MathML formulae – Schlage-Puchta, Jan-Christoph: Finiteness of a class of Rabinowitsch polynomials. (English). Archivum Mathematicum, vol. 40 (2004), issue 3, pp. 259-261

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Formula 1

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Original

m

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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>

Canonicalized

m

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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>

Diff

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1


Formula 2 
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Original 


  t


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>t</mi>
</math>



Canonicalized 


  t


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>t</mi>
</math>



Diff 
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1


Formula 3 
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Original 


  
    
      |
    
    
      n
      2
    
    
      +
      n
      -
      m
      |
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mrow>
      <mo>|</mo>
    </mrow>
    <msup>
      <mi>n</mi>
      <mn>2</mn>
    </msup>
    <mrow>
      <mo>+</mo>
      <mi>n</mi>
      <mo>-</mo>
      <mi>m</mi>
      <mo>|</mo>
    </mrow>
  </mrow>
</math>



Canonicalized 


  
    |
    
      n
      2
    
    
      +
      n
      -
      m
      |
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mo>|</mo>
    <msup>
      <mi>n</mi>
      <mn>2</mn>
    </msup>
    <mrow>
      <mo>+</mo>
      <mi>n</mi>
      <mo>-</mo>
      <mi>m</mi>
      <mo>|</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,19 +1,17 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
-    <mrow>
-      <mo>|</mo>
-    </mrow>
+    <mo>|</mo>
     <msup>
       <mi>n</mi>
       <mn>2</mn>
     </msup>
     <mrow>
       <mo>+</mo>
       <mi>n</mi>
       <mo>-</mo>
       <mi>m</mi>
       <mo>|</mo>
     </mrow>
   </mrow>
 </math>



Formula 4 
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Original 


  
    n
    ∈
    [
    t
    +
    1
    ,
    t
    +
    
      m
    
    ]
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>n</mi>
    <mo>∈</mo>
    <mo>[</mo>
    <mi>t</mi>
    <mo>+</mo>
    <mn>1</mn>
    <mo>,</mo>
    <mi>t</mi>
    <mo>+</mo>
    <msqrt>
      <mi>m</mi>
    </msqrt>
    <mo>]</mo>
  </mrow>
</math>



Canonicalized 


  
    n
    ∈
    
      [
      
        t
        +
        1
        ,
        t
        +
        
          m
        
      
      ]
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>n</mi>
    <mo>∈</mo>
    <mrow>
      <mo>[</mo>
      <mrow>
        <mi>t</mi>
        <mo>+</mo>
        <mn>1</mn>
        <mo>,</mo>
        <mi>t</mi>
        <mo>+</mo>
        <msqrt>
          <mi>m</mi>
        </msqrt>
      </mrow>
      <mo>]</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,18 +1,22 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <mi>n</mi>
     <mo>∈</mo>
-    <mo>[</mo>
-    <mi>t</mi>
-    <mo>+</mo>
-    <mn>1</mn>
-    <mo>,</mo>
-    <mi>t</mi>
-    <mo>+</mo>
-    <msqrt>
-      <mi>m</mi>
-    </msqrt>
-    <mo>]</mo>
+    <mrow>
+      <mo>[</mo>
+      <mrow>
+        <mi>t</mi>
+        <mo>+</mo>
+        <mn>1</mn>
+        <mo>,</mo>
+        <mi>t</mi>
+        <mo>+</mo>
+        <msqrt>
+          <mi>m</mi>
+        </msqrt>
+      </mrow>
+      <mo>]</mo>
+    </mrow>
   </mrow>
 </math>



Formula 5 
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Original 


  m


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Canonicalized 


  m


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Diff 
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1


Formula 6 
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Original 


  
    4
    m
    -
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <mi>m</mi>
    <mo>-</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    4
    m
    -
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <mi>m</mi>
    <mo>-</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
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Formula 7 
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Original 


  
    ℚ
    (
    
      
        1
        -
        4
        m
      
    
    )
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>ℚ</mi>
    <mo>(</mo>
    <msqrt>
      <mrow>
        <mn>1</mn>
        <mo>-</mo>
        <mn>4</mn>
        <mi>m</mi>
      </mrow>
    </msqrt>
    <mo>)</mo>
  </mrow>
</math>



Canonicalized 


  
    Q
    
      (
      
        1
        -
        4
        m
      
      )
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>Q</mi>
    <mrow>
      <mo>(</mo>
      <msqrt>
        <mn>1</mn>
        <mo>-</mo>
        <mn>4</mn>
        <mi>m</mi>
      </msqrt>
      <mo>)</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,16 +1,16 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
-    <mi>ℚ</mi>
-    <mo>(</mo>
-    <msqrt>
-      <mrow>
+    <mi>Q</mi>
+    <mrow>
+      <mo>(</mo>
+      <msqrt>
         <mn>1</mn>
         <mo>-</mo>
         <mn>4</mn>
         <mi>m</mi>
-      </mrow>
-    </msqrt>
-    <mo>)</mo>
+      </msqrt>
+      <mo>)</mo>
+    </mrow>
   </mrow>
 </math>



Formula 8 
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Original 


  
    
      n
      2
    
    +
    n
    +
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msup>
      <mi>n</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>n</mi>
    <mo>+</mo>
    <mi>m</mi>
  </mrow>
</math>



Canonicalized 


  
    
      n
      2
    
    +
    n
    +
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msup>
      <mi>n</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>n</mi>
    <mo>+</mo>
    <mi>m</mi>
  </mrow>
</math>



Diff 
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Formula 9 
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Original 


  
    0
    ≤
    n
    ≤
    m
    -
    3
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>0</mn>
    <mo>≤</mo>
    <mi>n</mi>
    <mo>≤</mo>
    <mi>m</mi>
    <mo>-</mo>
    <mn>3</mn>
  </mrow>
</math>



Canonicalized 


  
    0
    ≤
    n
    ≤
    m
    -
    3
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>0</mn>
    <mo>≤</mo>
    <mi>n</mi>
    <mo>≤</mo>
    <mi>m</mi>
    <mo>-</mo>
    <mn>3</mn>
  </mrow>
</math>



Diff 
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Formula 10 
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Original 


  
    
      f
      m
    
    
      (
      x
      )
    
    =
    
      x
      2
    
    +
    x
    -
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msub>
      <mi>f</mi>
      <mi>m</mi>
    </msub>
    <mrow>
      <mo>(</mo>
      <mi>x</mi>
      <mo>)</mo>
    </mrow>
    <mo>=</mo>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>x</mi>
    <mo>-</mo>
    <mi>m</mi>
  </mrow>
</math>



Canonicalized 


  
    
      f
      m
    
    
      (
      x
      )
    
    =
    
      x
      2
    
    +
    x
    -
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msub>
      <mi>f</mi>
      <mi>m</mi>
    </msub>
    <mrow>
      <mo>(</mo>
      <mi>x</mi>
      <mo>)</mo>
    </mrow>
    <mo>=</mo>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>x</mi>
    <mo>-</mo>
    <mi>m</mi>
  </mrow>
</math>



Diff 
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Formula 11 
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Original 


  t


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>t</mi>
</math>



Canonicalized 


  t


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>t</mi>
</math>



Diff 
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Formula 12 
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Original 


  
    
      |
    
    
      f
      m
    
    
      
        (
        n
        )
      
      |
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mrow>
      <mo>|</mo>
    </mrow>
    <msub>
      <mi>f</mi>
      <mi>m</mi>
    </msub>
    <mrow>
      <mrow>
        <mo>(</mo>
        <mi>n</mi>
        <mo>)</mo>
      </mrow>
      <mo>|</mo>
    </mrow>
  </mrow>
</math>



Canonicalized 


  
    |
    
      f
      m
    
    
      
        (
        n
        )
      
      |
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mo>|</mo>
    <msub>
      <mi>f</mi>
      <mi>m</mi>
    </msub>
    <mrow>
      <mrow>
        <mo>(</mo>
        <mi>n</mi>
        <mo>)</mo>
      </mrow>
      <mo>|</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,20 +1,18 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
-    <mrow>
-      <mo>|</mo>
-    </mrow>
+    <mo>|</mo>
     <msub>
       <mi>f</mi>
       <mi>m</mi>
     </msub>
     <mrow>
       <mrow>
         <mo>(</mo>
         <mi>n</mi>
         <mo>)</mo>
       </mrow>
       <mo>|</mo>
     </mrow>
   </mrow>
 </math>



Formula 13 
( show / hide formula code)
Original 


  
    n
    ∈
    [
    t
    +
    1
    ,
    t
    +
    
      m
    
    ]
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>n</mi>
    <mo>∈</mo>
    <mo>[</mo>
    <mi>t</mi>
    <mo>+</mo>
    <mn>1</mn>
    <mo>,</mo>
    <mi>t</mi>
    <mo>+</mo>
    <msqrt>
      <mi>m</mi>
    </msqrt>
    <mo>]</mo>
  </mrow>
</math>



