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Some simple examples of embedded semantic tree. Note that for readability the attributes have been abbreviated.
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A list of issues:
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* Currently I am rebuilding the MathML tree, by cloning the original node. Is that what we want?
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* What do we do with empty element or empty mrows. For illustration see below on Implicit multiplication.
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* Usually the MathML does not change significantly. There are exceptions, though. Mmultiscripts for example.
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Some simple examples of embedded semantic tree. Note that for readability the attributes of the MathML elements have been abbreviated. Usually they have a 'semantic-' prefix.
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## Single Operation
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| ... | ... | @@ -42,12 +37,12 @@ Semantic Tree: |
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Semantically enriched MathML:
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```html
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<math>
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<mrow semantic-type="infixop" semantic-role="addition" id="5" semantic-content="1,3" semantic-children="0,2,4">
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="5">a</mi>
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<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="5">+</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="5">b</mi>
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<mo semantic-type="operator" semantic-role="addition" id="3" semantic-operator="infixop,+" semantic-parent="5">+</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="5">c</mi>
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<mrow type="infixop" role="addition" id="5" content="1,3" children="0,2,4">
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<mi type="identifier" role="latinletter" id="0" parent="5">a</mi>
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<mo type="operator" role="addition" id="1" operator="infixop,+" parent="5">+</mo>
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<mi type="identifier" role="latinletter" id="2" parent="5">b</mi>
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<mo type="operator" role="addition" id="3" operator="infixop,+" parent="5">+</mo>
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<mi type="identifier" role="latinletter" id="4" parent="5">c</mi>
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</mrow>
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</math>
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```
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| ... | ... | @@ -68,13 +63,13 @@ Original MathML: |
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Semantically enriched MathML:
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```html
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<math>
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<mrow semantic-type="relseq" semantic-role="equality" id="6" semantic-content="1" semantic-children="0,5">
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<mn semantic-type="number" semantic-role="integer" id="0" semantic-parent="6">5</mn>
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<mo semantic-type="relation" semantic-role="equality" id="1" semantic-operator="relseq,=" semantic-parent="6">=</mo>
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<mrow semantic-type="infixop" semantic-role="addition" id="5" semantic-content="3" semantic-children="2,4" semantic-parent="6">
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<mn semantic-type="number" semantic-role="integer" id="2" semantic-parent="5">3</mn>
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<mo semantic-type="operator" semantic-role="addition" id="3" semantic-operator="infixop,+" semantic-parent="5">+</mo>
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<mn semantic-type="number" semantic-role="integer" id="4" semantic-parent="5">2</mn>
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<mrow type="relseq" role="equality" id="6" content="1" children="0,5">
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<mn type="number" role="integer" id="0" parent="6">5</mn>
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<mo type="relation" role="equality" id="1" operator="relseq,=" parent="6">=</mo>
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<mrow type="infixop" role="addition" id="5" content="3" children="2,4" parent="6">
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<mn type="number" role="integer" id="2" parent="5">3</mn>
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<mo type="operator" role="addition" id="3" operator="infixop,+" parent="5">+</mo>
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<mn type="number" role="integer" id="4" parent="5">2</mn>
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</mrow>
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</mrow>
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</math>
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| ... | ... | @@ -96,13 +91,13 @@ Original MathML: |
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Enriched MathML:
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```html
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<math>
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<mrow semantic-type="relseq" semantic-role="equality" id="6" semantic-content="1" semantic-children="0,5">
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<mi semantic-type="number" semantic-role="integer" id="0" semantic-parent="6">5</mi>
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<mo semantic-type="relation" semantic-role="equality" id="1" semantic-operator="relseq,=" semantic-parent="6">=</mo>
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<mrow semantic-type="infixop" semantic-role="addition" id="5" semantic-content="3" semantic-children="2,4" semantic-parent="6">
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<mi semantic-type="number" semantic-role="integer" id="2" semantic-parent="5">3</mi>
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<mo semantic-type="operator" semantic-role="addition" id="3" semantic-operator="infixop,+" semantic-parent="5">+</mo>
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<mi semantic-type="number" semantic-role="integer" id="4" semantic-parent="5">2</mi>
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<mrow type="relseq" role="equality" id="6" content="1" children="0,5">
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<mi type="number" role="integer" id="0" parent="6">5</mi>
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<mo type="relation" role="equality" id="1" operator="relseq,=" parent="6">=</mo>
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<mrow type="infixop" role="addition" id="5" content="3" children="2,4" parent="6">
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<mi type="number" role="integer" id="2" parent="5">3</mi>
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<mo type="operator" role="addition" id="3" operator="infixop,+" parent="5">+</mo>
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<mi type="number" role="integer" id="4" parent="5">2</mi>
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</mrow>
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</mrow>
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</math>
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| ... | ... | @@ -127,18 +122,18 @@ Original MathML: |
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Semantically enriched MathML:
