The MathML Handbook (Charles River Media Internet & Web Design)

13.2 Listing of Presentation Elements

For brevity, attributes common to all token elements are listed only once, in this section. They are not included in the list of attributes for each token element but are implied. Table 13.1 shows the style attributes of token elements.

maction

Syntax

<maction>(child)*</maction>

Description

The maction element is used to associate interactive actions with specific parts of a MathML expression. This element is provided as a means of hooking up interactivity features implemented in a specific application to a MathML expression. Hence, the type of actions supported, if any, depend on the rendering application.

Attributes

This element accepts the two attributes shown in Table 13.2.

These attributes have the following meaning:

• selection: is an integer that identifies one of the arguments of the maction element. The value 1 refers to the first argument, 2 to the second argument, and so on. The purpose of this attribute is to provide a way to refer to subexpressions of the <maction> element; for example, in cases where the intended action is to toggle between different subexpressions.

• actiontype: specifies the action to be performed. The allowed values of this attribute are not defined by the MathML specification. Instead, each MathML application is expected to define its own values, depending on the type of actions it supports. Some examples of possible values that may be supported are: toggle, statusline, highlight, and tooltip.

maligngroup

Syntax

<maligngroup/>

Description

The maligngroup element is used to indicate the start of a new alignment group in a table column.

Attributes

None.

malignmark

Syntax

<malignmark/>

Description

The malignmark element is used to indicate an alignment point inside an alignment group in a table column.

Attributes

This element accepts the one attribute shown in Table 13.3.

If edge="left", the alignment point is the left edge of the nearest element to the right of the malignmark element. If edge="right", the alignment point is the right edge of the nearest element to the left of the malignmark element.

menclose

Syntax

<menclose>(child)</menclose>

Description

The menclose element encloses its contents inside a notational symbol of a type specified by the value of its notation attribute.

Attributes

This element accepts the one attribute shown in Table 13.4.

The notation attribute determines the type of symbol placed around the contents.

merror

Syntax

<merror>(child)*</merror>

Description

The merror element is used to enclose information about syntax errors found when MathML markup is processed. The contents of the element are typically rendered in a different color or font style, to distinguish them from the surrounding text. The exact details of rendering depend on the specific processing application.

Attributes

None.

mfenced

Syntax

<mfenced>(child)*</mfenced>

Description

The mfenced element is used as a compact way to express common notational constructs involving fences, such as braces, brackets, or parentheses. By default, this element renders its contents enclosed in parentheses with arguments separated by commas.

Attributes

This element accepts the three attributes shown in Table 13.5.

These attributes have the following meaning:

• open: specifies the character used as the opening fence.

• close: specifies the character used as the closing fence.

• separators: specifies the characters used to separate the arguments. The value of this attribute is a list of characters, with successive members of the list used to separate successive pairs of arguments. If there are fewer characters than needed, the last one is repeated as many times as necessary. If there are more characters than needed, the extra ones are ignored.

mfrac

Syntax

<mfrac>numerator denominator</mfrac>

Description

The mfrac element is used to display fractions or fraction-like notation, such as binomial coefficients.

Attributes

This element accepts the four attributes shown in Table 13.6.

These attributes have the following meaning:

• linethickness: specifies the thickness of the line that separates the numerator and denominator

• numalign: specifies the horizontal alignment of the numerator

• denomalign: specifies the horizontal alignment of the denominator

• bevelled: when false, the numerator is shown above the denominator with a horizontal line between them; when true, a slightly raised numerator is shown to the left of a slightly lowered denominator with a diagonal line between them

mglyph

Syntax

<mglyph fontfamily="..." index="..." alt="..."/>

Description

The mglyph element is provided as an extension mechanism to allow arbitrary symbols and other extended characters to be displayed. It is displayed as a specific glyph in a specific font, the values of which are determined by its attributes.

Attributes

This element accepts the nine attributes common to all token elements. In addition, it accepts the three attributes shown in Table 13.7.