Canonicalized 


  
    n
    ∈
    
      [
      
        t
        +
        1
        ,
        t
        +
        
          m
        
      
      ]
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>n</mi>
    <mo>∈</mo>
    <mrow>
      <mo>[</mo>
      <mrow>
        <mi>t</mi>
        <mo>+</mo>
        <mn>1</mn>
        <mo>,</mo>
        <mi>t</mi>
        <mo>+</mo>
        <msqrt>
          <mi>m</mi>
        </msqrt>
      </mrow>
      <mo>]</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,18 +1,22 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <mi>n</mi>
     <mo>∈</mo>
-    <mo>[</mo>
-    <mi>t</mi>
-    <mo>+</mo>
-    <mn>1</mn>
-    <mo>,</mo>
-    <mi>t</mi>
-    <mo>+</mo>
-    <msqrt>
-      <mi>m</mi>
-    </msqrt>
-    <mo>]</mo>
+    <mrow>
+      <mo>[</mo>
+      <mrow>
+        <mi>t</mi>
+        <mo>+</mo>
+        <mn>1</mn>
+        <mo>,</mo>
+        <mi>t</mi>
+        <mo>+</mo>
+        <msqrt>
+          <mi>m</mi>
+        </msqrt>
+      </mrow>
+      <mo>]</mo>
+    </mrow>
   </mrow>
 </math>



Formula 14 
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Original 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
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Formula 15 
( show / hide formula code)
Original 


  
    m
    =
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    m
    =
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
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Formula 16 
( show / hide formula code)
Original 


  
    m
    =
    2
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <mn>2</mn>
  </mrow>
</math>



Canonicalized 


  
    m
    =
    2
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <mn>2</mn>
  </mrow>
</math>



Diff 
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Formula 17 
( show / hide formula code)
Original 


  
    m
    =
    
      p
      2
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <msup>
      <mi>p</mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math>



Canonicalized 


  
    m
    =
    
      p
      2
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <msup>
      <mi>p</mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math>



Diff 
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1


Formula 18 
( show / hide formula code)
Original 


  p


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Canonicalized 


  p


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Diff 
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Formula 19 
( show / hide formula code)
Original 


  
    m
    =
    
      t
      2
    
    +
    t
    ±
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>t</mi>
    <mo>±</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    m
    =
    
      t
      2
    
    +
    t
    ±
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>t</mi>
    <mo>±</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
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Formula 20 
( show / hide formula code)
Original 


  
    m
    =
    
      t
      2
    
    +
    t
    ±
    
      
        2
        t
        +
        1
      
      3
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>t</mi>
    <mo>±</mo>
    <mfrac>
      <mrow>
        <mn>2</mn>
        <mi>t</mi>
        <mo>+</mo>
        <mn>1</mn>
      </mrow>
      <mn>3</mn>
    </mfrac>
  </mrow>
</math>



Canonicalized 


  
    m
    =
    
      t
      2
    
    +
    t
    ±
    
      
        2
        t
        +
        1
      
      3
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>t</mi>
    <mo>±</mo>
    <mfrac>
      <mrow>
        <mn>2</mn>
        <mi>t</mi>
        <mo>+</mo>
        <mn>1</mn>
      </mrow>
      <mn>3</mn>
    </mfrac>
  </mrow>
</math>



Diff 
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Formula 21 
( show / hide formula code)
Original 


  
    
      2
      t
      +
      1
    
    3
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mfrac>
    <mrow>
      <mn>2</mn>
      <mi>t</mi>
      <mo>+</mo>
      <mn>1</mn>
    </mrow>
    <mn>3</mn>
  </mfrac>
</math>



Canonicalized 


  
    
      2
      t
      +
      1
    
    3
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mfrac>
    <mrow>
      <mn>2</mn>
      <mi>t</mi>
      <mo>+</mo>
      <mn>1</mn>
    </mrow>
    <mn>3</mn>
  </mfrac>
</math>



Diff 
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Formula 22 
( show / hide formula code)
Original 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
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Formula 23 
( show / hide formula code)
Original 


  
    ℚ
    (
    
      
        4
        m
        +
        1
      
    
    )
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>ℚ</mi>
    <mo>(</mo>
    <msqrt>
      <mrow>
        <mn>4</mn>
        <mi>m</mi>
        <mo>+</mo>
        <mn>1</mn>
      </mrow>
    </msqrt>
    <mo>)</mo>
  </mrow>
</math>



Canonicalized 


  
    Q
    
      (
      
        4
        m
        +
        1
      
      )
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>Q</mi>
    <mrow>
      <mo>(</mo>
      <msqrt>
        <mn>4</mn>
        <mi>m</mi>
        <mo>+</mo>
        <mn>1</mn>
      </msqrt>
      <mo>)</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,16 +1,16 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
-    <mi>ℚ</mi>
-    <mo>(</mo>
-    <msqrt>
-      <mrow>
+    <mi>Q</mi>
+    <mrow>
+      <mo>(</mo>
+      <msqrt>
         <mn>4</mn>
         <mi>m</mi>
         <mo>+</mo>
         <mn>1</mn>
-      </mrow>
-    </msqrt>
-    <mo>)</mo>
+      </msqrt>
+      <mo>)</mo>
+    </mrow>
   </mrow>
 </math>



Formula 24 
( show / hide formula code)
Original 


  1


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mn>1</mn>
</math>



Canonicalized 


  1


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mn>1</mn>
</math>



Diff 
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1


Formula 25 
( show / hide formula code)
Original 


  m


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Canonicalized 


  m


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Diff 
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Formula 26 
( show / hide formula code)
Original 


  
    4
    m
    +
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <mi>m</mi>
    <mo>+</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    4
    m
    +
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <mi>m</mi>
    <mo>+</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
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Formula 27 
( show / hide formula code)
Original 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
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1


Formula 28 
( show / hide formula code)
Original 


  m


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Canonicalized 


  m


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Diff 
(show/hide code)
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Formula 29 
( show / hide formula code)
Original 


  
    4
    m
    +
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <mi>m</mi>
    <mo>+</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    4
    m
    +
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <mi>m</mi>
    <mo>+</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
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Formula 30 
( show / hide formula code)
Original 


  
    m
    ≥
    0
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>≥</mo>
    <mn>0</mn>
  </mrow>
</math>



Canonicalized 


  
    m
    ≥
    0
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>≥</mo>
    <mn>0</mn>
  </mrow>
</math>



Diff 
(show/hide code)
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Formula 31 
( show / hide formula code)
Original 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
(show/hide code)
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Formula 32 
( show / hide formula code)
Original 


  
    4
    m
    +
    1
    =
    
      u
      2
    
    D
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <mi>m</mi>
    <mo>+</mo>
    <mn>1</mn>
    <mo>=</mo>
    <msup>
      <mi>u</mi>
      <mn>2</mn>
    </msup>
    <mi>D</mi>
  </mrow>
</math>



Canonicalized 


  
    4
    m
    +
    1
    =
    
      u
      2
    
    D
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <mi>m</mi>
    <mo>+</mo>
    <mn>1</mn>
    <mo>=</mo>
    <msup>
      <mi>u</mi>
      <mn>2</mn>
    </msup>
    <mi>D</mi>
  </mrow>
</math>



Diff 
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1


Formula 33 
( show / hide formula code)
Original 


  D


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>D</mi>
</math>



Canonicalized 


  D


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>D</mi>
</math>



Diff 
(show/hide code)
1


Formula 34 
( show / hide formula code)
Original 


  u


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>u</mi>
</math>



Canonicalized 


  u


(show/hide code)
1
2
3
4
<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>u</mi>
</math>



Diff 
(show/hide code)
1


Formula 35 
( show / hide formula code)
Original 


  
    D
    =
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    D
    =
    1
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
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1


Formula 36 
( show / hide formula code)
Original 


  
    1
    <
    D
    <
    
      m
      
        1
        /
        12
      
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>1</mn>
    <mo>&lt;</mo>
    <mi>D</mi>
    <mo>&lt;</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>12</mn>
      </mrow>
    </msup>
  </mrow>
</math>



Canonicalized 


  
    1
    <
    D
    <
    
      m
      
        1
        /
        12
      
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>1</mn>
    <mo>&lt;</mo>
    <mi>D</mi>
    <mo>&lt;</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>12</mn>
      </mrow>
    </msup>
  </mrow>
</math>



Diff 
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Formula 37 
( show / hide formula code)
Original 


  
    D
    ≥
    
      m
      
        1
        /
        12
      
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>≥</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>12</mn>
      </mrow>
    </msup>
  </mrow>
</math>



Canonicalized 


  
    D
    ≥
    
      m
      
        1
        /
        12
      
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>≥</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>12</mn>
      </mrow>
    </msup>
  </mrow>
</math>



Diff 
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Formula 38 
( show / hide formula code)
Original 


  
    4
    m
    +
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <mi>m</mi>
    <mo>+</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    4
    m
    +
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <mi>m</mi>
    <mo>+</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
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Formula 39 
( show / hide formula code)
Original 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
(show/hide code)
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Formula 40 
( show / hide formula code)
Original 


