_{D}^{k}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<msub>
- <mi>ϵ</mi>
+ <mi>ε</mi>
<mi>m</mi>
</msub>
<mo>=</mo>
- <msubsup>
- <mi>ϵ</mi>
- <mi>D</mi>
+ <msup>
+ <msub>
+ <mi>ε</mi>
+ <mi>D</mi>
+ </msub>
<mi>k</mi>
- </msubsup>
+ </msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>ϵ</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">m</ci>
</apply>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
+ <csymbol encoding="">superscript</csymbol>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>ϵ</ci>
- <ci>D</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">D</ci>
</apply>
- <ci>k</ci>
+ <ci encoding="">k</ci>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
+ <XMTok>=</XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
+ <XMTok/>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">k</XMTok>
+ <XMTok>k</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{m}=\epsilon_{D}^{k}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m10" class="ltx_Math" alttext="\epsilon_{D}<m" display="inline">
<semantics>
<mrow>
<msub>
<mi>ϵ</mi>
<mi>D</mi>
</msub>
<mo><</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>ϵ</ci>
<ci>D</ci>
</apply>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="less-than" role="RELOP"><</XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{D}<m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<msub>
<mi>ε</mi>
<mi>D</mi>
</msub>
<mo><</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">D</ci>
</apply>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok><</XMTok>
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>D</XMTok>
</XMApp>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{D}<m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 | @@ -1,38 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m10" class="ltx_Math" alttext="\epsilon_{D}<m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<msub>
- <mi>ϵ</mi>
+ <mi>ε</mi>
<mi>D</mi>
</msub>
<mo><</mo>
<mi>m</mi>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<lt/>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>ϵ</ci>
- <ci>D</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">D</ci>
</apply>
- <ci>m</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="less-than" role="RELOP"><</XMTok>
+ <XMTok><</XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\epsilon_{D}<m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m11" class="ltx_Math" alttext="\log(h(\mathbb{Q}(\sqrt{D}))\log|\epsilon_{D}|)\sim\log\sqrt{D}" display="inline">
<semantics>
<mrow>
<mrow>
<mi>log</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>h</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>ℚ</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo></mo>
<mrow>
<mi>log</mi>
<mo></mo>
<mrow>
<mo fence="true">|</mo>
<msub>
<mi>ϵ</mi>
<mi>D</mi>
</msub>
<mo fence="true">|</mo>
</mrow>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>∼</mo>
<mrow>
<mi>log</mi>
<mo></mo>
<msqrt>
<mi>D</mi>
</msqrt>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="latexml">similar-to</csymbol>
<apply>
<log/>
<apply>
<times/>
<ci>h</ci>
<apply>
<times/>
<ci>ℚ</ci>
<apply>
<root/>
<ci>D</ci>
</apply>
</apply>
<apply>
<log/>
<apply>
<abs/>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>ϵ</ci>
<ci>D</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<log/>
<apply>
<root/>
<ci>D</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="similar-to" name="sim" role="RELOP">∼</XMTok>
<XMApp>
<XMTok argclose=")" argopen="(" meaning="logarithm" role="OPFUNCTION">log</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok possibleFunction="yes" role="UNKNOWN" font="italic">h</XMTok>
<XMApp close=")" open="(">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
<XMApp close=")" open="(">
<XMTok meaning="square-root"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
<XMApp>
<XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
<XMApp>
<XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
<XMApp>
<XMTok meaning="square-root"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\log(h(\mathbb{Q}(\sqrt{D}))\log|\epsilon_{D}|)\sim\log\sqrt{D}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mi>log</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mi>log</mi>
