Integral Examples
Volker Sorge edited this page Apr 28, 2015
·
4 revisions
Example page. Back to Semantic Embedding Examples.
(Outdated! Integrals have changed now!)
Original MathML:
<math>
<mi>∫</mi>
<mi>a</mi>
<mo>+</mo>
<mi>b</mi>
<mi>dx</mi>
</math>Semantic Tree:
<stree>
<integral role="integral" id="6">
<children>
<largeop role="integral" id="0">∫</largeop>
<infixop role="addition" id="5">
+
<content>
<operator role="addition" id="2">+</operator>
</content>
<children>
<identifier role="latinletter" font="italic" id="1">a</identifier>
<identifier role="latinletter" font="italic" id="3">b</identifier>
</children>
</infixop>
<identifier role="unknown" font="normal" id="4">dx</identifier>
</children>
</integral>
</stree>Semantically enriched MathML:
<math type="integral" role="integral" id="6" children="0,5,4">
<mi type="largeop" role="integral" id="0" parent="6">∫</mi>
<mrow type="infixop" role="addition" id="5" children="1,3" content="2" parent="6">
<mi type="identifier" role="latinletter" id="1" parent="5">a</mi>
<mo type="operator" role="addition" id="2" operator="infixop,+" parent="5">+</mo>
<mi type="identifier" role="latinletter" id="3" parent="5">b</mi>
</mrow>
<mi type="identifier" role="unknown" id="4" parent="6">dx</mi>
</math>Original MathML:
<math>
<mi>∫</mi>
<mi>∫</mi>
<mi>∫</mi>
<mi>dx</mi>
<mi>dy</mi>
<mi>dz</mi>
</math>Semantic Tree:
<stree>
<integral role="integral" id="9">
<children>
<largeop role="integral" id="0">∫</largeop>
<integral role="integral" id="8">
<children>
<largeop role="integral" id="1">∫</largeop>
<integral role="integral" id="7">
<children>
<largeop role="integral" id="2">∫</largeop>
<empty role="unknown" id="6"/>
<identifier role="unknown" font="normal" id="3">dx</identifier>
</children>
</integral>
<identifier role="unknown" font="normal" id="4">dy</identifier>
</children>
</integral>
<identifier role="unknown" font="normal" id="5">dz</identifier>
</children>
</integral>
</stree>Semantically enriched MathML:
<math type="integral" role="integral" id="9" children="0,8,5">
<mi type="largeop" role="integral" id="0" parent="9">∫</mi>
<mrow type="integral" role="integral" id="8" children="1,7,4" parent="9">
<mi type="largeop" role="integral" id="1" parent="8">∫</mi>
<mrow type="integral" role="integral" id="7" children="2,6,3" parent="8">
<mi type="largeop" role="integral" id="2" parent="7">∫</mi>
<mrow type="empty" role="unknown" id="6" children="" parent="7"/>
<mi type="identifier" role="unknown" id="3" parent="7">dx</mi>
</mrow>
<mi type="identifier" role="unknown" id="4" parent="8">dy</mi>
</mrow>
<mi type="identifier" role="unknown" id="5" parent="9">dz</mi>
</math>Original MathML:
<math>
<munderover>
<mi>∫</mi>
<mn>0</mn>
<mn>10</mn>
</munderover>
<mi>x</mi>
<mi>dx</mi>
<mo>+</mo>
<munderover>
<mi>∫</mi>
<mn>10</mn>
<mn>20</mn>
</munderover>
<mi>x</mi>
<mi>dx</mi>
<mo>=</mo>
<munderover>
<mi>∫</mi>
<mn>0</mn>
<mn>20</mn>
</munderover>
<mi>x</mi>
<mi>dx</mi>
</math>Semantic Tree:
<stree>
<relseq role="equality" id="24">
=
<content>
<relation role="equality" id="13">=</relation>
</content>
<children>
<infixop role="addition" id="23">
+
<content>
<operator role="addition" id="6">+</operator>
</content>
<children>
<integral role="integral" id="22">
<children>
<limboth role="integral" id="3">
<children>
<largeop role="integral" id="0">∫</largeop>
<number role="integer" font="normal" id="1">0</number>
<number role="integer" font="normal" id="2">10</number>
</children>
</limboth>
<identifier role="latinletter" font="italic" id="4">x</identifier>
<identifier role="unknown" font="normal" id="5">dx</identifier>
</children>
</integral>
<integral role="integral" id="21">
<children>
<limboth role="integral" id="10">
<children>
<largeop role="integral" id="7">∫</largeop>
<number role="integer" font="normal" id="8">10</number>
<number role="integer" font="normal" id="9">20</number>
</children>
</limboth>
<identifier role="latinletter" font="italic" id="11">x</identifier>
<identifier role="unknown" font="normal" id="12">dx</identifier>
</children>
</integral>
</children>
</infixop>
<integral role="integral" id="20">
<children>
<limboth role="integral" id="17">
<children>
<largeop role="integral" id="14">∫</largeop>
<number role="integer" font="normal" id="15">0</number>
<number role="integer" font="normal" id="16">20</number>
</children>
</limboth>
<identifier role="latinletter" font="italic" id="18">x</identifier>
<identifier role="unknown" font="normal" id="19">dx</identifier>
</children>
</integral>
</children>
</relseq>
</stree>Semantically enriched MathML:
<math type="relseq" role="equality" id="24" children="23,20" content="13">
<mrow type="infixop" role="addition" id="23" children="22,21" content="6" parent="24">
<mrow type="integral" role="integral" id="22" children="3,4,5" parent="23">
<munderover type="limboth" role="integral" id="3" children="0,1,2" parent="22">
<mi type="largeop" role="integral" id="0" parent="3">∫</mi>
<mn type="number" role="integer" id="1" parent="3">0</mn>
<mn type="number" role="integer" id="2" parent="3">10</mn>
</munderover>
<mi type="identifier" role="latinletter" id="4" parent="22">x</mi>
<mi type="identifier" role="unknown" id="5" parent="22">dx</mi>
</mrow>
<mo type="operator" role="addition" id="6" operator="infixop,+" parent="23">+</mo>
<mrow type="integral" role="integral" id="21" children="10,11,12" parent="23">
<munderover type="limboth" role="integral" id="10" children="7,8,9" parent="21">
<mi type="largeop" role="integral" id="7" parent="10">∫</mi>
<mn type="number" role="integer" id="8" parent="10">10</mn>
<mn type="number" role="integer" id="9" parent="10">20</mn>
</munderover>
<mi type="identifier" role="latinletter" id="11" parent="21">x</mi>
<mi type="identifier" role="unknown" id="12" parent="21">dx</mi>
</mrow>
</mrow>
<mo type="relation" role="equality" id="13" operator="relseq,=" parent="24">=</mo>
<mrow type="integral" role="integral" id="20" children="17,18,19" parent="24">
<munderover type="limboth" role="integral" id="17" children="14,15,16" parent="20">
<mi type="largeop" role="integral" id="14" parent="17">∫</mi>
<mn type="number" role="integer" id="15" parent="17">0</mn>
<mn type="number" role="integer" id="16" parent="17">20</mn>
</munderover>
<mi type="identifier" role="latinletter" id="18" parent="20">x</mi>
<mi type="identifier" role="unknown" id="19" parent="20">dx</mi>
</mrow>
</math>