  
    D
    =
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    D
    =
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
(show/hide code)
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Formula 41 
( show / hide formula code)
Original 


  
    m
    =
    2
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <mn>2</mn>
  </mrow>
</math>



Canonicalized 


  
    m
    =
    2
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <mn>2</mn>
  </mrow>
</math>



Diff 
(show/hide code)
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Formula 42 
( show / hide formula code)
Original 


  
    m
    =
    
      t
      2
    
    +
    t
    +
    
      
        2
        t
        +
        1
      
      3
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>t</mi>
    <mo>+</mo>
    <mfrac>
      <mrow>
        <mn>2</mn>
        <mi>t</mi>
        <mo>+</mo>
        <mn>1</mn>
      </mrow>
      <mn>3</mn>
    </mfrac>
  </mrow>
</math>



Canonicalized 


  
    m
    =
    
      t
      2
    
    +
    t
    +
    
      
        2
        t
        +
        1
      
      3
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>t</mi>
    <mo>+</mo>
    <mfrac>
      <mrow>
        <mn>2</mn>
        <mi>t</mi>
        <mo>+</mo>
        <mn>1</mn>
      </mrow>
      <mn>3</mn>
    </mfrac>
  </mrow>
</math>



Diff 
(show/hide code)
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Formula 43 
( show / hide formula code)
Original 


  
    D
    =
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    D
    =
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
(show/hide code)
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Formula 44 
( show / hide formula code)
Original 


  
    4
    
      t
      2
    
    +
    
      
        20
        t
      
      3
    
    +
    
      7
      3
    
    =
    
      u
      2
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <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>
    <mo>=</mo>
    <msup>
      <mi>u</mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math>



Canonicalized 


  
    4
    
      t
      2
    
    +
    
      
        20
        t
      
      3
    
    +
    
      7
      3
    
    =
    
      u
      2
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <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>
    <mo>=</mo>
    <msup>
      <mi>u</mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math>



Diff 
(show/hide code)
1


Formula 45 
( show / hide formula code)
Original 


  
    4
    
      t
      2
    
    +
    4
    t
    +
    1
    <
    4
    
      t
      2
    
    +
    
      
        20
        t
      
      3
    
    +
    
      7
      3
    
    <
    4
    
      t
      2
    
    +
    8
    t
    +
    4
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
  <mrow>
    <mn>4</mn>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mn>4</mn>
    <mi>t</mi>
    <mo>+</mo>
    <mn>1</mn>
    <mo>&lt;</mo>
    <mn>4</mn>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <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>
    <mo>&lt;</mo>
    <mn>4</mn>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mn>8</mn>
    <mi>t</mi>
    <mo>+</mo>
    <mn>4</mn>
  </mrow>
</math>



Canonicalized 


  
    4
    
      t
      2
    
    +
    4
    t
    +
    1
    <
    4
    
      t
      2
    
    +
    
      
        20
        t
      
      3
    
    +
    
      7
      3
    
    <
    4
    
      t
      2
    
    +
    8
    t
    +
    4
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>4</mn>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mn>4</mn>
    <mi>t</mi>
    <mo>+</mo>
    <mn>1</mn>
    <mo>&lt;</mo>
    <mn>4</mn>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <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>
    <mo>&lt;</mo>
    <mn>4</mn>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mn>8</mn>
    <mi>t</mi>
    <mo>+</mo>
    <mn>4</mn>
  </mrow>
</math>



Diff 
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@@ -1,45 +1,45 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
+<math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <mn>4</mn>
     <msup>
       <mi>t</mi>
       <mn>2</mn>
     </msup>
     <mo>+</mo>
     <mn>4</mn>
     <mi>t</mi>
     <mo>+</mo>
     <mn>1</mn>
     <mo>&lt;</mo>
     <mn>4</mn>
     <msup>
       <mi>t</mi>
       <mn>2</mn>
     </msup>
     <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>
     <mo>&lt;</mo>
     <mn>4</mn>
     <msup>
       <mi>t</mi>
       <mn>2</mn>
     </msup>
     <mo>+</mo>
     <mn>8</mn>
     <mi>t</mi>
     <mo>+</mo>
     <mn>4</mn>
   </mrow>
 </math>



Formula 46 
( show / hide formula code)
Original 


  
    2
    t
    +
    1
    <
    u
    <
    2
    t
    +
    2
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>2</mn>
    <mi>t</mi>
    <mo>+</mo>
    <mn>1</mn>
    <mo>&lt;</mo>
    <mi>u</mi>
    <mo>&lt;</mo>
    <mn>2</mn>
    <mi>t</mi>
    <mo>+</mo>
    <mn>2</mn>
  </mrow>
</math>



Canonicalized 


  
    2
    t
    +
    1
    <
    u
    <
    2
    t
    +
    2
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>2</mn>
    <mi>t</mi>
    <mo>+</mo>
    <mn>1</mn>
    <mo>&lt;</mo>
    <mi>u</mi>
    <mo>&lt;</mo>
    <mn>2</mn>
    <mi>t</mi>
    <mo>+</mo>
    <mn>2</mn>
  </mrow>
</math>



Diff 
(show/hide code)
1


Formula 47 
( show / hide formula code)
Original 


  t


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>t</mi>
</math>



Canonicalized 


  t


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>t</mi>
</math>



Diff 
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1


Formula 48 
( show / hide formula code)
Original 


  u


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>u</mi>
</math>



Canonicalized 


  u


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>u</mi>
</math>



Diff 
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1


Formula 49 
( show / hide formula code)
Original 


  □


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mo>□</mo>
</math>



Canonicalized 


  □


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mo>□</mo>
</math>



Diff 
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1


Formula 50 
( show / hide formula code)
Original 


  m


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Canonicalized 


  m


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Diff 
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Formula 51 
( show / hide formula code)
Original 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
(show/hide code)
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Formula 52 
( show / hide formula code)
Original 


  
    1
    <
    D
    <
    
      m
      
        1
        /
        12
      
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>1</mn>
    <mo>&lt;</mo>
    <mi>D</mi>
    <mo>&lt;</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>12</mn>
      </mrow>
    </msup>
  </mrow>
</math>



Canonicalized 


  
    1
    <
    D
    <
    
      m
      
        1
        /
        12
      
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>1</mn>
    <mo>&lt;</mo>
    <mi>D</mi>
    <mo>&lt;</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>12</mn>
      </mrow>
    </msup>
  </mrow>
</math>



Diff 
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1


Formula 53 
( show / hide formula code)
Original 


  p


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Canonicalized 


  p


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Diff 
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Formula 54 
( show / hide formula code)
Original 


  
    p
    ≡
    1
    
    (
    mod
    
    4
    D
    )
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>p</mi>
    <mo>≡</mo>
    <mn>1</mn>
    <mspace width="4.44443pt"/>
    <mo>(</mo>
    <mo form="prefix">mod</mo>
    <mspace width="0.277778em"/>
    <mn>4</mn>
    <mi>D</mi>
    <mo>)</mo>
  </mrow>
</math>



Canonicalized 


  
    p
    ≡
    1
    
      (
      
        mod
        4
        D
      
      )
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>p</mi>
    <mo>≡</mo>
    <mn>1</mn>
    <mrow>
      <mo>(</mo>
      <mrow>
        <mo>mod</mo>
        <mn>4</mn>
        <mi>D</mi>
      </mrow>
      <mo>)</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,15 +1,17 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <mi>p</mi>
     <mo>≡</mo>
     <mn>1</mn>
-    <mspace width="4.44443pt"/>
-    <mo>(</mo>
-    <mo form="prefix">mod</mo>
-    <mspace width="0.277778em"/>
-    <mn>4</mn>
-    <mi>D</mi>
-    <mo>)</mo>
+    <mrow>
+      <mo>(</mo>
+      <mrow>
+        <mo>mod</mo>
+        <mn>4</mn>
+        <mi>D</mi>
+      </mrow>
+      <mo>)</mo>
+    </mrow>
   </mrow>
 </math>



Formula 55 
( show / hide formula code)
Original 


  
    (
    p
    ,
    m
    )
    =
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mo>(</mo>
    <mi>p</mi>
    <mo>,</mo>
    <mi>m</mi>
    <mo>)</mo>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    
      (
      
        p
        ,
        m
      
      )
    
    =
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mrow>
      <mo>(</mo>
      <mrow>
        <mi>p</mi>
        <mo>,</mo>
        <mi>m</mi>
      </mrow>
      <mo>)</mo>
    </mrow>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
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@@ -1,12 +1,16 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
-    <mo>(</mo>
-    <mi>p</mi>
-    <mo>,</mo>
-    <mi>m</mi>
-    <mo>)</mo>
+    <mrow>
+      <mo>(</mo>
+      <mrow>
+        <mi>p</mi>
+        <mo>,</mo>
+        <mi>m</mi>
+      </mrow>
+      <mo>)</mo>
+    </mrow>
     <mo>=</mo>
     <mn>1</mn>
   </mrow>
 </math>



