Annex C: MathML
Annex C: MathML
This Appendix is a supplement to Module: Math.
Tags and Attributes for Math
In addition to the <formula> tag that is described in section 10.7.3 (page 912) of the PDF 1.7 Reference, the following tags ("Structure Types") and attributes ("Structure Attributes") are used for math. These tags and attributes are specified in detail in the MathML 2.0 recommendation and are summarized below. With the exception of the <math> and <semantics> tags, these tags are part of chapter 3 (Presentation Markup) of the MathML 2.0 recommendation.
Tags for Math
The following tags are used to represent MathML inside of a <formula> tag:
| Structure Type | Description |
|---|---|
| math | The root element of the MathML. |
| mi | Leaf element whose content is an identifier. |
| mn | Leaf element whose content is a number. |
| mo | Leaf element whose content is an operator. |
| mtext | Leaf element whose content is arbitrary text. |
| mspace | Leaf element whose content is a space whose width and height are given by attributes. If this element is used, a physical whitespace character should be in the document. |
| ms | Leaf element whose content is a string. The delimiters of the string are given by the lquote and rqoute attributes. The delimiters should not be part of the content of the element. |
| mglyph | Leaf element whose content is an identifier. |
| mrow | Group any number of horizontally laid out elements together. |
| mfrac | A vertical or beveled fraction with exactly two children. |
| msqrt | A square root with exactly one child. |
| mroot | A radical with exactly two children: the index and the radicand. |
| mstyle | Change the style of how the child is displayed by changing attributes that are inherited by the children. |
| merror | Enclose a syntax error message from a preprocessor or otherwise indicate an error. |
| mpadded | Adjust the vertical or horizontal space around the child. |
| mphantom | Make the child invisible but preserve its size. If this element is used, either a white space character must be used or what is drawn should match the background so that it is invisible. It should not be spoken. |
| mfenced | Surround the children with "fences" (e.g., parenthesis) and add separators as specified by the open, close, and separators notations. Neither the fences nor the separator(s) should be children of this element. |
| menclose | Enclose the children with lines, circles, cross-outs, or other decorations as specified by the notation attribute. |
| msub | An expression with a subscript. Both the base and the subscript are children. |
| msup | An expression with a superscript. Both the base and the superscript are children. |
| msubsup | An expression with a subscript and a superscript. The base, subscript and superscript are children. |
| munder | An expression with underscript or lower limit. |
| mover | An expression with overscript or upper limit. |
| munderover | An expression with both an underscript/lower limit and an overscript/upper limit. |
| mmultiscripts | An expression with prescripts (sub/superscripts to the left of the base) or tensor indices. The base of the multiscript should be the first child, followed by pairs of lower and upper indices (subscripts/superscripts). Missing scripts are indicated using the none elements. Pairs of prescripts follow the postscripts and must be preceded by a mprescripts element. |
| none | Valid as a child of mmultiscripts. none is used to indicate a unused subscript or superscript as part of a subscript/superscript pair. In MathML, this is an empty element but because of the requirements for structure elements in PDF, it must point to some content. It is recommended that applications insert a whitespace character in the empty position so this element can refer to some content. |
| mprescripts | Valid as a child of mmultiscripts. mprescripts is used to indicate the start of prescript subscript/superscript pairs. In MathML, this is an empty element but because of the requirements for structure elements in PDF, it must point to some content. It is recommended that applications insert a whitespace character immediately before or after the notation so this element can point to some content. |
| mtable | A matrix or other tabular mathematical layout. MathML tables are similar to HTML tables and consist of one or more table rows (mtr or mlabeledtr). Unlike PDF tables, MathML tables have no headers or captions because headers are not mathematical expressions. |
| mtr | A row in a mtable. Its parent must be mtable. |
| mlabeledtr | A row in a table that has a label on either the left or right side, as determined by the side attribute. The label is the first child of mlabeledtr The rest of the children represent the contents of the row and are identical to those used for mtr; all of the children except the first must be mtd elements. Like mtr, its parent must be mtable. |
| mtd | One entry, or cell, in a table or matrix. An mtd element is only allowed as a direct child of an mtr or an mlabeledtr element. |