<mrow>
<mo>|</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>ε</mi>
<mi>D</mi>
</msub>
<mo>|</mo>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>∼</mo>
<mrow>
<mi>log</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">similar-to</csymbol>
<apply>
<log/>
<apply>
<times/>
<ci encoding="">h</ci>
<apply>
<times/>
<ci encoding="">Q</ci>
<apply>
<root/>
<ci encoding="">D</ci>
</apply>
</apply>
<apply>
<log/>
<apply>
<abs/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">D</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<log/>
<apply>
<root/>
<ci encoding="">D</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>∼</XMTok>
<XMApp>
<XMTok>log</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>h</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>Q</XMTok>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok>log</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
<XMApp>
<XMTok>log</XMTok>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\log(h(\mathbb{Q}(\sqrt{D}))\log|\epsilon_{D}|)\sim\log\sqrt{D}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 | @@ -1,134 +1,138 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m11" class="ltx_Math" alttext="\log(h(\mathbb{Q}(\sqrt{D}))\log|\epsilon_{D}|)\sim\log\sqrt{D}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mi>log</mi>
- <mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>h</mi>
- <mo></mo>
<mrow>
<mo>(</mo>
<mrow>
- <mi>ℚ</mi>
- <mo></mo>
+ <mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
- <mo></mo>
<mrow>
<mi>log</mi>
- <mo></mo>
<mrow>
- <mo fence="true">|</mo>
- <msub>
- <mi>ϵ</mi>
- <mi>D</mi>
- </msub>
- <mo fence="true">|</mo>
+ <mo>|</mo>
+ <mrow>
+ <mo>(</mo>
+ <mrow>
+ <msub>
+ <mi>ε</mi>
+ <mi>D</mi>
+ </msub>
+ <mo>|</mo>
+ </mrow>
+ <mo>)</mo>
+ </mrow>
</mrow>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>∼</mo>
<mrow>
<mi>log</mi>
- <mo></mo>
- <msqrt>
- <mi>D</mi>
- </msqrt>
+ <mrow>
+ <mo>(</mo>
+ <msqrt>
+ <mi>D</mi>
+ </msqrt>
+ <mo>)</mo>
+ </mrow>
</mrow>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="latexml">similar-to</csymbol>
+ <csymbol encoding="">similar-to</csymbol>
<apply>
<log/>
<apply>
<times/>
- <ci>h</ci>
+ <ci encoding="">h</ci>
<apply>
<times/>
- <ci>ℚ</ci>
+ <ci encoding="">Q</ci>
<apply>
<root/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
<apply>
<log/>
<apply>
<abs/>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>ϵ</ci>
- <ci>D</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<log/>
<apply>
<root/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="similar-to" name="sim" role="RELOP">∼</XMTok>
+ <XMTok>∼</XMTok>
<XMApp>
- <XMTok argclose=")" argopen="(" meaning="logarithm" role="OPFUNCTION">log</XMTok>
+ <XMTok>log</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="italic">h</XMTok>
- <XMApp close=")" open="(">
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
- <XMApp close=")" open="(">
- <XMTok meaning="square-root"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok></XMTok>
+ <XMTok>h</XMTok>
+ <XMApp>
+ <XMTok></XMTok>
+ <XMTok>Q</XMTok>
+ <XMApp>
+ <XMTok/>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
<XMApp>
- <XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
+ <XMTok>log</XMTok>
<XMApp>
- <XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
+ <XMTok/>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
<XMApp>
- <XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
+ <XMTok>log</XMTok>
<XMApp>
- <XMTok meaning="square-root"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\log(h(\mathbb{Q}(\sqrt{D}))\log|\epsilon_{D}|)\sim\log\sqrt{D}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m12" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">f</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m12" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">f</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m13" class="ltx_Math" alttext="h(\mathbb{Q}(\sqrt{D}))=1" display="inline">
<semantics>
<mrow>
<mrow>
<mi>h</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>ℚ</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<ci>h</ci>