These attributes have the following meaning:

• fontfamily: specifies the font in which the desired glyph appears

• index: is an integer that specifies the position of the desired glyph in the font

• alt: specifies some alternative text that is displayed as a fallback if the glyph specified by the other two attributes is not found

mi

Syntax

<mi>PCDATA</mi>

Description

This element is used to represent identifiers such as names of variables and functions. The content of an mi element is displayed in italics if it is a single character and in an upright font otherwise.

Attributes

This element accepts the nine attributes common to all token elements.

mlabeledtr

Syntax

<mlabeledtr>label (<mtd>)*</mlabeledtr>

Description

The mlabeledtr element is used to represent a single labeled row in a table or matrix. It can occur only as a child element of an mtable element. It takes zero or more mtd elements, each of which corresponds to a single cell of the table or matrix.

Attributes

This element accepts the three attributes shown in Table 13.8.

These attributes have the same meaning as in the mtable element.

mmultiscripts

Syntax

<mmultiscripts> base (subscript superscript)* [<mprescripts/> (presubscript presuperscript)*] </mmultiscripts>

Description

The mmultiscripts element is used to attach prescripts and tensor indices to a base. It increments scriptlevel by 1, and sets displaystyle to false, within each of its arguments except base. It leaves both attributes unchanged within base.

Attributes

This element has the two attributes shown in Table 13.9.

These attributes have the following meaning:

• subscriptshift: specifies the minimum amount by which the subscript should be shifted down relative to the baseline of the base expression

• superscriptshift: specifies the minimum amount by which the superscript should be shifted up relative to the baseline of the base expression

mn

Syntax

<mn>PCDATA</mn>

Description

The mn element is used to represent a numeric literal; that is, a string that represents a number. A numeric literal can consist of an optional "+" or "-" sign followed by an arbitrary number of digits, possibly separated by a decimal point. The number can be in any base and any standard notation. The contents of the mn element are typically displayed in an upright font.

Numbers that have some structure (such as negative numbers, complex numbers, fractions, and symbolic constants) cannot be specified as simple mn elements and require additional presentation elements.

Attributes

The mn element accepts the nine attributes common to all token elements.

mo

Syntax

<mo>PCDATA</mo>

Description

The mo element is used to represent operators, fences, separators, and accents. Fences include all characters used as delimiters such as braces, brackets, parentheses, and absolute value bars.

This element has a large collection of attributes that affect the details of how it is rendered. An operator dictionary, which specifies the values of attributes for most common operators, determines the default value of the attributes. If an attribute value is not specified in the operator dictionary, the attribute takes a generic default value, specified in Table 13.10.

Attributes

The mo element accepts the nine attributes common to all token elements. In addition, it has twelve other attributes, shown in Table 13.10. The default values for most of these attributes are typically determined from the operator dictionary. Some default values in Table 13.10 are shown with an asterisk to indicate that they are generic default values, to be used only if no match is found for that attribute in the operator dictionary.

These attributes have the following meaning:

• form: specifies whether the operator occurs in the prefix, postfix, or infix position. This, in turn, determines the amount of space rendered on either side of the operator by default.

• lspace: specifies the amount of space that should be added to the left of an operator. It is usually specified as a number followed by a unit of horizontal distance. If no unit is specified, a value in ems is assumed.

• rspace: specifies the amount of space that should be added to the right of an operator. It is usually specified as a number followed by a unit of horizontal distance. If no unit is specified, a value in ems is assumed.

• stretchy: specifies whether an operator should stretch to accommodate its contents.

• symmetric: specifies whether an operator for which stretchy="true" should always remain vertically symmetric with respect to its contents. That is, when symmetric="true", the height of the operator above and the depth below its contents are always kept equal.

• maxsize: specifies the maximum size an operator can stretch to accommodate its contents. This attribute is either specified in absolute terms (that is, as a number with a unit) or in relative terms (that is, as a number). If it is specified as a number, the number is multiplied by the normal size of the operator to determine the maximum size.

