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MATHML_EXAMPLES.md

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MathML Examples

This document provides comprehensive examples of MathML markup patterns that comply with the Nordic MathML Guidelines 2024. These examples demonstrate proper usage of the new MathML requirements and can be used for testing and reference. Version 2.0.0 includes enhanced validation and backward compatibility support.

Basic Mathematical Expressions

Simple Arithmetic

Addition:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mn>3</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>5</mn>
</math>

Subtraction:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mn>10</mn><mo>&#x2212;</mo><mn>4</mn><mo>=</mo><mn>6</mn>
</math>

Multiplication:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mn>4</mn><mo>&#x2062;</mo><mn>5</mn><mo>=</mo><mn>20</mn>
</math>

Division:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mn>15</mn><mo>/</mo><mn>3</mn><mo>=</mo><mn>5</mn>
</math>

Variables and Expressions

Simple variable:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mi>x</mi><mo>+</mo><mn>5</mn>
</math>

Variable with coefficient:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mn>3</mn><mo>&#x2062;</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>&#x2062;</mo><mi>y</mi>
</math>

Equation:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en" display="block">
  <mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>10</mn>
</math>

Invisible Operators

Invisible Multiplication

Number and variable:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mn>3</mn><mo>&#x2062;</mo><mi>x</mi>
</math>

Variable and variable:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mi>x</mi><mo>&#x2062;</mo><mi>y</mi>
</math>

Number with unit:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mn>100</mn><mo>&#x2062;</mo><mi mathvariant="normal">m</mi>
</math>

Invisible Function Application

Function call:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mi>f</mi><mo>&#x2061;</mo><mo>(</mo><mi>x</mi><mo>)</mo>
</math>

Multiple arguments:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mi>g</mi><mo>&#x2061;</mo><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo>
</math>

Special Characters

Mathematical Symbols

Minus sign (not hyphen):

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mn>5</mn><mo>&#x2212;</mo><mn>3</mn>
</math>

Prime:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mi>x</mi><mo>&#x2032;</mo>
</math>

Element of:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mi>x</mi><mo>&#x2208;</mo><mi>A</mi>
</math>

Greek Letters

Alpha, beta, gamma:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mi>&#x3B1;</mi><mo>+</mo><mi>&#x3B2;</mi><mo>=</mo><mi>&#x3B3;</mi>
</math>

Delta:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mi>&#x394;</mi><mi>x</mi>
</math>

Pi:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mi>&#x3C0;</mi><mo>&#x2062;</mo><mi>r</mi><mo>&#x2072;</mo>
</math>

Chemistry Markup

Chemical Formulas

Water (H₂O):

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <msub><mi>H</mi><mn>2</mn></msub><mi>O</mi>
</math>

Carbon dioxide (CO₂):

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mi>C</mi><msub><mi>O</mi><mn>2</mn></msub>
</math>

Isotope Notation

Carbon-14:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mmultiscripts>
    <mi>C</mi>
    <mn>14</mn>
    <none/>
    <mn>6</mn>
  </mmultiscripts>
</math>

Labeled Equations

Simple Labeled Equation

Equation with label:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en" display="block">
  <mtable>
    <mtr>
      <mtd><mi>E</mi><mo>=</mo><mi>m</mi><mo>&#x2062;</mo><msup><mi>c</mi><mn>2</mn></msup></mtd>
      <mtd><mo>(</mo><mn>1</mn><mo>)</mo></mtd>
    </mtr>
  </mtable>
</math>

Crossed Out Math

Diagonal Strike

Crossed out expression:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <menclose notation="updiagonalstrike">
    <mn>3</mn><mo>+</mo><mn>2</mn>
  </menclose>
</math>

Fill-in-the-blanks

Simple Blank

Single blank:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mn>3</mn><mo>+</mo><mi>&#x9109;</mi><mo>=</mo><mn>5</mn>
</math>

Units

Basic Units

Meters:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mn>100</mn><mo>&#x2062;</mo><mi mathvariant="normal">m</mi>
</math>

Kilometers per hour:

<math xmlns="http://www.w3.org/1998/Math/MathML" xml:lang="en">
  <mn>50</mn><mo>&#x2062;</mo><mi mathvariant="normal">km/h</mi>
</math>

Common Mistakes to Avoid

Deprecated Elements

❌ Don't use mfenced:

<!-- DEPRECATED -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mfenced><mn>3</mn><mo>+</mo><mn>2</mn></mfenced>
</math>

✅ Use mo elements instead:

<!-- CORRECT -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mo>(</mo><mn>3</mn><mo>+</mo><mn>2</mn><mo>)</mo>
</math>

Deprecated Namespace

❌ Don't use m: prefix:

<!-- DEPRECATED -->
<m:math xmlns:m="http://www.w3.org/1998/Math/MathML">
  <m:mn>3</m:mn><m:mo>+</m:mo><m:mn>2</m:mn>
</m:math>

✅ Use direct namespace:

<!-- CORRECT -->
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mn>3</mn><mo>+</mo><mn>2</mn>
</math>

Testing Examples

Basic Test

curl -H 'Content-Type: application/json' \
  -d '{
    "contentType": "math",
    "content": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\" xml:lang=\"en\"><mn>3</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>5</mn></math>"
  }' \
  -X POST \
  http://localhost:3000/

Chemistry Test

curl -H 'Content-Type: application/json' \
  -d '{
    "contentType": "math",
    "content": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>H</mi><mn>2</mn></msub><mi>O</mi></math>"
  }' \
  -X POST \
  http://localhost:3000/

Version Detection Test

curl -H 'Content-Type: application/json' \
  -d '{
    "content": "<m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mn>3</m:mn><m:mo>+</m:mo><m:mn>2</m:mn></m:math>"
  }' \
  -X POST \
  http://localhost:3000/detect-version

Migration Test

curl -H 'Content-Type: application/json' \
  -d '{
    "content": "<m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mn>3</m:mn><m:mo>+</m:mo><m:mn>2</m:mn></m:math>"
  }' \
  -X POST \
  http://localhost:3000/migrate