<apply>
<times/>
<ci>ℚ</ci>
<apply>
<root/>
<ci>D</ci>
</apply>
</apply>
</apply>
<cn type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="equals" role="RELOP">=</XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok possibleFunction="yes" role="UNKNOWN" font="italic">h</XMTok>
<XMApp close=")" open="(">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
<XMApp close=")" open="(">
<XMTok meaning="square-root"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
</XMApp>
<XMTok meaning="1" role="NUMBER">1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">h(\mathbb{Q}(\sqrt{D}))=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
<ci encoding="">h</ci>
<apply>
<times/>
<ci encoding="">Q</ci>
<apply>
<root/>
<ci encoding="">D</ci>
</apply>
</apply>
</apply>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>=</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>h</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>Q</XMTok>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
<XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">h(\mathbb{Q}(\sqrt{D}))=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 | @@ -1,67 +1,65 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m13" class="ltx_Math" alttext="h(\mathbb{Q}(\sqrt{D}))=1" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mi>h</mi>
- <mo></mo>
<mrow>
<mo>(</mo>
<mrow>
- <mi>ℚ</mi>
- <mo></mo>
+ <mi>Q</mi>
<mrow>
<mo>(</mo>
<msqrt>
<mi>D</mi>
</msqrt>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>=</mo>
<mn>1</mn>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<eq/>
<apply>
<times/>
- <ci>h</ci>
+ <ci encoding="">h</ci>
<apply>
<times/>
- <ci>ℚ</ci>
+ <ci encoding="">Q</ci>
<apply>
<root/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
</apply>
- <cn type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="equals" role="RELOP">=</XMTok>
+ <XMTok>=</XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="italic">h</XMTok>
- <XMApp close=")" open="(">
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="blackboard">Q</XMTok>
- <XMApp close=")" open="(">
- <XMTok meaning="square-root"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok></XMTok>
+ <XMTok>h</XMTok>
+ <XMApp>
+ <XMTok></XMTok>
+ <XMTok>Q</XMTok>
+ <XMApp>
+ <XMTok/>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">h(\mathbb{Q}(\sqrt{D}))=1</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex5.m1" class="ltx_Math" alttext="\log|\epsilon_{D}|\leq\log|\epsilon_{m}|<\log m\leq 12\log D," display="block">
<semantics>
<mrow>
<mrow>
<mrow>
<mi>log</mi>
<mo></mo>
<mrow>
<mo fence="true">|</mo>
<msub>
<mi>ϵ</mi>
<mi>D</mi>
</msub>
<mo fence="true">|</mo>
</mrow>
</mrow>
<mo>≤</mo>
<mrow>
<mi>log</mi>
<mo></mo>
<mrow>
<mo fence="true">|</mo>
<msub>
<mi>ϵ</mi>
<mi>m</mi>
</msub>
<mo fence="true">|</mo>
</mrow>
</mrow>
<mo><</mo>
<mrow>
<mi>log</mi>
<mo></mo>
<mi>m</mi>
</mrow>
<mo>≤</mo>
<mrow>
<mn>12</mn>
<mo></mo>
<mrow>
<mi>log</mi>
<mo></mo>
<mi>D</mi>
</mrow>
</mrow>
</mrow>
<mo>,</mo>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<leq/>
<apply>
<log/>
<apply>
<abs/>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>ϵ</ci>
<ci>D</ci>
</apply>
</apply>
</apply>
<apply xml:id="S0.Ex5.m1.sh1g.cmml">
<log xml:id="S0.Ex5.m1.sh1.cmml"/>
<apply xml:id="S0.Ex5.m1.sh1f.cmml">
<abs xml:id="S0.Ex5.m1.sh1a.cmml"/>
<apply xml:id="S0.Ex5.m1.sh1e.cmml">
<csymbol cd="ambiguous" xml:id="S0.Ex5.m1.sh1b.cmml">subscript</csymbol>
<ci xml:id="S0.Ex5.m1.sh1c.cmml">ϵ</ci>
<ci xml:id="S0.Ex5.m1.sh1d.cmml">m</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<share href="#S0.Ex5.m1.sh1.cmml"/>
<apply xml:id="S0.Ex5.m1.sh2b.cmml">
<log xml:id="S0.Ex5.m1.sh2.cmml"/>
<ci xml:id="S0.Ex5.m1.sh2a.cmml">m</ci>
</apply>
</apply>
<apply>
<leq/>
<share href="#S0.Ex5.m1.sh2.cmml"/>
<apply xml:id="S0.Ex5.m1.sh3e.cmml">
<times xml:id="S0.Ex5.m1.sh3.cmml"/>
<cn type="integer" xml:id="S0.Ex5.m1.sh3a.cmml">12</cn>
<apply xml:id="S0.Ex5.m1.sh3d.cmml">
<log xml:id="S0.Ex5.m1.sh3b.cmml"/>
<ci xml:id="S0.Ex5.m1.sh3c.cmml">D</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp punctuation=",">