• minsize: specifies the minimum size an operator can stretch to accommodate its contents. This attribute is either specified in absolute terms (that is, as a number with a unit) or in relative terms (that is, as a number). If it is set to a number, the number is multiplied by the normal size of the operator to determine the maximum size.

• largeop: specifies whether the operator should be drawn in a larger size when display in that operator's environment. The operators that represent integrals, sums, and products, for example, typically have largeop set to true by default.

• movablelimits: specifies whether underscripts and overscripts attached to an operator should be rendered as subscripts and superscripts when display in that operator's environment. The operators that represent integrals, sums, and products, for example, typically have movablelimits set to true by default.

• fence: specifies whether the operator should be treated as if it were a fence. A fence is any character that plays the role of a delimiter, such as braces, brackets, parentheses, and absolute value bars. This attribute has no effect on the visual rendering of the operator. It is provided only as way of passing this information to applications that need to interpret the semantic meaning of the presentation markup.

• separator: specifies whether an operator should be treated as a separator for the purposes of rendering. It is provided as a means of giving linebreaking information to rendering applications. Setting separator="true" for an operator indicates that a linebreak should be avoided after the operator; that is, it is preferable to place the operator at the beginning of a broken line rather than at the end.

• accent: specifies whether an operator should be treated as an accent (or diacritical mark) when used as an underscript or overscript. Accents are typically rendered in normal size and closer to the base, while limits are rendered in a smaller size and farther away from the base.

mover

Syntax

<mover> base overscript </mover>

Description

The mover element is used for representing an overscript attached to a base.

By default, the mover element sets displaystyle to false in overscript and increments scriptlevel by 1 if accent="false". It leaves both attributes unchanged within base.

Attributes

This element has the one attribute shown in Table 13.11.

The accent attribute specifies whether the expression that appears in the overscript position should be treated as an accent or a limit. Accents are rendered in normal size and closer to the base, while limits are rendered in a smaller size and farther away from the base.

mpadded

Syntax

<mpadded>(child)*</mpadded>

Description

The mpadded element is used to make precise adjustments to the position of an expression relative to its surrounding elements. It changes the position of the bounding box used for rendering its contents by an amount determined by its attributes.

Attributes

This element accepts the four attributes shown in Table 13.12.

These attributes have the following meaning:

• width: specifies the horizontal width of the bounding box

• lspace: specifies the amount of blank space inserted before the left edge of the bounding box

• height: specifies the vertical distance between the baseline and the top of the bounding box

• depth: specifies the vertical distance between the baseline and the bottom of the bounding box

mphantom

Syntax

<mphantom>(child)*</mphantom>

Description

The mphantom element is used to render an expression invisibly. It inserts an amount of blank space equal to the space that would have been needed to render its contents if they were not enclosed in an mphantom element. This property is useful in aligning certain types of expressions.

Attributes

None.

mprescripts

Syntax

<mmultiscripts> base (subscript superscript)* [<mprescripts/> (presubscript presuperscript)*] </mmultiscripts>

Description

This is an empty element used as a child element of the <mmultiscripts> element to indicate that the elements after it should be displayed in the prescript position.

Attributes

None.

mroot

Syntax

<mroot>base index</mroot>

Description

The mroot element is used to display arbitrary roots. The base is displayed enclosed in a radical sign with the index placed outside the radical sign, which is the conventional notation for roots.

Attributes

None.

mrow

Syntax

<mrow>(child)*</mrow>

Description

The mrow element is used to group any number of subexpressions. Its elements are displayed in a horizontal row, from left to right.

Attributes

None.

ms

Syntax

<ms>PCDATA</ms>

Description

The ms element is used to represent string literals, a concept of importance for programming languages and computer algebra systems. By default, its contents are rendered enclosed in quotation marks.