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```html
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<math>
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<mrow semantic-type="infixop" semantic-role="addition" id="9" semantic-content="5" semantic-children="8,6">
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<mrow semantic-type="infixop" semantic-role="subtraction" id="8" semantic-content="3" semantic-children="7,4" semantic-parent="9">
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<mrow semantic-type="infixop" semantic-role="addition" id="7" semantic-content="1" semantic-children="0,2" semantic-parent="8">
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="7">a</mi>
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<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="7">+</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="7">b</mi>
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<mrow type="infixop" role="addition" id="9" content="5" children="8,6">
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<mrow type="infixop" role="subtraction" id="8" content="3" children="7,4" parent="9">
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<mrow type="infixop" role="addition" id="7" content="1" children="0,2" parent="8">
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<mi type="identifier" role="latinletter" id="0" parent="7">a</mi>
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<mo type="operator" role="addition" id="1" operator="infixop,+" parent="7">+</mo>
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<mi type="identifier" role="latinletter" id="2" parent="7">b</mi>
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</mrow>
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<mo semantic-type="operator" semantic-role="subtraction" id="3" semantic-operator="infixop,-" semantic-parent="8">-</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="8">c</mi>
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<mo type="operator" role="subtraction" id="3" operator="infixop,-" parent="8">-</mo>
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<mi type="identifier" role="latinletter" id="4" parent="8">c</mi>
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</mrow>
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<mo semantic-type="operator" semantic-role="addition" id="5" semantic-operator="infixop,+" semantic-parent="9">+</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="6" semantic-parent="9">d</mi>
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<mo type="operator" role="addition" id="5" operator="infixop,+" parent="9">+</mo>
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<mi type="identifier" role="latinletter" id="6" parent="9">d</mi>
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</mrow>
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</math>
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```
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| ... | ... | @@ -165,23 +160,23 @@ Original MathML: |
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Semantically enriched MathML:
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```html
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<math>
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<mrow semantic-type="infixop" semantic-role="addition" id="10" semantic-content="1,6" semantic-children="0,13,14">
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="10">a</mi>
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<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="10">+</mo>
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<mrow semantic-type="infixop" semantic-role="multiplication" id="13" semantic-content="3" semantic-children="2,12" semantic-parent="10">
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<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="13">b</mi>
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<mo semantic-type="operator" semantic-role="multiplication" id="3" semantic-operator="infixop,∘" semantic-parent="13">∘</mo>
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<mrow semantic-type="infixop" semantic-role="implicit" id="12" semantic-content="11" semantic-children="4,5" semantic-parent="13">
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<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="12">c</mi>
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<mrow semantic-type="operator" semantic-role="multiplication" id="11" semantic-children="" semantic-operator="infixop," semantic-parent="12"/>
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<mi semantic-type="identifier" semantic-role="latinletter" id="5" semantic-parent="12">d</mi>
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<mrow type="infixop" role="addition" id="10" content="1,6" children="0,13,14">
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<mi type="identifier" role="latinletter" id="0" parent="10">a</mi>
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<mo type="operator" role="addition" id="1" operator="infixop,+" parent="10">+</mo>
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<mrow type="infixop" role="multiplication" id="13" content="3" children="2,12" parent="10">
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<mi type="identifier" role="latinletter" id="2" parent="13">b</mi>
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<mo type="operator" role="multiplication" id="3" operator="infixop,∘" parent="13">∘</mo>
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<mrow type="infixop" role="implicit" id="12" content="11" children="4,5" parent="13">
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<mi type="identifier" role="latinletter" id="4" parent="12">c</mi>
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<mrow type="operator" role="multiplication" id="11" children="" operator="infixop," parent="12"/>
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<mi type="identifier" role="latinletter" id="5" parent="12">d</mi>
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</mrow>
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</mrow>
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<mo semantic-type="operator" semantic-role="addition" id="6" semantic-operator="infixop,+" semantic-parent="10">+</mo>
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<mrow semantic-type="infixop" semantic-role="multiplication" id="14" semantic-content="8" semantic-children="7,9" semantic-parent="10">
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<mi semantic-type="identifier" semantic-role="latinletter" id="7" semantic-parent="14">e</mi>
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<mo semantic-type="operator" semantic-role="multiplication" id="8" semantic-operator="infixop,∘" semantic-parent="14">∘</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="9" semantic-parent="14">f</mi>
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<mo type="operator" role="addition" id="6" operator="infixop,+" parent="10">+</mo>
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<mrow type="infixop" role="multiplication" id="14" content="8" children="7,9" parent="10">
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<mi type="identifier" role="latinletter" id="7" parent="14">e</mi>
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<mo type="operator" role="multiplication" id="8" operator="infixop,∘" parent="14">∘</mo>
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<mi type="identifier" role="latinletter" id="9" parent="14">f</mi>
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</mrow>
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</mrow>
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</math>
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| ... | ... | @@ -222,10 +217,10 @@ Semantic Tree: |