<XMTok meaning="multirelation"/>
<XMApp>
<XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
<XMApp>
<XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
</XMApp>
<XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
<XMApp xml:id="S0.Ex5.m1.sh1.xm" fragid="S0.Ex5.m1.sh1.xm">
<XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
<XMApp>
<XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMApp>
</XMApp>
<XMTok meaning="less-than" role="RELOP"><</XMTok>
<XMApp xml:id="S0.Ex5.m1.sh2.xm" fragid="S0.Ex5.m1.sh2.xm">
<XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
<XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
<XMApp xml:id="S0.Ex5.m1.sh3.xm" fragid="S0.Ex5.m1.sh3.xm">
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="12" role="NUMBER">12</XMTok>
<XMApp>
<XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\log|\epsilon_{D}|\leq\log|\epsilon_{m}|<\log m\leq 12\log D,</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mrow>
<mi>log</mi>
<mrow>
<mo>|</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>ε</mi>
<mi>D</mi>
</msub>
<mo>|</mo>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mo>≤</mo>
<mrow>
<mi>log</mi>
<mrow>
<mo>|</mo>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>ε</mi>
<mi>m</mi>
</msub>
<mo>|</mo>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mo><</mo>
<mrow>
<mi>log</mi>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>≤</mo>
<mrow>
<mn>12</mn>
<mrow>
<mi>log</mi>
<mrow>
<mo>(</mo>
<mi>D</mi>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
<mo>,</mo>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<leq/>
<apply>
<log/>
<apply>
<abs/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">D</ci>
</apply>
</apply>
</apply>
<apply>
<log encoding=""/>
<apply>
<abs encoding=""/>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">ε</ci>
<ci encoding="">m</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<share/>
<apply>
<log encoding=""/>
<ci encoding="">m</ci>
</apply>
</apply>
<apply>
<leq/>
<share/>
<apply>
<times encoding=""/>
<cn encoding="" base="10" type="integer">12</cn>
<apply>
<log encoding=""/>
<ci encoding="">D</ci>
</apply>
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<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMApp>
<XMTok>log</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
<XMTok>≤</XMTok>
<XMApp>
<XMTok>log</XMTok>
<XMApp>
<XMTok/>
<XMApp>
<XMTok/>
<XMTok>ε</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMApp>
<XMTok><</XMTok>
<XMApp>
<XMTok>log</XMTok>
<XMTok>m</XMTok>
</XMApp>
<XMTok>≤</XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>12</XMTok>
<XMApp>
<XMTok>log</XMTok>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\log|\epsilon_{D}|\leq\log|\epsilon_{m}|<\log m\leq 12\log D,</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 | @@ -1,146 +1,161 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex5.m1" class="ltx_Math" alttext="\log|\epsilon_{D}|\leq\log|\epsilon_{m}|<\log m\leq 12\log D," display="block">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mrow>
<mi>log</mi>
- <mo></mo>
<mrow>
- <mo fence="true">|</mo>
- <msub>
- <mi>ϵ</mi>
- <mi>D</mi>
- </msub>
- <mo fence="true">|</mo>
+ <mo>|</mo>
+ <mrow>
+ <mo>(</mo>
+ <mrow>
+ <msub>
+ <mi>ε</mi>
+ <mi>D</mi>
+ </msub>
+ <mo>|</mo>
+ </mrow>
+ <mo>)</mo>
+ </mrow>
</mrow>
</mrow>
<mo>≤</mo>
<mrow>
<mi>log</mi>
- <mo></mo>
<mrow>
- <mo fence="true">|</mo>
- <msub>
- <mi>ϵ</mi>
- <mi>m</mi>
- </msub>
- <mo fence="true">|</mo>
+ <mo>|</mo>
+ <mrow>
+ <mo>(</mo>
+ <mrow>
+ <msub>
+ <mi>ε</mi>
+ <mi>m</mi>
+ </msub>
+ <mo>|</mo>
+ </mrow>
+ <mo>)</mo>
+ </mrow>
</mrow>
</mrow>
<mo><</mo>
<mrow>
<mi>log</mi>
- <mo></mo>
- <mi>m</mi>
+ <mrow>
+ <mo>(</mo>
+ <mi>m</mi>
+ <mo>)</mo>
+ </mrow>
</mrow>
<mo>≤</mo>
<mrow>
<mn>12</mn>
- <mo></mo>
<mrow>
<mi>log</mi>
- <mo></mo>
- <mi>D</mi>
+ <mrow>
+ <mo>(</mo>
+ <mi>D</mi>
+ <mo>)</mo>
+ </mrow>
</mrow>
</mrow>
</mrow>
<mo>,</mo>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<and/>
<apply>
<leq/>
<apply>
<log/>
<apply>
<abs/>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>ϵ</ci>
- <ci>D</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
</apply>