Attributes

This element accepts the nine attributes common to all token elements. In addition, it accepts the two attributes shown in Table 13.13.

These attributes have the following meaning:

• lquote: specifies the character that appears at the start of the string

• rquote: specifies the character that appears at the end of the string

mspace

Syntax

<mspace/>

Description

The mspace element is used to insert a blank space of arbitrary size. The size of the space inserted is determined by the value of its attributes. The default values of the attributes are chosen to have no effect on visual rendering. Hence, to insert any additional space, you must use this element with explicit attribute values specified.

Attributes

This element accepts the nine attributes common to all token elements. In addition, it accepts the three attributes shown in Table 13.14.

These attributes have the following meaning:

• width: is the distance from the left edge of the bounding box that defines the space

• height: is the distance from the baseline to the top of the bounding box

• depth: is the distance from the baseline to the bottom of the bounding box

msqrt

Syntax

<msqrt>base</msqrt>

Description

The msqrt element is used to display square roots. It takes a single child element, which is displayed with a square root sign around its contents. If it is written with more than one child element, an mrow element is inferred around the contents.

Attributes

None.

mstyle

Syntax

<mstyle>(child)*</mstyle>

Description

The mstyle element is used to set the default value of an attribute throughout a given piece of presentation markup. If an attribute is specified explicitly on an mstyle element, the specified value is inherited by all elements contained within the mstyle element directly or indirectly. In other words, that value will be used as the default on every element contained within that mstyle element, unless the value is explicitly changed by another attribute specification.

The mstyle element displays its children in a horizontal row aligned along the baseline, similar to the mrow element.

Attributes

This element accepts the thirteen attributes shown in Table 13.15. In addition, it accepts all attributes of all other presentation elements, except for those attributes that have a required value.

The first six of these attributes have the following meaning:

• scriptlevel: controls the font size. The higher the script level, the smaller the font size. The change in the font size depends on the value of the attribute scriptsizemultiplier.

• displaystyle: controls the value of two other attributes in mo elements, namely largeop and movablescripts. These attributes can take one of several values, depending on the value of the displaystyle attribute in their environment. In general, the displaystyle attribute has the value true for equations intended for display and false for equations that occur inline as well as for tables, fractions, or scripts. Presentation elements that typically cause their content to be displayed in a smaller size or with less vertical spacing (such as subscripts, superscripts, fractions, square roots, and tables) typically set displaystyle to false and increase the value of scriptlevel. Ten elements change the value of either displaystyle or scriptlevel: msub, msup, msubsup, munder, mover, munderover, mmultiscripts, mfrac, mroot, and mtable.

• scriptsizemultiplier: is a number that determines the change in font size caused by scriptlevel. The new font size is equal to the old font size multiplied by the scriptsizemultiplier to the power of the change in scriptlevel.

• scriptminsize: is the minimum size to which a font can be reduced as a consequence of changes in scriptlevel.

• color: specifies the color in which the markup is rendered in RGB notation.

• background: specifies the background color in RGB notation.

Spacing between operators is typically one of a small set of values. The <mstyle> element has the following seven named attributes that set the size of these values:

• veryverythinmathspace

• verythinmathspace

• thinmathspace

• mediummathspace

• thickmathspace

• verythickmathspace

• veryverythickmathspace

Each of these attributes defines a fixed horizontal space, with the default value ranging between 1/18 em to 7/18 em. Since the spacing between operators in the operator dictionary is defined in terms of these values, setting these values to a larger or smaller value can make the spacing between all operators looser or tighter.

msub

Syntax

<msub>base subscript</msub>

Description

The msub element is used for representing a subscript attached to a base.

By default, the msub element automatically increments scriptlevel by 1 and sets displaystyle to false in subscript but leaves both attributes unchanged within base.

Attributes

This element has the one attribute shown in Table 13.16.