Formula 56 
( show / hide formula code)
Original 


  
    p
    <
    
      D
      C
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>p</mi>
    <mo>&lt;</mo>
    <msup>
      <mi>D</mi>
      <mi>C</mi>
    </msup>
  </mrow>
</math>



Canonicalized 


  
    p
    <
    
      D
      C
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>p</mi>
    <mo>&lt;</mo>
    <msup>
      <mi>D</mi>
      <mi>C</mi>
    </msup>
  </mrow>
</math>



Diff 
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Formula 57 
( show / hide formula code)
Original 


  C


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>C</mi>
</math>



Canonicalized 


  C


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>C</mi>
</math>



Diff 
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1


Formula 58 
( show / hide formula code)
Original 


  D


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>D</mi>
</math>



Canonicalized 


  D


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>D</mi>
</math>



Diff 
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Formula 59 
( show / hide formula code)
Original 


  
    C
    =
    5
    .
    5
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>C</mi>
    <mo>=</mo>
    <mn>5</mn>
    <mo>.</mo>
    <mn>5</mn>
  </mrow>
</math>



Canonicalized 


  
    C
    =
    5
    .
    5
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>C</mi>
    <mo>=</mo>
    <mn>5</mn>
    <mo>.</mo>
    <mn>5</mn>
  </mrow>
</math>



Diff 
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Formula 60 
( show / hide formula code)
Original 


  
    D
    0
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>D</mi>
    <mn>0</mn>
  </msub>
</math>



Canonicalized 


  
    D
    0
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>D</mi>
    <mn>0</mn>
  </msub>
</math>



Diff 
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Formula 61 
( show / hide formula code)
Original 


  
    D
    >
    
      D
      0
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>&gt;</mo>
    <msub>
      <mi>D</mi>
      <mn>0</mn>
    </msub>
  </mrow>
</math>



Canonicalized 


  
    D
    >
    
      D
      0
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>&gt;</mo>
    <msub>
      <mi>D</mi>
      <mn>0</mn>
    </msub>
  </mrow>
</math>



Diff 
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Formula 62 
( show / hide formula code)
Original 


  
    p
    <
    
      m
      
        1
        /
        2
      
    
    /
    6
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>p</mi>
    <mo>&lt;</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>2</mn>
      </mrow>
    </msup>
    <mo>/</mo>
    <mn>6</mn>
  </mrow>
</math>



Canonicalized 


  
    p
    <
    
      m
      
        1
        /
        2
      
    
    /
    6
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>p</mi>
    <mo>&lt;</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>2</mn>
      </mrow>
    </msup>
    <mo>/</mo>
    <mn>6</mn>
  </mrow>
</math>



Diff 
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1


Formula 63 
( show / hide formula code)
Original 


  p


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Canonicalized 


  p


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Diff 
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Formula 64 
( show / hide formula code)
Original 


  p


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Canonicalized 


  p


(show/hide code)
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2
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Diff 
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1


Formula 65 
( show / hide formula code)
Original 


  n


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>n</mi>
</math>



Canonicalized 


  n


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>n</mi>
</math>



Diff 
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Formula 66 
( show / hide formula code)
Original 


  
    x
    -
    
      
        1
        +
        u
        
          D
        
      
      2
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>x</mi>
    <mo>-</mo>
    <mfrac>
      <mrow>
        <mn>1</mn>
        <mo>+</mo>
        <mi>u</mi>
        <msqrt>
          <mi>D</mi>
        </msqrt>
      </mrow>
      <mn>2</mn>
    </mfrac>
  </mrow>
</math>



Canonicalized 


  
    x
    -
    
      
        1
        +
        u
        
          D
        
      
      2
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>x</mi>
    <mo>-</mo>
    <mfrac>
      <mrow>
        <mn>1</mn>
        <mo>+</mo>
        <mi>u</mi>
        <msqrt>
          <mi>D</mi>
        </msqrt>
      </mrow>
      <mn>2</mn>
    </mfrac>
  </mrow>
</math>



Diff 
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1


Formula 67 
( show / hide formula code)
Original 


  p


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Canonicalized 


  p


(show/hide code)
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2
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Diff 
(show/hide code)
1


Formula 68 
( show / hide formula code)
Original 


  p


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Canonicalized 


  p


(show/hide code)
1
2
3
4
<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>p</mi>
</math>



Diff 
(show/hide code)
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Formula 69 
( show / hide formula code)
Original 


  
    
      n
      2
    
    +
    n
    -
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msup>
      <mi>n</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>n</mi>
    <mo>-</mo>
    <mi>m</mi>
  </mrow>
</math>



Canonicalized 


  
    
      n
      2
    
    +
    n
    -
    m
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msup>
      <mi>n</mi>
      <mn>2</mn>
    </msup>
    <mo>+</mo>
    <mi>n</mi>
    <mo>-</mo>
    <mi>m</mi>
  </mrow>
</math>



Diff 
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Formula 70 
( show / hide formula code)
Original 


  
    f
    m
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


(show/hide code)
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7
<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
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Formula 71 
( show / hide formula code)
Original 


  
    
      f
      m
    
    
      (
      n
      )
    
    =
    ±
    p
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msub>
      <mi>f</mi>
      <mi>m</mi>
    </msub>
    <mrow>
      <mo>(</mo>
      <mi>n</mi>
      <mo>)</mo>
    </mrow>
    <mo>=</mo>
    <mo>±</mo>
    <mi>p</mi>
  </mrow>
</math>



Canonicalized 


  
    
      f
      m
    
    
      (
      n
      )
    
    =
    ±
    p
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msub>
      <mi>f</mi>
      <mi>m</mi>
    </msub>
    <mrow>
      <mo>(</mo>
      <mi>n</mi>
      <mo>)</mo>
    </mrow>
    <mo>=</mo>
    <mo>±</mo>
    <mi>p</mi>
  </mrow>
</math>



Diff 
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Formula 72 
( show / hide formula code)
Original 


  
    f
    m
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


(show/hide code)
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7
<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
(show/hide code)
1


Formula 73 
( show / hide formula code)
Original 


  n


(show/hide code)
1
2
3
4
<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>n</mi>
</math>



Canonicalized 


  n


(show/hide code)
1
2
3
4
<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>n</mi>
</math>



Diff 
(show/hide code)
1


Formula 74 
( show / hide formula code)
Original 


  
    p
    <
    
      m
      
        1
        /
        2
      
    
    /
    6
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>p</mi>
    <mo>&lt;</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>2</mn>
      </mrow>
    </msup>
    <mo>/</mo>
    <mn>6</mn>
  </mrow>
</math>



Canonicalized 


  
    p
    <
    
      m
      
        1
        /
        2
      
    
    /
    6
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>p</mi>
    <mo>&lt;</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>2</mn>
      </mrow>
    </msup>
    <mo>/</mo>
    <mn>6</mn>
  </mrow>
</math>



Diff 
(show/hide code)
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Formula 75 
( show / hide formula code)
Original 


  
    m
    
      1
      /
      2
    
  


(show/hide code)
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11
<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msup>
    <mi>m</mi>
    <mrow>
      <mn>1</mn>
      <mo>/</mo>
      <mn>2</mn>
    </mrow>
  </msup>
</math>



Canonicalized 


  
    m
    
      1
      /
      2
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msup>
    <mi>m</mi>
    <mrow>
      <mn>1</mn>
      <mo>/</mo>
      <mn>2</mn>
    </mrow>
  </msup>
</math>



Diff 
(show/hide code)
1


Formula 76 
( show / hide formula code)
Original 


  n


(show/hide code)
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4
<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>n</mi>
</math>



Canonicalized 


  n


(show/hide code)
1
2
3
4
<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>n</mi>
</math>



Diff 
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Formula 77 
( show / hide formula code)
Original 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
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Formula 78 
( show / hide formula code)
Original 


  
    
      p
      D
    
    ≡
    1
    
    
      (
      mod
      
      4
      D
      )
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msub>
      <mi>p</mi>
      <mi>D</mi>
    </msub>
    <mo>≡</mo>
    <mn>1</mn>
    <mspace width="4.44443pt"/>
    <mrow>
      <mo>(</mo>
      <mo form="prefix">mod</mo>
      <mspace width="0.277778em"/>
      <mn>4</mn>
      <mi>D</mi>
      <mo>)</mo>
    </mrow>
  </mrow>
</math>



Canonicalized 


  
    
      p
      D
    
    ≡
    1
    
      (
      
        mod
        4
        D
      
      )
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msub>
      <mi>p</mi>
      <mi>D</mi>
    </msub>
    <mo>≡</mo>
    <mn>1</mn>
    <mrow>
      <mo>(</mo>
      <mrow>
        <mo>mod</mo>
        <mn>4</mn>
        <mi>D</mi>
      </mrow>
      <mo>)</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,20 +1,20 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <msub>
       <mi>p</mi>
       <mi>D</mi>
     </msub>
     <mo>≡</mo>
     <mn>1</mn>
-    <mspace width="4.44443pt"/>
     <mrow>
       <mo>(</mo>
-      <mo form="prefix">mod</mo>
-      <mspace width="0.277778em"/>
-      <mn>4</mn>
-      <mi>D</mi>
+      <mrow>
+        <mo>mod</mo>
+        <mn>4</mn>
+        <mi>D</mi>
+      </mrow>
       <mo>)</mo>
     </mrow>
   </mrow>
 </math>