- <apply xml:id="S0.Ex5.m1.sh1g.cmml">
- <log xml:id="S0.Ex5.m1.sh1.cmml"/>
- <apply xml:id="S0.Ex5.m1.sh1f.cmml">
- <abs xml:id="S0.Ex5.m1.sh1a.cmml"/>
- <apply xml:id="S0.Ex5.m1.sh1e.cmml">
- <csymbol cd="ambiguous" xml:id="S0.Ex5.m1.sh1b.cmml">subscript</csymbol>
- <ci xml:id="S0.Ex5.m1.sh1c.cmml">ϵ</ci>
- <ci xml:id="S0.Ex5.m1.sh1d.cmml">m</ci>
+ <apply>
+ <log encoding=""/>
+ <apply>
+ <abs encoding=""/>
+ <apply>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">ε</ci>
+ <ci encoding="">m</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
- <share href="#S0.Ex5.m1.sh1.cmml"/>
- <apply xml:id="S0.Ex5.m1.sh2b.cmml">
- <log xml:id="S0.Ex5.m1.sh2.cmml"/>
- <ci xml:id="S0.Ex5.m1.sh2a.cmml">m</ci>
+ <share/>
+ <apply>
+ <log encoding=""/>
+ <ci encoding="">m</ci>
</apply>
</apply>
<apply>
<leq/>
- <share href="#S0.Ex5.m1.sh2.cmml"/>
- <apply xml:id="S0.Ex5.m1.sh3e.cmml">
- <times xml:id="S0.Ex5.m1.sh3.cmml"/>
- <cn type="integer" xml:id="S0.Ex5.m1.sh3a.cmml">12</cn>
- <apply xml:id="S0.Ex5.m1.sh3d.cmml">
- <log xml:id="S0.Ex5.m1.sh3b.cmml"/>
- <ci xml:id="S0.Ex5.m1.sh3c.cmml">D</ci>
+ <share/>
+ <apply>
+ <times encoding=""/>
+ <cn encoding="" base="10" type="integer">12</cn>
+ <apply>
+ <log encoding=""/>
+ <ci encoding="">D</ci>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMApp punctuation=",">
- <XMTok meaning="multirelation"/>
+ <XMApp>
+ <XMTok/>
<XMApp>
- <XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
+ <XMTok>log</XMTok>
<XMApp>
- <XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
+ <XMTok/>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
- <XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
- <XMApp xml:id="S0.Ex5.m1.sh1.xm" fragid="S0.Ex5.m1.sh1.xm">
- <XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
+ <XMTok>≤</XMTok>
+ <XMApp>
+ <XMTok>log</XMTok>
<XMApp>
- <XMTok argclose="|" argopen="|" meaning="absolute-value" role="FENCED"/>
+ <XMTok/>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok name="epsilon" role="UNKNOWN" font="italic">ϵ</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>ε</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMApp>
</XMApp>
- <XMTok meaning="less-than" role="RELOP"><</XMTok>
- <XMApp xml:id="S0.Ex5.m1.sh2.xm" fragid="S0.Ex5.m1.sh2.xm">
- <XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok><</XMTok>
+ <XMApp>
+ <XMTok>log</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
- <XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
- <XMApp xml:id="S0.Ex5.m1.sh3.xm" fragid="S0.Ex5.m1.sh3.xm">
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="12" role="NUMBER">12</XMTok>
+ <XMTok>≤</XMTok>
+ <XMApp>
+ <XMTok></XMTok>
+ <XMTok>12</XMTok>
<XMApp>
- <XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok>log</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">\log|\epsilon_{D}|\leq\log|\epsilon_{m}|<\log m\leq 12\log D,</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex6.m1" class="ltx_Math" alttext="12\log D>D^{1/2+o(1)}" display="block">
<semantics>
<mrow>
<mrow>
<mn>12</mn>
<mo></mo>
<mrow>
<mi>log</mi>
<mo></mo>
<mi>D</mi>
</mrow>
</mrow>
<mo>></mo>
<msup>
<mi>D</mi>
<mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mo>+</mo>
<mrow>
<mi>o</mi>
<mo></mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<apply>
<times/>
<cn type="integer">12</cn>
<apply>
<log/>
<ci>D</ci>
</apply>
</apply>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>D</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn type="integer">1</cn>
<cn type="integer">2</cn>
</apply>
<apply>
<times/>
<ci>o</ci>
<cn type="integer">1</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="greater-than" role="RELOP">></XMTok>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok meaning="12" role="NUMBER">12</XMTok>
<XMApp>
<XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
<XMApp>
<XMTok meaning="plus" role="ADDOP">+</XMTok>
<XMApp>
<XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
<XMTok meaning="1" role="NUMBER">1</XMTok>
<XMTok meaning="2" role="NUMBER">2</XMTok>
</XMApp>
<XMApp>
<XMTok meaning="times" role="MULOP"></XMTok>
<XMTok possibleFunction="yes" role="UNKNOWN" font="italic">o</XMTok>