The subscriptshift attribute specifies the minimum amount by which the subscript should be shifted down relative to the baseline of the base expression.

msubsup

Syntax

<msubsup>base subscript superscript</msubsup>

Description

The msubsup element is used for representing a subscript attached to a base.

By default, the msubsup element automatically increments scriptlevel by 1 and sets displaystyle to false in both subscript and superscript but leaves both attributes unchanged within base.

Attributes

This element has the two attributes shown in Table 13.17.

These attributes have the following meaning:

• subscriptshift: specifies the minimum amount by which the subscript should be shifted down relative to the baseline of the base expression

• superscriptshift: specifies the minimum amount by which the superscript should be shifted up relative to the baseline of the base expression

msup

Syntax

<msup>base superscript</msup>

Description

The msup element is used for representing a superscript attached to a base.

By default, the msup element automatically increments scriptlevel by 1 and sets displaystyle to false in superscript but leaves both attributes unchanged within base.

Attributes

This element has the one attribute shown in Table 13.18.

The superscriptshift attribute specifies the minimum amount by which the superscript should be shifted up relative to the baseline of the base expression.

mtable

Syntax

<mtable>(child)*</mtable>

Description

The mtable element is used to represent tables or matrices. It takes zero or more mtr or mlabeledtr elements, each of which corresponds to a single row of the table or matrix.

Attributes

This element accepts the eighteen attributes shown in Table 13.19.

For several of these attributes, the value can be a sequence of zero or more entries. In such cases, the first entry applies to the first row or column, the second entry to the second row/column, and so on. If there are fewer entries than rows/columns in the table, the last entry is repeated as many times as necessary. If there are more entries than rows/columns, the extra entries are ignored.

These attributes have the following meaning:

• align: specifies where to align the table with respect to its environment. If the value of this attribute ends with a number between 1 and n (for a table with n rows), the value of that entry is applied to that row of the table only. The top row is numbered 1 and the bottom row is numbered n. Alternatively, you can use a negative number between -1 and -n, in which case the top row is referred to as -n and the bottom row as -1. Possible values of this attribute are:

• top: aligns the top of the table along the environment's baseline

• bottom: aligns the bottom of the table along the environment's baseline

• center: aligns the center of the table (that is, the midpoint of the table's vertical extent) along the environment's baseline

• baseline: same as center

• axis: aligns the center of the table along the environment's axis (that is, the line on which the minus sign typically lies)

• rowalign: specifies how the entries in each row should be aligned.

Possible values are:

• top:specifies that the top of all entries in the row should be aligned

• bottom: specifies that the bottom of all entries in the row should be aligned

• center: specifies that the center of all entries in the row should be aligned

• baseline :specifies that the baseline of all entries in the row should be aligned

• axis: specifies that the axis of all entries in the row should be aligned

• columnalign: specifies how the entries in each column should be aligned. Possible values are:

• left: specifies that the left edge of all entries in the column should be aligned

• center: specifies that the center of all entries in the column should be aligned

• right: specifies that the right edge of all entries in the column should be aligned

• columnwidth: specifies how wide a column should be. Possible values are:

  • auto: specifies that the column is as wide as needed to accommodate its contents

  • number h-unit or namedspace: specifies a fixed width either by giving a number and a unit or any of the seven named spaces, each of which define a fixed width between 1/18 em and 7/18 em

  • fit: adjusts the width of the columns so the table spans the width of the page; the width of each column that is set to a fixed width or auto is subtracted from the page width and the resulting number is divided by the remaining number of columns

• width: specifies the width of the entire table. It can be set to a fixed number or auto, which means that the renderer should adjust the width of the table, depending on its contents.

• rowspacing: specifies the amount of space between any two rows. The spacing before the first row and after the last row is determined by the attribute framespacing.

• columnspacing: specifies the amount of space between any two columns. The spacing before the first column and after the last column is determined by the attribute framespacing.

• rowlines: specifies the type of line to be drawn between any two rows, if any.