Formula 79 
( show / hide formula code)
Original 


  
    D
    ≤
    
      D
      0
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>≤</mo>
    <msub>
      <mi>D</mi>
      <mn>0</mn>
    </msub>
  </mrow>
</math>



Canonicalized 


  
    D
    ≤
    
      D
      0
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>≤</mo>
    <msub>
      <mi>D</mi>
      <mn>0</mn>
    </msub>
  </mrow>
</math>



Diff 
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Formula 80 
( show / hide formula code)
Original 


  
    m
    >
    6
    max
    
      p
      D
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>&gt;</mo>
    <mn>6</mn>
    <mo movablelimits="true" form="prefix">max</mo>
    <msub>
      <mi>p</mi>
      <mi>D</mi>
    </msub>
  </mrow>
</math>



Canonicalized 


  
    m
    >
    6
    max
    
      p
      D
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>&gt;</mo>
    <mn>6</mn>
    <mo>max</mo>
    <msub>
      <mi>p</mi>
      <mi>D</mi>
    </msub>
  </mrow>
</math>



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@@ -1,13 +1,13 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <mi>m</mi>
     <mo>&gt;</mo>
     <mn>6</mn>
-    <mo movablelimits="true" form="prefix">max</mo>
+    <mo>max</mo>
     <msub>
       <mi>p</mi>
       <mi>D</mi>
     </msub>
   </mrow>
 </math>



Formula 81 
( show / hide formula code)
Original 


  □


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mo>□</mo>
</math>



Canonicalized 


  □


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mo>□</mo>
</math>



Diff 
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Formula 82 
( show / hide formula code)
Original 


  m


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Canonicalized 


  m


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Diff 
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Formula 83 
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Original 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
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Formula 84 
( show / hide formula code)
Original 


  
    D
    ≥
    
      m
      
        1
        /
        12
      
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>≥</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>12</mn>
      </mrow>
    </msup>
  </mrow>
</math>



Canonicalized 


  
    D
    ≥
    
      m
      
        1
        /
        12
      
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>D</mi>
    <mo>≥</mo>
    <msup>
      <mi>m</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>12</mn>
      </mrow>
    </msup>
  </mrow>
</math>



Diff 
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Formula 85 
( show / hide formula code)
Original 


  
    m
    =
    2
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <mn>2</mn>
  </mrow>
</math>



Canonicalized 


  
    m
    =
    2
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>=</mo>
    <mn>2</mn>
  </mrow>
</math>



Diff 
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Formula 86 
( show / hide formula code)
Original 


  
    ϵ
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>ϵ</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    ε
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>ε</mi>
    <mi>m</mi>
  </msub>
</math>



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@@ -1,7 +1,7 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <msub>
-    <mi>ϵ</mi>
+    <mi>ε</mi>
     <mi>m</mi>
   </msub>
 </math>



Formula 87 
( show / hide formula code)
Original 


  
    ℚ
    (
    
      D
    
    )
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>ℚ</mi>
    <mo>(</mo>
    <msqrt>
      <mi>D</mi>
    </msqrt>
    <mo>)</mo>
  </mrow>
</math>



Canonicalized 


  
    Q
    
      (
      
        D
      
      )
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>Q</mi>
    <mrow>
      <mo>(</mo>
      <msqrt>
        <mi>D</mi>
      </msqrt>
      <mo>)</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,11 +1,13 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
-    <mi>ℚ</mi>
-    <mo>(</mo>
-    <msqrt>
-      <mi>D</mi>
-    </msqrt>
-    <mo>)</mo>
+    <mi>Q</mi>
+    <mrow>
+      <mo>(</mo>
+      <msqrt>
+        <mi>D</mi>
+      </msqrt>
+      <mo>)</mo>
+    </mrow>
   </mrow>
 </math>



Formula 88 
( show / hide formula code)
Original 


  
    
      1
      <
      |
    
    
      ϵ
      m
    
    
      |
      ≪
      m
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mrow>
      <mn>1</mn>
      <mo>&lt;</mo>
      <mo>|</mo>
    </mrow>
    <msub>
      <mi>ϵ</mi>
      <mi>m</mi>
    </msub>
    <mrow>
      <mo>|</mo>
      <mo>≪</mo>
      <mi>m</mi>
    </mrow>
  </mrow>
</math>



Canonicalized 


  
    
      1
      <
      |
    
    
      ε
      m
    
    
      |
      ≪
      m
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mrow>
      <mn>1</mn>
      <mo>&lt;</mo>
      <mo>|</mo>
    </mrow>
    <msub>
      <mi>ε</mi>
      <mi>m</mi>
    </msub>
    <mrow>
      <mo>|</mo>
      <mo>≪</mo>
      <mi>m</mi>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,19 +1,19 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <mrow>
       <mn>1</mn>
       <mo>&lt;</mo>
       <mo>|</mo>
     </mrow>
     <msub>
-      <mi>ϵ</mi>
+      <mi>ε</mi>
       <mi>m</mi>
     </msub>
     <mrow>
       <mo>|</mo>
       <mo>≪</mo>
       <mi>m</mi>
     </mrow>
   </mrow>
 </math>



Formula 89 
( show / hide formula code)
Original 


  
    
      
      
        
          m
          =
          
            t
            2
          
        
      
      
        :
      
      
        
          
          
            ϵ
            m
          
          =
          2
          t
          +
          
            
              4
              m
              +
              1
            
          
        
      
    
    
      
      
        
          m
          =
          
            t
            2
          
          +
          t
          ±
          1
        
      
      
        :
      
      
        
          
          
            ϵ
            m
          
          =
          
            
              2
              t
              +
              1
              +
              
                
                  4
                  m
                  +
                  1
                
              
            
            2
          
        
      
    
    
      
      
        
          m
          =
          
            t
            2
          
          +
          t
          ±
          
            
              2
              t
              +
              1
            
            3
          
          
        
      
      
        :
      
      
        
          
          
            ϵ
            m
          
          =
          
            
              6
              t
              +
              3
              ±
              2
              +
              3
              
                
                  4
                  m
                  +
                  1
                
              
            
            2
          
        
      
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
  <mtable displaystyle="true">
    <mtr>
      <mtd/>
      <mtd columnalign="left">
        <mrow>
          <mi>m</mi>
          <mo>=</mo>
          <msup>
            <mi>t</mi>
            <mn>2</mn>
          </msup>
        </mrow>
      </mtd>
      <mtd columnalign="right">
        <mo>:</mo>
      </mtd>
      <mtd columnalign="left">
        <mrow>
          <mspace width="1.em"/>
          <msub>
            <mi>ϵ</mi>
            <mi>m</mi>
          </msub>
          <mo>=</mo>
          <mn>2</mn>
          <mi>t</mi>
          <mo>+</mo>
          <msqrt>
            <mrow>
              <mn>4</mn>
              <mi>m</mi>
              <mo>+</mo>
              <mn>1</mn>
            </mrow>
          </msqrt>
        </mrow>
      </mtd>
    </mtr>
    <mtr>
      <mtd/>
      <mtd columnalign="left">
        <mrow>
          <mi>m</mi>
          <mo>=</mo>
          <msup>
            <mi>t</mi>
            <mn>2</mn>
          </msup>
          <mo>+</mo>
          <mi>t</mi>
          <mo>±</mo>
          <mn>1</mn>
        </mrow>
      </mtd>
      <mtd columnalign="right">
        <mo>:</mo>
      </mtd>
      <mtd columnalign="left">
        <mrow>
          <mspace width="1.em"/>
          <msub>
            <mi>ϵ</mi>
            <mi>m</mi>
          </msub>
          <mo>=</mo>
          <mfrac>
            <mrow>
              <mn>2</mn>
              <mi>t</mi>
              <mo>+</mo>
              <mn>1</mn>
              <mo>+</mo>
              <msqrt>
                <mrow>
                  <mn>4</mn>
                  <mi>m</mi>
                  <mo>+</mo>
                  <mn>1</mn>
                </mrow>
              </msqrt>
            </mrow>
            <mn>2</mn>
          </mfrac>
        </mrow>
      </mtd>
    </mtr>
    <mtr>
      <mtd/>
      <mtd columnalign="left">
        <mrow>
          <mi>m</mi>
          <mo>=</mo>
          <msup>
            <mi>t</mi>
            <mn>2</mn>
          </msup>
          <mo>+</mo>
          <mi>t</mi>
          <mo>±</mo>
          <mfrac>
            <mrow>
              <mn>2</mn>
              <mi>t</mi>
              <mo>+</mo>
              <mn>1</mn>
            </mrow>
            <mn>3</mn>
          </mfrac>
          <mspace width="1.em"/>
        </mrow>
      </mtd>
      <mtd columnalign="right">
        <mo>:</mo>
      </mtd>
      <mtd columnalign="left">
        <mrow>
          <mspace width="1.em"/>
          <msub>
            <mi>ϵ</mi>
            <mi>m</mi>
          </msub>
          <mo>=</mo>
          <mfrac>
            <mrow>
              <mn>6</mn>
              <mi>t</mi>
              <mo>+</mo>
              <mn>3</mn>
              <mo>±</mo>
              <mn>2</mn>
              <mo>+</mo>
              <mn>3</mn>
              <msqrt>
                <mrow>
                  <mn>4</mn>
                  <mi>m</mi>
                  <mo>+</mo>
                  <mn>1</mn>
                </mrow>
              </msqrt>
            </mrow>
            <mn>2</mn>
          </mfrac>
        </mrow>
      </mtd>
    </mtr>
  </mtable>
</math>



