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Content MathML Cookbook

Module by: Connexions, Kyle Barnhart. E-mail the authors

Summary: A series of code examples explaining how to build basic algebra, calculus, trigonometry, and differential expressions using Content MathML

Content MathML, like any language, is difficult to "learn" completely. Becoming comfortable with the semantics and structure of Content MathML is a lot easier than memorizing every possible element

This MathML "cookbook" provides you with the "ingredients" (or helpful examples) to begin writing your own MathML expressions. Namespaces are not included, so please be sure to include an appropriate namespace if combining these snippets with other XML languages.

Algebra

2+2=4 2 2 4 

<math>
<apply>
  <eq/>
  <apply>
    <plus/>
    <cn>2</cn>
    <cn>2</cn>
  </apply>
  <cn>4</cn>
</apply>
</math>

x2+2⁢x+3=(x−1)⁢(x+3) x 2 2 x 3 x 1 x 3 

<math>
<apply>
  <eq/>
  <apply>
    <plus/>
    <apply>
      <power/>
      <ci>x</ci>
      <cn>2</cn>
    </apply>
    <apply>
      <times/>
      <cn>2</cn>
      <ci>x</ci>
    </apply>
    <cn>3</cn>
  </apply>
  <apply>
    <times/>
    <apply>
      <minus/>
      <ci>x</ci>
      <cn>1</cn>
    </apply>
    <apply>
      <plus/>
      <ci>x</ci>
      <cn>3</cn>
    </apply>
  </apply>
</apply>
</math>

x=c−ba x c b a 

<math>
<apply>
  <eq/>
  <ci>x</ci>
  <apply>
    <divide/>
    <apply>
      <minus/>
      <ci>c</ci>
      <ci>b</ci>
    </apply>
    <ci>a</ci>
  </apply>
</apply>
</math>

b3=log 2 a 3 b 2 a 

<math>
<apply>
  <eq/>
  <apply>
    <root/>
    <degree>
      <cn>3</cn>
    </degree>
    <ci>b</ci>
  </apply>
  <apply>
    <log/>
    <logbase>
      <cn>2</cn>
    </logbase>
    <ci>a</ci>
  </apply>
</apply>
</math>

Trigonometry

sin2θ+cos2θ=1 θ 2 θ 2 1 

<math>
  <apply>
    <eq/>
    <apply>
      <plus/>
      <apply>
        <power/>
        <apply>
          <sin/>
          <ci>?</ci>
        </apply>
        <cn>2</cn>
      </apply>
      <apply>
        <power/>
        <apply>
          <cos/>
          <ci>?</ci>
        </apply>
        <cn>2</cn>
      </apply>
    </apply>
    <cn>1</cn>
  </apply>
</math>

Calculus

limit   h → 0 f⁢x+h−f⁢xh h 0 f x h f x h 

<math>
  <apply>
    <limit/>
    <bvar>
      <ci>h</ci>
    </bvar>
    <lowlimit>
      <cn>0</cn>
    </lowlimit>
    <apply>
      <divide/>
      <apply>
        <minus/>
        <apply>
          <ci>f</ci>
          <apply>
            <plus/>
            <ci>x</ci>
            <ci>h</ci>
          </apply>
        </apply>
        <apply>
          <ci>f</ci>
          <ci>x</ci>
        </apply>
      </apply>
      <ci>h</ci>
    </apply>
  </apply>
</math>

F⁢x=∫axf⁢td t F x t a x f t 

<math>
  <apply>
    <eq/>
    <apply>
      <ci>F</ci>
      <ci>x</ci>
    </apply>
    <apply>
      <int/>
      <bvar>
        <ci>t</ci>
      </bvar>
      <lowlimit>
        <ci>a</ci>
      </lowlimit>
      <uplimit>
        <ci>x</ci>
      </uplimit>
      <apply>
        <ci>f</ci>
        <ci>t</ci>
      </apply>
    </apply>
  </apply>
</math>

Differential Equations

dd x f ⁢ y x f y 

<math>
<apply>
  <diff/>
  <bvar><ci> x </ci></bvar>
  <apply><ci> f </ci>
    <ci> y </ci>
  </apply>
</apply>
</math>

∂2f⁢xy∂ x ∂ y x y f x y 

<math>
  <apply>
    <partialdiff/>
    <bvar>
      <ci>x</ci>
    </bvar>
    <bvar>
      <ci>y</ci>
    </bvar>
    <apply>
      <ci type="function">f</ci>
      <ci>x</ci>
      <ci>y</ci>
    </apply>
  </apply>
</math>

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