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Created Big Operator and Function Examples (markdown) authored by Volker Sorge's avatar Volker Sorge
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Example page. Back to [[Semantic Embedding Examples]].
### Sums and Products
In Bigop type nodes the content pointer leads to the large operator.
Original MathML:
```html
<math>
<mrow>
<munderover>
<mi>∑</mi>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>∞</mi>
</munderover>
<munderover>
<mi>∏</mi>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>∞</mi>
</munderover>
<msup>
<mi>n</mi>
<mi>m</mi>
</msup>
</mrow>
</math>
```
Semantically enriched MathML:
```html
<math>
<mrow type="bigop" role="sum" id="18" children="6,17" content="0">
<munderover type="limboth" role="sum" id="6" children="0,4,5" parent="18">
<mi type="largeop" role="sum" id="0" parent="18" operator="bigop">∑</mi>
<mrow type="relseq" role="equality" id="4" children="1,3" content="2" parent="6">
<mi type="identifier" role="latinletter" id="1" parent="4">n</mi>
<mo type="relation" role="equality" id="2" parent="4" operator="relseq,=">=</mo>
<mn type="number" role="integer" id="3" parent="4">0</mn>
</mrow>
<mi type="identifier" role="unknown" id="5" parent="6">∞</mi>
</munderover>
<mrow type="bigop" role="sum" id="17" children="13,16" content="7" parent="18">
<munderover type="limboth" role="sum" id="13" children="7,11,12" parent="17">
<mi type="largeop" role="sum" id="7" parent="17" operator="bigop">∏</mi>
<mrow type="relseq" role="equality" id="11" children="8,10" content="9" parent="13">
<mi type="identifier" role="latinletter" id="8" parent="11">m</mi>
<mo type="relation" role="equality" id="9" parent="11" operator="relseq,=">=</mo>
<mn type="number" role="integer" id="10" parent="11">0</mn>
</mrow>
<mi type="identifier" role="unknown" id="12" parent="13">∞</mi>
</munderover>
<msup type="superscript" role="latinletter" id="16" children="14,15" parent="17">
<mi type="identifier" role="latinletter" id="14" parent="16">n</mi>
<mi type="identifier" role="latinletter" id="15" parent="16">m</mi>
</msup>
</mrow>
</mrow>
</math>
```
### Integrals
Integrals are similar to big op types.
Original MathML:
```html
<math>
<munder>
<mi>∫</mi>
<mi>X</mi>
</munder>
<mi>x</mi>
<mi>dx</mi>
</math>
```
Semantically enriched MathML:
```html
<math type="integral" role="integral" id="5" children="2,3,4" content="0">
<munder type="limlower" role="integral" id="2" children="0,1" parent="5">
<mi type="largeop" role="integral" id="0" parent="5" operator="integral">∫</mi>
<mi type="identifier" role="latinletter" id="1" parent="2">X</mi>
</munder>
<mi type="identifier" role="latinletter" id="3" parent="5">x</mi>
<mi type="identifier" role="unknown" id="4" parent="5">dx</mi>
</math>
```
### Functions
Functions have two content pointers: The first pointing to the invisible function application element that is given as an explicit operator. The second points to the function name.
Original MathML:
```html
<math>
<mrow>
<mi>sin</mi>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
</math>
```
Semantically enriched MathML:
```html
<math>
<mrow type="appl" role="prefix function" id="6" children="0,4" content="5,0">
<mi type="function" role="prefix function" id="0" parent="6" operator="appl">sin</mi>
<mo type="punctuation" role="application" id="5" parent="6" added="true" operator="appl">⁡</mo>
<mrow type="fenced" role="leftright" id="4" children="2" content="1,3" parent="6">
<mo type="fence" role="open" id="1" parent="4" operator="fenced">(</mo>
<mi type="identifier" role="latinletter" id="2" parent="4">x</mi>
<mo type="fence" role="close" id="3" parent="4" operator="fenced">)</mo>
</mrow>
</mrow>
</math>
```
The same holds for "simple" functions. Here's a nested example:
Original MathML:
```html
<math>
<mrow>
<mi>g</mi>
<mo>(</mo>
<mi>f</mi>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
</math>
```
Semantically enriched MathML:
```html
<math>
<mrow type="appl" role="simple function" id="12" children="0,10" content="11,0">
<mi type="identifier" role="simple function" id="0" parent="12" operator="appl">g</mi>
<mo type="punctuation" role="application" id="11" parent="12" added="true" operator="appl">⁡</mo>
<mrow type="fenced" role="leftright" id="10" children="9" content="1,6" parent="12">
<mo type="fence" role="open" id="1" parent="10" operator="fenced">(</mo>
<mrow type="appl" role="simple function" id="9" children="2,7" content="8,2" parent="10">
<mi type="identifier" role="simple function" id="2" parent="9" operator="appl">f</mi>
<mo type="punctuation" role="application" id="8" parent="9" added="true" operator="appl">⁡</mo>
<mrow type="fenced" role="leftright" id="7" children="4" content="3,5" parent="9">
<mo type="fence" role="open" id="3" parent="7" operator="fenced">(</mo>
<mi type="identifier" role="latinletter" id="4" parent="7">x</mi>
<mo type="fence" role="close" id="5" parent="7" operator="fenced">)</mo>
</mrow>
</mrow>
<mo type="fence" role="close" id="6" parent="10" operator="fenced">)</mo>
</mrow>
</mrow>
</math>
```