<XMTok close=")" meaning="1" open="(" role="NUMBER">1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">12\log D>D^{1/2+o(1)}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mrow>
<mn>12</mn>
<mrow>
<mi>log</mi>
<mrow>
<mo>(</mo>
<mi>D</mi>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mo>></mo>
<msup>
<mi>D</mi>
<mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mo>+</mo>
<mrow>
<mi>o</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<apply>
<times/>
<cn encoding="" base="10" type="integer">12</cn>
<apply>
<log/>
<ci encoding="">D</ci>
</apply>
</apply>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">D</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn encoding="" base="10" type="integer">1</cn>
<cn encoding="" base="10" type="integer">2</cn>
</apply>
<apply>
<times/>
<ci encoding="">o</ci>
<cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>></XMTok>
<XMApp>
<XMTok></XMTok>
<XMTok>12</XMTok>
<XMApp>
<XMTok>log</XMTok>
<XMTok>D</XMTok>
</XMApp>
</XMApp>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
<XMApp>
<XMTok>+</XMTok>
<XMApp>
<XMTok>/</XMTok>
<XMTok>1</XMTok>
<XMTok>2</XMTok>
</XMApp>
<XMApp>
<XMTok></XMTok>
<XMTok>o</XMTok>
<XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">12\log D>D^{1/2+o(1)}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 | @@ -1,100 +1,101 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex6.m1" class="ltx_Math" alttext="12\log D>D^{1/2+o(1)}" display="block">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mrow>
<mn>12</mn>
- <mo></mo>
<mrow>
<mi>log</mi>
- <mo></mo>
- <mi>D</mi>
+ <mrow>
+ <mo>(</mo>
+ <mi>D</mi>
+ <mo>)</mo>
+ </mrow>
</mrow>
</mrow>
<mo>></mo>
<msup>
<mi>D</mi>
<mrow>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mo>+</mo>
<mrow>
<mi>o</mi>
- <mo></mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<apply>
<times/>
- <cn type="integer">12</cn>
+ <cn encoding="" base="10" type="integer">12</cn>
<apply>
<log/>
- <ci>D</ci>
+ <ci encoding="">D</ci>
</apply>
</apply>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>D</ci>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">D</ci>
<apply>
<plus/>
<apply>
<divide/>
- <cn type="integer">1</cn>
- <cn type="integer">2</cn>
+ <cn encoding="" base="10" type="integer">1</cn>
+ <cn encoding="" base="10" type="integer">2</cn>
</apply>
<apply>
<times/>
- <ci>o</ci>
- <cn type="integer">1</cn>
+ <ci encoding="">o</ci>
+ <cn encoding="" base="10" type="integer">1</cn>
</apply>
</apply>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="greater-than" role="RELOP">></XMTok>
+ <XMTok>></XMTok>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok meaning="12" role="NUMBER">12</XMTok>
+ <XMTok></XMTok>
+ <XMTok>12</XMTok>
<XMApp>
- <XMTok meaning="logarithm" role="OPFUNCTION">log</XMTok>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok>log</XMTok>
+ <XMTok>D</XMTok>
</XMApp>
</XMApp>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok/>
+ <XMTok>D</XMTok>
<XMApp>
- <XMTok meaning="plus" role="ADDOP">+</XMTok>
+ <XMTok>+</XMTok>
<XMApp>
- <XMTok mathstyle="inline" meaning="divide" role="MULOP">/</XMTok>
- <XMTok meaning="1" role="NUMBER">1</XMTok>
- <XMTok meaning="2" role="NUMBER">2</XMTok>
+ <XMTok>/</XMTok>
+ <XMTok>1</XMTok>
+ <XMTok>2</XMTok>
</XMApp>
<XMApp>
- <XMTok meaning="times" role="MULOP"></XMTok>
- <XMTok possibleFunction="yes" role="UNKNOWN" font="italic">o</XMTok>
- <XMTok close=")" meaning="1" open="(" role="NUMBER">1</XMTok>
+ <XMTok></XMTok>
+ <XMTok>o</XMTok>
+ <XMTok>1</XMTok>
</XMApp>
</XMApp>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">12\log D>D^{1/2+o(1)}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m14" class="ltx_Math" alttext="D" display="inline">
<semantics>
<mi>D</mi>
<annotation-xml encoding="MathML-Content">
<ci>D</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">D</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>D</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">D</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>D</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m14" class="ltx_Math" alttext="D" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>D</mi>