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Semantically enriched MathML:
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```html
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<math>
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<mrow semantic-type="infixop" semantic-role="implicit" id="3" semantic-content="2" semantic-children="0,1">
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="3">a</mi>
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<mrow semantic-type="operator" semantic-role="multiplication" id="2" semantic-children="" semantic-operator="infixop," semantic-parent="3"/>
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<mi semantic-type="identifier" semantic-role="latinletter" id="1" semantic-parent="3">b</mi>
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<mrow type="infixop" role="implicit" id="3" content="2" children="0,1">
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<mi type="identifier" role="latinletter" id="0" parent="3">a</mi>
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<mrow type="operator" role="multiplication" id="2" children="" operator="infixop," parent="3"/>
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<mi type="identifier" role="latinletter" id="1" parent="3">b</mi>
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</mrow>
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</math>
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| ... | ... | @@ -241,10 +236,10 @@ Original MathML: |
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Semantically enriched MathML:
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<math>
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<mrow semantic-type="infixop" semantic-role="implicit" id="3" semantic-content="2" semantic-children="0,1">
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="3">a</mi>
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<mrow semantic-type="operator" semantic-role="multiplication" id="2" semantic-children="" semantic-operator="infixop," semantic-parent="3"/>
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<mi semantic-type="identifier" semantic-role="latinletter" id="1" semantic-parent="3">b</mi>
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<mrow type="infixop" role="implicit" id="3" content="2" children="0,1">
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<mi type="identifier" role="latinletter" id="0" parent="3">a</mi>
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<mrow type="operator" role="multiplication" id="2" children="" operator="infixop," parent="3"/>
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<mi type="identifier" role="latinletter" id="1" parent="3">b</mi>
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</mrow>
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</math>
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| ... | ... | @@ -268,23 +263,23 @@ Original MathML: |
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Semantically enriched MathML:
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<math>
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<mrow semantic-type="infixop" semantic-role="addition" id="10" semantic-content="1,6" semantic-children="0,13,14">
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<mi semantic-type="identifier" semantic-role="latinletter" id="0" semantic-parent="10">a</mi>
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<mo semantic-type="operator" semantic-role="addition" id="1" semantic-operator="infixop,+" semantic-parent="10">+</mo>
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<mrow semantic-type="infixop" semantic-role="multiplication" id="13" semantic-content="3" semantic-children="2,12" semantic-parent="10">
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<mi semantic-type="identifier" semantic-role="latinletter" id="2" semantic-parent="13">b</mi>
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<mo semantic-type="operator" semantic-role="multiplication" id="3" semantic-operator="infixop,∘" semantic-parent="13">∘</mo>
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<mrow semantic-type="infixop" semantic-role="implicit" id="12" semantic-content="11" semantic-children="4,5" semantic-parent="13">
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<mi semantic-type="identifier" semantic-role="latinletter" id="4" semantic-parent="12">c</mi>
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<mrow semantic-type="operator" semantic-role="multiplication" id="11" semantic-children="" semantic-operator="infixop," semantic-parent="12"/>
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<mi semantic-type="identifier" semantic-role="latinletter" id="5" semantic-parent="12">d</mi>
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<mrow type="infixop" role="addition" id="10" content="1,6" children="0,13,14">
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<mi type="identifier" role="latinletter" id="0" parent="10">a</mi>
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<mo type="operator" role="addition" id="1" operator="infixop,+" parent="10">+</mo>
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<mrow type="infixop" role="multiplication" id="13" content="3" children="2,12" parent="10">
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<mi type="identifier" role="latinletter" id="2" parent="13">b</mi>
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<mo type="operator" role="multiplication" id="3" operator="infixop,∘" parent="13">∘</mo>
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<mrow type="infixop" role="implicit" id="12" content="11" children="4,5" parent="13">
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<mi type="identifier" role="latinletter" id="4" parent="12">c</mi>
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<mrow type="operator" role="multiplication" id="11" children="" operator="infixop," parent="12"/>
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<mi type="identifier" role="latinletter" id="5" parent="12">d</mi>
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</mrow>
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</mrow>
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<mo semantic-type="operator" semantic-role="addition" id="6" semantic-operator="infixop,+" semantic-parent="10">+</mo>
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<mrow semantic-type="infixop" semantic-role="multiplication" id="14" semantic-content="8" semantic-children="7,9" semantic-parent="10">
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<mi semantic-type="identifier" semantic-role="latinletter" id="7" semantic-parent="14">e</mi>
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<mo semantic-type="operator" semantic-role="multiplication" id="8" semantic-operator="infixop,∘" semantic-parent="14">∘</mo>
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<mi semantic-type="identifier" semantic-role="latinletter" id="9" semantic-parent="14">f</mi>
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<mo type="operator" role="addition" id="6" operator="infixop,+" parent="10">+</mo>
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<mrow type="infixop" role="multiplication" id="14" content="8" children="7,9" parent="10">
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<mi type="identifier" role="latinletter" id="7" parent="14">e</mi>
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<mo type="operator" role="multiplication" id="8" operator="infixop,∘" parent="14">∘</mo>
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<mi type="identifier" role="latinletter" id="9" parent="14">f</mi>
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</mrow>
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</mrow>
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</math> |