Canonicalized 


  
    
      
      
        m
        =
        
          t
          2
        
      
      
        /
      
      
        
          ε
          m
        
        =
        2
        t
        +
        
          4
          m
          +
          1
        
      
    
    
      
      
        m
        =
        
          t
          2
        
        +
        t
        ±
        1
      
      
        /
      
      
        
          ε
          m
        
        =
        
          
            2
            t
            +
            1
            +
            
              4
              m
              +
              1
            
          
          2
        
      
    
    
      
      
        m
        =
        
          t
          2
        
        +
        t
        ±
        
          
            2
            t
            +
            1
          
          3
        
      
      
        /
      
      
        
          ε
          m
        
        =
        
          
            6
            t
            +
            3
            ±
            2
            +
            3
            
              4
              m
              +
              1
            
          
          2
        
      
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mtable>
    <mtr>
      <mtd/>
      <mtd>
        <mi>m</mi>
        <mo>=</mo>
        <msup>
          <mi>t</mi>
          <mn>2</mn>
        </msup>
      </mtd>
      <mtd>
        <mo>/</mo>
      </mtd>
      <mtd>
        <msub>
          <mi>ε</mi>
          <mi>m</mi>
        </msub>
        <mo>=</mo>
        <mn>2</mn>
        <mi>t</mi>
        <mo>+</mo>
        <msqrt>
          <mn>4</mn>
          <mi>m</mi>
          <mo>+</mo>
          <mn>1</mn>
        </msqrt>
      </mtd>
    </mtr>
    <mtr>
      <mtd/>
      <mtd>
        <mi>m</mi>
        <mo>=</mo>
        <msup>
          <mi>t</mi>
          <mn>2</mn>
        </msup>
        <mo>+</mo>
        <mi>t</mi>
        <mo>±</mo>
        <mn>1</mn>
      </mtd>
      <mtd>
        <mo>/</mo>
      </mtd>
      <mtd>
        <msub>
          <mi>ε</mi>
          <mi>m</mi>
        </msub>
        <mo>=</mo>
        <mfrac>
          <mrow>
            <mn>2</mn>
            <mi>t</mi>
            <mo>+</mo>
            <mn>1</mn>
            <mo>+</mo>
            <msqrt>
              <mn>4</mn>
              <mi>m</mi>
              <mo>+</mo>
              <mn>1</mn>
            </msqrt>
          </mrow>
          <mn>2</mn>
        </mfrac>
      </mtd>
    </mtr>
    <mtr>
      <mtd/>
      <mtd>
        <mi>m</mi>
        <mo>=</mo>
        <msup>
          <mi>t</mi>
          <mn>2</mn>
        </msup>
        <mo>+</mo>
        <mi>t</mi>
        <mo>±</mo>
        <mfrac>
          <mrow>
            <mn>2</mn>
            <mi>t</mi>
            <mo>+</mo>
            <mn>1</mn>
          </mrow>
          <mn>3</mn>
        </mfrac>
      </mtd>
      <mtd>
        <mo>/</mo>
      </mtd>
      <mtd>
        <msub>
          <mi>ε</mi>
          <mi>m</mi>
        </msub>
        <mo>=</mo>
        <mfrac>
          <mrow>
            <mn>6</mn>
            <mi>t</mi>
            <mo>+</mo>
            <mn>3</mn>
            <mo>±</mo>
            <mn>2</mn>
            <mo>+</mo>
            <mn>3</mn>
            <msqrt>
              <mn>4</mn>
              <mi>m</mi>
              <mo>+</mo>
              <mn>1</mn>
            </msqrt>
          </mrow>
          <mn>2</mn>
        </mfrac>
      </mtd>
    </mtr>
  </mtable>
</math>



Diff 
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@@ -1,150 +1,128 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
-  <mtable displaystyle="true">
+<math xmlns="http://www.w3.org/1998/Math/MathML">
+  <mtable>
     <mtr>
       <mtd/>
-      <mtd columnalign="left">
-        <mrow>
-          <mi>m</mi>
-          <mo>=</mo>
-          <msup>
-            <mi>t</mi>
-            <mn>2</mn>
-          </msup>
-        </mrow>
+      <mtd>
+        <mi>m</mi>
+        <mo>=</mo>
+        <msup>
+          <mi>t</mi>
+          <mn>2</mn>
+        </msup>
       </mtd>
-      <mtd columnalign="right">
-        <mo>:</mo>
+      <mtd>
+        <mo>/</mo>
       </mtd>
-      <mtd columnalign="left">
-        <mrow>
-          <mspace width="1.em"/>
-          <msub>
-            <mi>ϵ</mi>
-            <mi>m</mi>
-          </msub>
-          <mo>=</mo>
-          <mn>2</mn>
-          <mi>t</mi>
+      <mtd>
+        <msub>
+          <mi>ε</mi>
+          <mi>m</mi>
+        </msub>
+        <mo>=</mo>
+        <mn>2</mn>
+        <mi>t</mi>
+        <mo>+</mo>
+        <msqrt>
+          <mn>4</mn>
+          <mi>m</mi>
           <mo>+</mo>
-          <msqrt>
-            <mrow>
-              <mn>4</mn>
-              <mi>m</mi>
-              <mo>+</mo>
-              <mn>1</mn>
-            </mrow>
-          </msqrt>
-        </mrow>
+          <mn>1</mn>
+        </msqrt>
       </mtd>
     </mtr>
     <mtr>
       <mtd/>
-      <mtd columnalign="left">
-        <mrow>
-          <mi>m</mi>
-          <mo>=</mo>
-          <msup>
-            <mi>t</mi>
-            <mn>2</mn>
-          </msup>
-          <mo>+</mo>
+      <mtd>
+        <mi>m</mi>
+        <mo>=</mo>
+        <msup>
           <mi>t</mi>
-          <mo>±</mo>
-          <mn>1</mn>
-        </mrow>
+          <mn>2</mn>
+        </msup>
+        <mo>+</mo>
+        <mi>t</mi>
+        <mo>±</mo>
+        <mn>1</mn>
       </mtd>
-      <mtd columnalign="right">
-        <mo>:</mo>
+      <mtd>
+        <mo>/</mo>
       </mtd>
-      <mtd columnalign="left">
-        <mrow>
-          <mspace width="1.em"/>
-          <msub>
-            <mi>ϵ</mi>
-            <mi>m</mi>
-          </msub>
-          <mo>=</mo>
-          <mfrac>
-            <mrow>
-              <mn>2</mn>
-              <mi>t</mi>
+      <mtd>
+        <msub>
+          <mi>ε</mi>
+          <mi>m</mi>
+        </msub>
+        <mo>=</mo>
+        <mfrac>
+          <mrow>
+            <mn>2</mn>
+            <mi>t</mi>
+            <mo>+</mo>
+            <mn>1</mn>
+            <mo>+</mo>
+            <msqrt>
+              <mn>4</mn>
+              <mi>m</mi>
               <mo>+</mo>
               <mn>1</mn>
-              <mo>+</mo>
-              <msqrt>
-                <mrow>
-                  <mn>4</mn>
-                  <mi>m</mi>
-                  <mo>+</mo>
-                  <mn>1</mn>
-                </mrow>
-              </msqrt>
-            </mrow>
-            <mn>2</mn>
-          </mfrac>
-        </mrow>
+            </msqrt>
+          </mrow>
+          <mn>2</mn>
+        </mfrac>
       </mtd>
     </mtr>
     <mtr>
       <mtd/>
-      <mtd columnalign="left">
-        <mrow>
+      <mtd>
+        <mi>m</mi>
+        <mo>=</mo>
+        <msup>
+          <mi>t</mi>
+          <mn>2</mn>
+        </msup>
+        <mo>+</mo>
+        <mi>t</mi>
+        <mo>±</mo>
+        <mfrac>
+          <mrow>
+            <mn>2</mn>
+            <mi>t</mi>
+            <mo>+</mo>
+            <mn>1</mn>
+          </mrow>
+          <mn>3</mn>
+        </mfrac>
+      </mtd>
+      <mtd>
+        <mo>/</mo>
+      </mtd>
+      <mtd>
+        <msub>
+          <mi>ε</mi>
           <mi>m</mi>
-          <mo>=</mo>
-          <msup>
+        </msub>
+        <mo>=</mo>
+        <mfrac>
+          <mrow>
+            <mn>6</mn>
             <mi>t</mi>
+            <mo>+</mo>
+            <mn>3</mn>
+            <mo>±</mo>
             <mn>2</mn>
-          </msup>
-          <mo>+</mo>
-          <mi>t</mi>
-          <mo>±</mo>
-          <mfrac>
-            <mrow>
-              <mn>2</mn>
-              <mi>t</mi>
-              <mo>+</mo>
-              <mn>1</mn>
-            </mrow>
+            <mo>+</mo>
             <mn>3</mn>
-          </mfrac>
-          <mspace width="1.em"/>
-        </mrow>
-      </mtd>
-      <mtd columnalign="right">
-        <mo>:</mo>
-      </mtd>
-      <mtd columnalign="left">
-        <mrow>
-          <mspace width="1.em"/>
-          <msub>
-            <mi>ϵ</mi>
-            <mi>m</mi>
-          </msub>
-          <mo>=</mo>
-          <mfrac>
-            <mrow>
-              <mn>6</mn>
-              <mi>t</mi>
+            <msqrt>
+              <mn>4</mn>
+              <mi>m</mi>
               <mo>+</mo>
-              <mn>3</mn>
-              <mo>±</mo>
-              <mn>2</mn>
-              <mo>+</mo>
-              <mn>3</mn>
-              <msqrt>
-                <mrow>
-                  <mn>4</mn>
-                  <mi>m</mi>
-                  <mo>+</mo>
-                  <mn>1</mn>
-                </mrow>
-              </msqrt>
-            </mrow>
-            <mn>2</mn>
-          </mfrac>
-        </mrow>
+              <mn>1</mn>
+            </msqrt>
+          </mrow>
+          <mn>2</mn>
+        </mfrac>
       </mtd>
     </mtr>
   </mtable>
 </math>