<annotation-xml encoding="MathML-Content">
- <ci>D</ci>
+ <ci encoding="">D</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
+ <XMTok>D</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">D</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m15" class="ltx_Math" alttext="m\leq D^{12}" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>≤</mo>
<msup>
<mi>D</mi>
<mn>12</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<leq/>
<ci>m</ci>
<apply>
<csymbol cd="ambiguous">superscript</csymbol>
<ci>D</ci>
<cn type="integer">12</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">D</XMTok>
<XMTok meaning="12" role="NUMBER">12</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m\leq D^{12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>≤</mo>
<msup>
<mi>D</mi>
<mn>12</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<leq/>
<ci encoding="">m</ci>
<apply>
<csymbol encoding="">superscript</csymbol>
<ci encoding="">D</ci>
<cn encoding="" base="10" type="integer">12</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>≤</XMTok>
<XMTok>m</XMTok>
<XMApp>
<XMTok/>
<XMTok>D</XMTok>
<XMTok>12</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m\leq D^{12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,38 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m15" class="ltx_Math" alttext="m\leq D^{12}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>≤</mo>
<msup>
<mi>D</mi>
<mn>12</mn>
</msup>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<leq/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
<apply>
- <csymbol cd="ambiguous">superscript</csymbol>
- <ci>D</ci>
- <cn type="integer">12</cn>
+ <csymbol encoding="">superscript</csymbol>
+ <ci encoding="">D</ci>
+ <cn encoding="" base="10" type="integer">12</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>≤</XMTok>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">D</XMTok>
- <XMTok meaning="12" role="NUMBER">12</XMTok>
+ <XMTok/>
+ <XMTok>D</XMTok>
+ <XMTok>12</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m\leq D^{12}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m16" class="ltx_Math" alttext="m" display="inline">
<semantics>
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci>m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p8.m16" class="ltx_Math" alttext="m" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>m</mi>
<annotation-xml encoding="MathML-Content">
- <ci>m</ci>
+ <ci encoding="">m</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>m</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p9.m1" class="ltx_Math" alttext="m_{0}" display="inline">
<semantics>
<msub>
<mi>m</mi>
<mn>0</mn>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>m</ci>
<cn type="integer">0</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMTok meaning="0" role="NUMBER">0</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>m</mi>
<mn>0</mn>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">m</ci>
<cn encoding="" base="10" type="integer">0</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>m</XMTok>
<XMTok>0</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p9.m1" class="ltx_Math" alttext="m_{0}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>m</mi>
<mn>0</mn>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>m</ci>
- <cn type="integer">0</cn>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">m</ci>
+ <cn encoding="" base="10" type="integer">0</cn>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
- <XMTok meaning="0" role="NUMBER">0</XMTok>
+ <XMTok/>
+ <XMTok>m</XMTok>
+ <XMTok>0</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p9.m2" class="ltx_Math" alttext="m>m_{0}" display="inline">
<semantics>
<mrow>
<mi>m</mi>
<mo>></mo>
<msub>
<mi>m</mi>
<mn>0</mn>
</msub>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<ci>m</ci>
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>m</ci>
<cn type="integer">0</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok meaning="greater-than" role="RELOP">></XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
<XMTok meaning="0" role="NUMBER">0</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m>m_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mrow>