• columnlines: specifies the type of line to be drawn between any two columns, if any.

• equalrows: if true, forces all the rows to have the same height.

• equalcolumns: if true, forces all the columns to have the same width.

• frame: specifies if a frame should be drawn around the table.

• framespacing: if frame is set to either solid or dashed, determines how much space should be left between the frame and the first and last row or column. It is given as a sequence of two numbers; the first one determines the spacing between the frame and the first and last row, and the second determines the spacing between the frame and the first and last column.

• displaystyle: specifies the display mode for each cell of the table. The default value is false and is appropriate when the table is embedded in a block of text. A value of true is appropriate if the table is displayed in a separate block by itself. In either case, the value of scriptlevel in the cells of the table is unchanged.

• side: specifies on what side of the table the label for a labeled row should be displayed. The label is displayed on the left if set to left and on the right if set to right. If the table fits on the page without the label but does not fit when the label is added, the label overlaps the row and is shown above the row if rowalign for that row is top and below the row otherwise.

• minlabelspacing: specifies the minimum space allowed between a label and the adjacent entry in the corresponding row.

• groupalign: specifies the alignment point for alignment groups defined using the maligngroup element.

• alignmentscope: specifies if alignment information defined using the maligngroup and malignmark elements should be interpreted or ignored.

mtd

Syntax

<mtd>(child)*</mtd>

Description

The mtd element is used to represent a single cell in a table or matrix. It can occur only as a child element of an mtr or mlabeledtr element.

Attributes

This element accepts the five attributes shown in Table 13.20.

These attributes have the following meaning:

• rowalign, columnalign, and groupalign: have the same meaning as in the mtable element

• rowspan: allows a given cell in the table to occupy the specified number of rows

• columnspan: allows a given cell in the table to occupy the specified number of columns

mtext

Syntax

<mtext>PCDATA</mtext>

Description

The mtext element is used to represent plain text that must be included literally in a mathematical expression.

Attributes

The mtext element accepts the nine attributes common to all token elements.

mtr

Syntax

<mtr>(<mtd>)*</mtr>

Description

The mtr element is used to represent a single row in a table or matrix. It takes zero or more mtd elements, each of which corresponds to a single cell of the table or matrix.

Attributes

This element accepts the three attributes shown in Table 13.21.

These attributes have the same meaning as in the mtable element.

munder

Syntax

<munder>base underscript</munder>

Description

The munder element is used for representing an underscript attached to a base.

By default, the munder element sets displaystyle to false in underscript and increments scriptlevel by 1 if accentunder="false". It leaves both attributes unchanged within base.

Attributes

This element has the one attribute shown in Table 13.22.

The accentunder attribute specifies whether the expression that appears in the underscript position should be treated as an accent or a limit. Accents are rendered in normal size and closer to the base, while limits are rendered in a smaller size and farther away from the base.

munderover

Syntax

<munderover>base underscript overscript</munderover>

Description

The munderover element is used for representing an underscript and overscript attached to a base.

By default, the munderover element sets displaystyle to false in underscript and overscript and increments scriptlevel by 1 only when accentunder="false". It leaves both attributes unchanged within base.

Attributes

This element has the two attributes shown in Table 13.23.

These attributes have the following meaning:

• accentunder: specifies whether the expression that appears in the underscript position should be treated as an accent or a limit. Accents are rendered in normal size and closer to the base, while limits are rendered in a smaller size and farther away from the base.

• accent: specifies whether the expression that appears in the overscript position should be treated as an accent or a limit. Accents are rendered in normal size and closer to the base, while limits are rendered in a smaller size and farther away from the base.

none

Syntax

<mmultiscripts> base (subscript|<none/> superscript|<none/>)* [<mprescripts/> (presubscript|<none/> presuperscript|<none/>)*] </mmultiscripts>

Description

The none element is used as a child element of the mmultiscripts element to indicate that the position opposite to a particular subscript or superscript is blank.

Attributes

None.