Formula 90 
( show / hide formula code)
Original 


  
    
      ϵ
      D
    
    >
    1
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msub>
      <mi>ϵ</mi>
      <mi>D</mi>
    </msub>
    <mo>&gt;</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    
      ε
      D
    
    >
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msub>
      <mi>ε</mi>
      <mi>D</mi>
    </msub>
    <mo>&gt;</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
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@@ -1,11 +1,11 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <msub>
-      <mi>ϵ</mi>
+      <mi>ε</mi>
       <mi>D</mi>
     </msub>
     <mo>&gt;</mo>
     <mn>1</mn>
   </mrow>
 </math>



Formula 91 
( show / hide formula code)
Original 


  
    ℚ
    (
    
      D
    
    )
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>ℚ</mi>
    <mo>(</mo>
    <msqrt>
      <mi>D</mi>
    </msqrt>
    <mo>)</mo>
  </mrow>
</math>



Canonicalized 


  
    Q
    
      (
      
        D
      
      )
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>Q</mi>
    <mrow>
      <mo>(</mo>
      <msqrt>
        <mi>D</mi>
      </msqrt>
      <mo>)</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,11 +1,13 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
-    <mi>ℚ</mi>
-    <mo>(</mo>
-    <msqrt>
-      <mi>D</mi>
-    </msqrt>
-    <mo>)</mo>
+    <mi>Q</mi>
+    <mrow>
+      <mo>(</mo>
+      <msqrt>
+        <mi>D</mi>
+      </msqrt>
+      <mo>)</mo>
+    </mrow>
   </mrow>
 </math>



Formula 92 
( show / hide formula code)
Original 


  
    ℚ
    (
    
      D
    
    )
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>ℚ</mi>
    <mo>(</mo>
    <msqrt>
      <mi>D</mi>
    </msqrt>
    <mo>)</mo>
  </mrow>
</math>



Canonicalized 


  
    Q
    
      (
      
        D
      
      )
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>Q</mi>
    <mrow>
      <mo>(</mo>
      <msqrt>
        <mi>D</mi>
      </msqrt>
      <mo>)</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,11 +1,13 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
-    <mi>ℚ</mi>
-    <mo>(</mo>
-    <msqrt>
-      <mi>D</mi>
-    </msqrt>
-    <mo>)</mo>
+    <mi>Q</mi>
+    <mrow>
+      <mo>(</mo>
+      <msqrt>
+        <mi>D</mi>
+      </msqrt>
+      <mo>)</mo>
+    </mrow>
   </mrow>
 </math>



Formula 93 
( show / hide formula code)
Original 


  k


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>k</mi>
</math>



Canonicalized 


  k


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>k</mi>
</math>



Diff 
(show/hide code)
1


Formula 94 
( show / hide formula code)
Original 


  
    
      ϵ
      m
    
    =
    
      ϵ
      D
      k
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msub>
      <mi>ϵ</mi>
      <mi>m</mi>
    </msub>
    <mo>=</mo>
    <msubsup>
      <mi>ϵ</mi>
      <mi>D</mi>
      <mi>k</mi>
    </msubsup>
  </mrow>
</math>



Canonicalized 


  
    
      ε
      m
    
    =
    
      
        ε
        D
      
      k
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <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>
</math>



Diff 
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@@ -1,15 +1,17 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <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>
 </math>



Formula 95 
( show / hide formula code)
Original 


  
    
      ϵ
      D
    
    <
    m
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msub>
      <mi>ϵ</mi>
      <mi>D</mi>
    </msub>
    <mo>&lt;</mo>
    <mi>m</mi>
  </mrow>
</math>



Canonicalized 


  
    
      ε
      D
    
    <
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <msub>
      <mi>ε</mi>
      <mi>D</mi>
    </msub>
    <mo>&lt;</mo>
    <mi>m</mi>
  </mrow>
</math>



Diff 
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@@ -1,11 +1,11 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <msub>
-      <mi>ϵ</mi>
+      <mi>ε</mi>
       <mi>D</mi>
     </msub>
     <mo>&lt;</mo>
     <mi>m</mi>
   </mrow>
 </math>



Formula 96 
( show / hide formula code)
Original 


  
    
      log
      (
      h
    
    
      (
      ℚ
      
        (
        
          D
        
        )
      
      )
    
    
      log
      |
    
    
      ϵ
      D
    
    
      |
      )
    
    ∼
    log
    
      D
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mrow>
      <mo form="prefix">log</mo>
      <mo>(</mo>
      <mi>h</mi>
    </mrow>
    <mrow>
      <mo>(</mo>
      <mi>ℚ</mi>
      <mrow>
        <mo>(</mo>
        <msqrt>
          <mi>D</mi>
        </msqrt>
        <mo>)</mo>
      </mrow>
      <mo>)</mo>
    </mrow>
    <mrow>
      <mo form="prefix">log</mo>
      <mo>|</mo>
    </mrow>
    <msub>
      <mi>ϵ</mi>
      <mi>D</mi>
    </msub>
    <mrow>
      <mo>|</mo>
      <mo>)</mo>
    </mrow>
    <mo>∼</mo>
    <mo form="prefix">log</mo>
    <msqrt>
      <mi>D</mi>
    </msqrt>
  </mrow>
</math>



Canonicalized 


  
    
      log
      (
      h
    
    
      (
      
        Q
        
          (
          
            D
          
          )
        
      
      )
    
    
      log
      |
    
    
      ε
      D
    
    
      |
      )
    
    ∼
    log
    
      D
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mrow>
      <mo>log</mo>
      <mo>(</mo>
      <mi>h</mi>
    </mrow>
    <mrow>
      <mo>(</mo>
      <mrow>
        <mi>Q</mi>
        <mrow>
          <mo>(</mo>
          <msqrt>
            <mi>D</mi>
          </msqrt>
          <mo>)</mo>
        </mrow>
      </mrow>
      <mo>)</mo>
    </mrow>
    <mrow>
      <mo>log</mo>
      <mo>|</mo>
    </mrow>
    <msub>
      <mi>ε</mi>
      <mi>D</mi>
    </msub>
    <mrow>
      <mo>|</mo>
      <mo>)</mo>
    </mrow>
    <mo>∼</mo>
    <mo>log</mo>
    <msqrt>
      <mi>D</mi>
    </msqrt>
  </mrow>
</math>



Diff 
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@@ -1,39 +1,41 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <mrow>
-      <mo form="prefix">log</mo>
+      <mo>log</mo>
       <mo>(</mo>
       <mi>h</mi>
     </mrow>
     <mrow>
       <mo>(</mo>
-      <mi>ℚ</mi>
       <mrow>
-        <mo>(</mo>
-        <msqrt>
-          <mi>D</mi>
-        </msqrt>
-        <mo>)</mo>
+        <mi>Q</mi>
+        <mrow>
+          <mo>(</mo>
+          <msqrt>
+            <mi>D</mi>
+          </msqrt>
+          <mo>)</mo>
+        </mrow>
       </mrow>
       <mo>)</mo>
     </mrow>
     <mrow>
-      <mo form="prefix">log</mo>
+      <mo>log</mo>
       <mo>|</mo>
     </mrow>
     <msub>
-      <mi>ϵ</mi>
+      <mi>ε</mi>
       <mi>D</mi>
     </msub>
     <mrow>
       <mo>|</mo>
       <mo>)</mo>
     </mrow>
     <mo>∼</mo>
-    <mo form="prefix">log</mo>
+    <mo>log</mo>
     <msqrt>
       <mi>D</mi>
     </msqrt>
   </mrow>
 </math>