| maligngroup | An alignment marker that is used to help vertically align specified points within a column of MathML expressions. maligngroup is a space-like leaf element that is used divide a column up into groups; see the MathML recommendation for more details. In MathML, this is an empty element. It is recommended that applications insert a whitespace character that corresponds to the maligngroup element. |
| malignmark | An alignment marker that is used to help vertically align specified points within a column of MathML expressions. It specifies a specific alignment point within a maligngroup. Like maligngroup, it is a space-like leaf element; see the MathML recommendation for more details. In MathML, this is an empty element. It is recommended that applications insert a whitespace character that corresponds to the malignmark element. |
| maction | In MathML, maction is used to to bind actions to expressions. In a PDF document, no action is associated with this element although a plug-in could be written to enliven the expression. maction is mainly provided for compatibility. maction takes an arbitrary number of children, although only one child is displayed. Children that are not rendered can not be part of the structure tree and their representation in PDF is currently not specified |
| semantics | Associates a specific notation with a notation-independent representation that carries more semantic information. For PDF, the first child must be the MathML for the notation being displayed. In MathML, subsequent elements (annotation, annotation-xml) specify alternative encodings and are not rendered. Children that are not rendered can not be part of the structure tree and their representation in PDF is currently not specified |
| annotation | A child element of semantics whose child provides an alternative non-XML representation of the contents of the semantics element. This element cannot currently be part of the structure tree. For more information, see semantics. |
| annotation-xml | A child element of semantics whose child provides an alternative XML-based representation of the contents of the semantics element. This element cannot currently be part of the structure tree. For more information, see semantics. |
MathML contains a set of "content" tags that are notation-independent semantic tags. These tags are not allowed in PDF unless they are inside of a <semantics> tag.
Attributes for Math
The (new) attribute owner "MathML" shall be associated with the attributes listed below.
The following tables list all of the attributes associated with the MathML tags listed in the previous section. The description of each attribute is given in MathML 2.0 recommendation. They are listed below for completeness.
Unless otherwise noted:
- these attributes are not inherited (i.e., they apply only to the current element of the structure tree, not the children of the element);
- these attributes are optional
- the "type" for each value is "string"
- "class", "id", "style", "xref", and "xlink:href" are legal attributes for all tags
The attributes exist for compatibility with MathML generation tools and to allow translation of the math to an XML dialect.
| Structure Elements | Attributes |
|---|---|
| math | display, altimg, alttext |
| mi, mn, mtext | mathvariant, mathsize, mathcolor, mathbackground |
| mo | mathvariant, mathsize, mathcolor, mathbackground, form, fence, separator, lspace, rspace, stretchy, symmetric, maxsize, minsize, largeop, movablelimits, accent |
| mspace | mathvariant, mathsize, mathcolor, mathbackground, width, height, depth, linebreak |
| ms | mathvariant, mathsize, mathcolor, mathbackground, lquote, rquote |
| mglyph | mathvariant, mathsize, mathcolor, mathbackground, alt (required), fontfamily (required), index (required) |
| mfrac | linethickness, numalign, denomalign, bevelled |
| mstyle | All optional attributes listed for the tags. In addition, the following are valid: scriptlevel, displaystyle, scriptsizemultiplier, scriptminsize, background, veryverythinmathspace, verythinmathspace, thinmathspace, mediummathspace, thickmathspace, verythickmathspace, veryverythickmathspace.
All values are inherited. |
| mpadded | width, lspace, height, depth |
| mfenced | open, close, separators |
| menclose | notation |
| msub | subscriptshift |
| msup | superscriptshift |
| msubsup | subscriptshift, superscriptshift |
| munder | accentunder |
| mover | accent |
| munderover | accentunder, accent |
| mmultiscripts | subscriptshift, superscriptshift |
| mtable | align, rowalign, columnalign, groupalign, alignmentscope, columnwidth, width, rowspacing, columnspacing, rowlines, columnlines, frame, framespacing, equalrows, equalcolumns, displaystyle, side, minlabelspacing |
| mtr, mlabeledtr | rowalign, columnalign, groupalign |
| mtd | rowspan, columnspan, rowalign, columnalign, groupalign |
| maligngroup | groupalign |
| malignmark | edge |
| maction | actiontype (required), selection |
| semantics, annotation, annotation-xml | definitionURL, encoding |
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