(Translator page, or embed within page)
Consult the W3C Specification for MathML 2.0, specifically Chapter 4.
| Source: | Content MathML: | Rendered: | |
| Number: | 1 | 1]]> |
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| Basic Identifier: | x | x]]> |
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| Selector: | x_1 |
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| Multiple Selector: | A_{0 1} |
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| Negation: | -1 |
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| Stand-alone Element: | \pi; | ]]> |
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| Special Character: | θ | θ]]> |
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| Basic Infix Operator: | x+y |
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| Basic Function: | f(x,y) |
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| Implied Multiplication: | 2\pi; |
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| Factorial: | n! |
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| Basic Infix Relation: | x<y |
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| Infix Element: | x\in|C |
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| Infix Attribute: | x\tendsto@above|c |
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| Applied Element: | \sin{x} |
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| Qualifier: | \int[v:x]{\sin{x}} |
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| Nested Qualifier: | \diff[v:x[n:2]]{f(x)} |
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| Element Attribute: | \tendsto@above{x c} |
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| Environment: | \begin{interval}
0 1
\end{interval} |
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| Environment Qualifier: | \begin[v:x]{lambda}
f(x)
\end{lambda}
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| Environment Attribute: | \begin{interval}
@open-closed
0 1
\end{interval} |
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| Separator: | \begin{cn}
@complex-cartesian
3 || 2
\end{cn} |
3 |
| Source: | Content MathML: |
| Source: | Content MathML: |
| foo(...) |
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| \foo; | <foo/> |
| x\foo|y |
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| x\foo@bar|y |
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| &foo; | &foo;]]> |
| \foo{...} |
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| \foo@bar{...} |
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| \begin{foo}...\end{foo} | ... ]]> |
| \begin{foo}@bar...\end{foo} | ... ]]> |
Applied elements ("\foo{...}") and environments ("\begin{foo}...\end{foo}") both support n-ary lists of arguments, separated by spaces. In some cases, grouping (using either "(...)" or "{...}") may be necessary in lists to resolve issues of ambiguous syntax, e.g. with implied multiplication. For example, in the matrix example below, in the segment "\begin{matrixrow}\cos{θ} (-\sin{θ})\end{matrixrow}," the parentheses around the "-\sin{θ}" indicate that it is a separate entry in the matrix, not part of an expression for the difference of the two entries in the "matrixrow." Lists of arguments in basic function expressions ("f(x,y)") may be separated using either commas or spaces, but if spaces are used, the same restrictions as above apply.
Also, any time an infix element ("x\foo|y") appears inside another element as part of an n-ary list it must be enclosed in brackets ("{x\foo|y}"), even if it is the only item in the list. For example, in the limit example below, the brackets are required around the "\tendsto|" element in the qualifier "[c:{x\tendsto@above|0}]." Brackets are otherwise usually not necessary around the standard infix relations or operators in a list, though. The brackets prevent the translator from getting confused between an infix element in the current item in the list and an applied element at the beginning of the next item.
| Binary Operators: | +, -, *, /, ^, with standard precedence and grouping by (...) |
| Binary Relations: | <, <=, >, >=, /=, with grouping by {...} |
| Other: | factorial x!, some limited support for implied multiplication |
Qualifiers work with applied elements or environments, as seen in the above examples, "\int[v:x]{\sin{x}}," in which the qualifier tag specifies the bound variable for the integral, and "\begin[v:x]{lambda}f(x)\end{lambda}," in which the qualifier tag specifies the bound variable for the lambda-calculus operator. The tags support n-ary lists of items within the tags, separated by spaces. The "[s:...]" tag, corresponding to the "<list>" qualifier, is mostly used with the "<partialdiff/>" tag when no bound variables are specified, to give a list of the variables with respect to which the derivatives are taken. In some rare instances, qualifier tags can be nested, as for example when specifying the order of a derivative with respect to a certain variable, as in the above example, "\diff[v:x[n:2]]{f(x)}." In this case, the inner qualifier tag(s) must be the last item(s) in the list of elements within the outer tag.
The "@" construct in source allows certain tags to support attributes, although the syntax does not allow any tag to support more than one attribute. Only infix elements, applied elements, and environments in the source syntax support attributes. When the "@" construct appears in an environment, it must be the first element in the environment. The table below indicates which tags support which attributes, with possible values.
| Element: | Attribute: | Allowed values: |
| cn | type | real, integer, rational, e-notation, complex-cartesian, complex-polar |
| ci | type | many -- see W3C documentation (generally do not affect rendering) |
| tendsto | type | two-sided, above, below |
| set | type | normal, multiset |
| interval | closure | closed, open, open-closed, closed-open |
| list | order | numerical, lexicographic |
Note: The \tendsto element may be used in either infix or applied form, and in either form the "@" construct adds the "type" attribute as indicated in the above table. The other elements which support attributes must all be used in environment form. In particular, in order to use the type attribute for the <cn> tag, the tag must be treated as an environment in the source syntax. In this situation, the source element "||" is an abbreviation for the "<sep/>" tag, to separate the parts of "e-notation," "rational," "complex-cartesian," or "complex-polar" type tokens.
Since the source-to-destination mapping is essentially syntactic (except for the qualifier tags and attributes), all other Content MathML elements should be supported, in one form or another. However, in particular since certain attributes are not supported in the source syntax, users should learn enough Content MathML to be able to find the affected elements and modify them as needed to include the desired attributes.
| Source: | Content MathML: | Rendered: |
| \int[v:x][l:0][u:\pi;]{\sin{x}}=2 |
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\limit[v:x][c:{x\tendsto@above|0}]{\sin{x}/x}=1 |
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=0
\end{piece}
\begin{otherwise}
-x
\end{otherwise}
\end{piecewise}]]> |
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x_1=(-b+\root{b^2-4a*c})/2a |
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\sum[v:n][l:1][u:\infinity;]{1/n^2}=\pi;^2/6
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\int[v:x][l:-\infinity;][u:\infinity;]
{\exp{-(x^2)}}=\root{\pi;}
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\diff[v:x]{
\int[v:t][l:a][u:x]{f(t)}
}=f(x)
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\begin{apply}
\partialdiff[s:x y]{f} x y
\end{apply}
=\partialdiff[v:x][v:y]{f(x,y)} |
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Note: I have modified the XSLT stylesheet "ctop.xsl" from W3C to improve the mapping from Content MathML to Presentation MathML. In particular, I have:
The translator page and this page both use the modified version of the stylesheet. The ability to test quickly the changes in the stylesheet has demonstrated the strength of the translator. However, Design Science MathPlayer seems to use its own stylesheet and ignores the locally loaded stylesheet. Their stylesheet is better than the W3C stylesheet, but still has problems. For example, the numerator exponent in a high-order mixed partial derivative is not rendered correctly, and the stylesheet doesn't seem to recognize certain types when applied to the <cn> tag.