Formula 97 
( show / hide formula code)
Original 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
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1


Formula 98 
( show / hide formula code)
Original 


  
    h
    (
    ℚ
    
      (
      
        D
      
      )
    
    )
    =
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>h</mi>
    <mo>(</mo>
    <mi>ℚ</mi>
    <mrow>
      <mo>(</mo>
      <msqrt>
        <mi>D</mi>
      </msqrt>
      <mo>)</mo>
    </mrow>
    <mo>)</mo>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Canonicalized 


  
    h
    
      (
      
        Q
        
          (
          
            D
          
          )
        
      
      )
    
    =
    1
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <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>
    <mo>=</mo>
    <mn>1</mn>
  </mrow>
</math>



Diff 
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@@ -1,18 +1,22 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <mi>h</mi>
-    <mo>(</mo>
-    <mi>ℚ</mi>
     <mrow>
       <mo>(</mo>
-      <msqrt>
-        <mi>D</mi>
-      </msqrt>
+      <mrow>
+        <mi>Q</mi>
+        <mrow>
+          <mo>(</mo>
+          <msqrt>
+            <mi>D</mi>
+          </msqrt>
+          <mo>)</mo>
+        </mrow>
+      </mrow>
       <mo>)</mo>
     </mrow>
-    <mo>)</mo>
     <mo>=</mo>
     <mn>1</mn>
   </mrow>
 </math>



Formula 99 
( show / hide formula code)
Original 


  
    
      log
      |
    
    
      ϵ
      D
    
    
      |
      ≤
      log
      |
    
    
      ϵ
      m
    
    
      |
      <
      log
      m
      ≤
      12
      log
      D
      ,
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
  <mrow>
    <mrow>
      <mo form="prefix">log</mo>
      <mo>|</mo>
    </mrow>
    <msub>
      <mi>ϵ</mi>
      <mi>D</mi>
    </msub>
    <mrow>
      <mo>|</mo>
      <mo>≤</mo>
      <mo form="prefix">log</mo>
      <mo>|</mo>
    </mrow>
    <msub>
      <mi>ϵ</mi>
      <mi>m</mi>
    </msub>
    <mrow>
      <mo>|</mo>
      <mo>&lt;</mo>
      <mo form="prefix">log</mo>
      <mi>m</mi>
      <mo>≤</mo>
      <mn>12</mn>
      <mo form="prefix">log</mo>
      <mi>D</mi>
      <mo>,</mo>
    </mrow>
  </mrow>
</math>



Canonicalized 


  
    
      log
      |
    
    
      ε
      D
    
    
      |
      ≤
      log
      |
    
    
      ε
      m
    
    
      |
      <
      log
      m
      ≤
      12
      log
      D
      ,
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mrow>
      <mo>log</mo>
      <mo>|</mo>
    </mrow>
    <msub>
      <mi>ε</mi>
      <mi>D</mi>
    </msub>
    <mrow>
      <mo>|</mo>
      <mo>≤</mo>
      <mo>log</mo>
      <mo>|</mo>
    </mrow>
    <msub>
      <mi>ε</mi>
      <mi>m</mi>
    </msub>
    <mrow>
      <mo>|</mo>
      <mo>&lt;</mo>
      <mo>log</mo>
      <mi>m</mi>
      <mo>≤</mo>
      <mn>12</mn>
      <mo>log</mo>
      <mi>D</mi>
      <mo>,</mo>
    </mrow>
  </mrow>
</math>



Diff 
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@@ -1,34 +1,34 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
+<math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <mrow>
-      <mo form="prefix">log</mo>
+      <mo>log</mo>
       <mo>|</mo>
     </mrow>
     <msub>
-      <mi>ϵ</mi>
+      <mi>ε</mi>
       <mi>D</mi>
     </msub>
     <mrow>
       <mo>|</mo>
       <mo>≤</mo>
-      <mo form="prefix">log</mo>
+      <mo>log</mo>
       <mo>|</mo>
     </mrow>
     <msub>
-      <mi>ϵ</mi>
+      <mi>ε</mi>
       <mi>m</mi>
     </msub>
     <mrow>
       <mo>|</mo>
       <mo>&lt;</mo>
-      <mo form="prefix">log</mo>
+      <mo>log</mo>
       <mi>m</mi>
       <mo>≤</mo>
       <mn>12</mn>
-      <mo form="prefix">log</mo>
+      <mo>log</mo>
       <mi>D</mi>
       <mo>,</mo>
     </mrow>
   </mrow>
 </math>



Formula 100 
( show / hide formula code)
Original 


  
    12
    log
    D
    >
    
      D
      
        1
        /
        2
        +
        o
        (
        1
        )
      
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
  <mrow>
    <mn>12</mn>
    <mo form="prefix">log</mo>
    <mi>D</mi>
    <mo>&gt;</mo>
    <msup>
      <mi>D</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>2</mn>
        <mo>+</mo>
        <mi>o</mi>
        <mo>(</mo>
        <mn>1</mn>
        <mo>)</mo>
      </mrow>
    </msup>
  </mrow>
</math>



Canonicalized 


  
    12
    log
    D
    >
    
      D
      
        1
        /
        2
        +
        o
        
          (
          1
          )
        
      
    
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mn>12</mn>
    <mo>log</mo>
    <mi>D</mi>
    <mo>&gt;</mo>
    <msup>
      <mi>D</mi>
      <mrow>
        <mn>1</mn>
        <mo>/</mo>
        <mn>2</mn>
        <mo>+</mo>
        <mi>o</mi>
        <mrow>
          <mo>(</mo>
          <mn>1</mn>
          <mo>)</mo>
        </mrow>
      </mrow>
    </msup>
  </mrow>
</math>



Diff 
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@@ -1,22 +1,24 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display">
+<math xmlns="http://www.w3.org/1998/Math/MathML">
   <mrow>
     <mn>12</mn>
-    <mo form="prefix">log</mo>
+    <mo>log</mo>
     <mi>D</mi>
     <mo>&gt;</mo>
     <msup>
       <mi>D</mi>
       <mrow>
         <mn>1</mn>
         <mo>/</mo>
         <mn>2</mn>
         <mo>+</mo>
         <mi>o</mi>
-        <mo>(</mo>
-        <mn>1</mn>
-        <mo>)</mo>
+        <mrow>
+          <mo>(</mo>
+          <mn>1</mn>
+          <mo>)</mo>
+        </mrow>
       </mrow>
     </msup>
   </mrow>
 </math>



Formula 101 
( show / hide formula code)
Original 


  D


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>D</mi>
</math>



Canonicalized 


  D


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>D</mi>
</math>



Diff 
(show/hide code)
1


Formula 102 
( show / hide formula code)
Original 


  
    m
    ≤
    
      D
      12
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>≤</mo>
    <msup>
      <mi>D</mi>
      <mn>12</mn>
    </msup>
  </mrow>
</math>



Canonicalized 


  
    m
    ≤
    
      D
      12
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>≤</mo>
    <msup>
      <mi>D</mi>
      <mn>12</mn>
    </msup>
  </mrow>
</math>



Diff 
(show/hide code)
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Formula 103 
( show / hide formula code)
Original 


  m


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Canonicalized 


  m


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>m</mi>
</math>



Diff 
(show/hide code)
1


Formula 104 
( show / hide formula code)
Original 


  □


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mo>□</mo>
</math>



Canonicalized 


  □


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mo>□</mo>
</math>



Diff 
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Formula 105 
( show / hide formula code)
Original 


  
    m
    0
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>m</mi>
    <mn>0</mn>
  </msub>
</math>



Canonicalized 


  
    m
    0
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>m</mi>
    <mn>0</mn>
  </msub>
</math>



Diff 
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Formula 106 
( show / hide formula code)
Original 


  
    m
    >
    
      m
      0
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>&gt;</mo>
    <msub>
      <mi>m</mi>
      <mn>0</mn>
    </msub>
  </mrow>
</math>



Canonicalized 


  
    m
    >
    
      m
      0
    
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mrow>
    <mi>m</mi>
    <mo>&gt;</mo>
    <msub>
      <mi>m</mi>
      <mn>0</mn>
    </msub>
  </mrow>
</math>



Diff 
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Formula 107 
( show / hide formula code)
Original 


  
    f
    m
  


(show/hide code)
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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Canonicalized 


  
    f
    m
  


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>f</mi>
    <mi>m</mi>
  </msub>
</math>



Diff 
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1


Formula 108 
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Original 


  L


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>L</mi>
</math>



Canonicalized 


  L


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<?xml version="1.0" encoding="UTF-8"?>
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>L</mi>
</math>



Diff 
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1