<mi>m</mi>
<mo>></mo>
<msub>
<mi>m</mi>
<mn>0</mn>
</msub>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
<ci encoding="">m</ci>
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">m</ci>
<cn encoding="" base="10" type="integer">0</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok>></XMTok>
<XMTok>m</XMTok>
<XMApp>
<XMTok/>
<XMTok>m</XMTok>
<XMTok>0</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m>m_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | @@ -1,38 +1,38 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p9.m2" class="ltx_Math" alttext="m>m_{0}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mrow>
<mi>m</mi>
<mo>></mo>
<msub>
<mi>m</mi>
<mn>0</mn>
</msub>
</mrow>
<annotation-xml encoding="MathML-Content">
<apply>
<gt/>
- <ci>m</ci>
+ <ci encoding="">m</ci>
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>m</ci>
- <cn type="integer">0</cn>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">m</ci>
+ <cn encoding="" base="10" type="integer">0</cn>
</apply>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok meaning="greater-than" role="RELOP">></XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok>></XMTok>
+ <XMTok>m</XMTok>
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
- <XMTok meaning="0" role="NUMBER">0</XMTok>
+ <XMTok/>
+ <XMTok>m</XMTok>
+ <XMTok>0</XMTok>
</XMApp>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">m>m_{0}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p9.m3" class="ltx_Math" alttext="f_{m}" display="inline">
<semantics>
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol cd="ambiguous">subscript</csymbol>
<ci>f</ci>
<ci>m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
<XMTok role="UNKNOWN" font="italic">f</XMTok>
<XMTok role="UNKNOWN" font="italic">m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
<csymbol encoding="">subscript</csymbol>
<ci encoding="">f</ci>
<ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
<XMTok/>
<XMTok>f</XMTok>
<XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | @@ -1,26 +1,26 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="p9.m3" class="ltx_Math" alttext="f_{m}" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<msub>
<mi>f</mi>
<mi>m</mi>
</msub>
<annotation-xml encoding="MathML-Content">
<apply>
- <csymbol cd="ambiguous">subscript</csymbol>
- <ci>f</ci>
- <ci>m</ci>
+ <csymbol encoding="">subscript</csymbol>
+ <ci encoding="">f</ci>
+ <ci encoding="">m</ci>
</apply>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMApp>
- <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
- <XMTok role="UNKNOWN" font="italic">f</XMTok>
- <XMTok role="UNKNOWN" font="italic">m</XMTok>
+ <XMTok/>
+ <XMTok>f</XMTok>
+ <XMTok>m</XMTok>
</XMApp>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">f_{m}</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="bib.bib3.m1" class="ltx_Math" alttext="L" display="inline">
<semantics>
<mi>L</mi>
<annotation-xml encoding="MathML-Content">
<ci>L</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok role="UNKNOWN">L</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">L</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | <?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics encoding="">
<mi>L</mi>
<annotation-xml encoding="MathML-Content">
<ci encoding="">L</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
<XMTok>L</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">L</annotation>
</semantics>
</math>
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | @@ -1,15 +1,15 @@
<?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" id="bib.bib3.m1" class="ltx_Math" alttext="L" display="inline">
- <semantics>
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+ <semantics encoding="">
<mi>L</mi>
<annotation-xml encoding="MathML-Content">
- <ci>L</ci>
+ <ci encoding="">L</ci>
</annotation-xml>
<annotation-xml encoding="application/x-latexml">
<XMath xmlns="http://dlmf.nist.gov/LaTeXML">
- <XMTok role="UNKNOWN">L</XMTok>
+ <XMTok>L</XMTok>
</XMath>
</annotation-xml>
<annotation encoding="application/x-tex">L</annotation>
</semantics>
</math>
|