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FMath - MathML 3.0 Implementation

2 MathML Fundamentals
    2.1 MathML Syntax and Grammar
        2.1.5 MathML Attribute Values
            2.1.5.2 Length Valued Attributes
            2.1.5.3 Color Valued Attributes
        2.1.6 Attributes Shared by all MathML Elements
        2.1.7 Collapsing Whitespace in Input
    2.2 The Top-Level math Element
3 Presentation Markup
    3.1 Introduction
        3.1.10 Mathematics style attributes common to presentation elements
    3.2 Token Elements
        3.2.1 MathML characters in token elements
            3.2.1.1 Alphanumeric symbol characters
            3.2.1.2 <mglyph/>
        3.2.2 Mathematics style attributes common to token elements
            3.2.2.1 Deprecated style attributes on token elements
        3.2.3 Identifier <mi>
        3.2.4 Number <mn>
        3.2.5 Operator, Fence, Separator or Accent<mo>
        3.2.6 Text <mtext>
        3.2.7 Space <mspace/>
        3.2.8 String Literal <ms>
    3.3 General Layout Schemata
        3.3.1 Horizontally Group Sub-Expressions <mrow>
        3.3.2 Fractions <mfrac>
        3.3.3 Radicals <msqrt>, <mroot>
        3.3.4 Style Change <mstyle>
        3.3.5 Error Message <merror>
        3.3.6 Adjust Space Around Content<mpadded>
        3.3.7 Making Sub-Expressions Invisible <mphantom>
        3.3.8 Expression Inside Pair of Fences<mfenced>
        3.3.9 Enclose Expression Inside Notation<menclose>
    3.4 Script and Limit Schemata
        3.4.1 Subscript <msub>
        3.4.2 Superscript <msup>
        3.4.3 Subscript-superscript Pair <msubsup>
        3.4.4 Underscript <munder>
        3.4.5 Overscript <mover>
        3.4.6 Underscript-overscript Pair<munderover>
        3.4.7 Prescripts and Tensor Indices<mmultiscripts>
    3.5 Tabular Math
        3.5.1 Table or Matrix<mtable>
        3.5.2 Row in Table or Matrix <mtr>
        3.5.3 Labeled Row in Table or Matrix<mlabeledtr>
        3.5.4 Entry in Table or Matrix <mtd>
    3.6 Elementary Math
        3.6.1 Stacks of Characters <mstack>
        3.6.2 Long Division <mlongdiv>
        3.6.3 Group Rows with Similiar Positions <msgroup>
        3.6.4 Rows in Elementary Math <msrow>
        3.6.5 Carries, Borrows, and Crossouts <mscarries>
        3.6.6 A Single Carry <mscarry>
        3.6.7 Horizontal Line <msline/>
    3.7 Enlivening Expressions
        3.7.1 Bind Action to Sub-Expression<maction>
4 Content Markup
    4.2 Content MathML Elements Encoding Expression Structure
        4.2.1 Numbers <cn>
        4.2.2 Content Identifiers <ci>
        4.2.3 Content Symbols <csymbol>
        4.2.4 String Literals <cs>
        4.2.5 Function Application <apply>
        4.2.6 Bindings and Bound Variables <bind> and <bvar>
        4.2.7 Structure Sharing <share>
        4.2.8 Attribution via semantics
        4.2.9 Error Markup <cerror>
    4.4 Content MathML for Specific Operators and Constants
        4.4.1 Functions and Inverses
        4.4.2 Arithmetic, Algebra and Logic
        4.4.3 Relations
        4.4.4 Calculus and Vector Calculus
        4.4.5 Theory of Sets
        4.4.6 Sequences and Series
        4.4.7 Elementary classical functions
        4.4.8 Statistics
        4.4.9 Linear Algebra
        4.4.10 Constant and Symbol Elements

3 Presentation Markup

3.2 Token Elements

3.2.5 Operator, Fence, Separator or Accent <mo>

3.2.5.1 Description

An mo element represents an operator or anything that should be rendered as an operator.

3.2.5.2 Attributes

mo elements accept the attributes listed in Section 3.2.2 Mathematics style attributes common to token elements and the additional attributes listed here.

Most attributes get their default values from an enclosing mstyle element, math element, or from the "The operator dictionary". The attributes may also appear on any ancestor of the math element, if permitted by the containing document, to provide defaults for all contained math elements. In such cases, the attributes would be in the MathML namespace.

3.2.5.2.1 Dictionary-based attributes
Name values default
form "prefix" | "infix" | "postfix" set by position of operator in an mrow
Specifies the role of the operator in the enclosing expression. This role and the operator content affect the lookup of the operator in the operator dictionary which affects the spacing and other default properties;
fence "true" | "false" set by dictionary (false)
Specifies whether the operator represents a ‘fence’, such as a parenthesis. This attribute generally has no direct effect on the visual rendering, but may be useful in specific cases, such as non-visual renderers.
separator "true" | "false" set by dictionary (false)
Specifies whether the operator represents a ‘separator’, or punctuation. This attribute generally has no direct effect on the visual rendering, but may be useful in specific cases, such as non-visual renderers.
lspace length set by dictionary (thickmathspace)
Specifies the leading space appearing before the operator;
rspace length set by dictionary (thickmathspace)
Specifies the trailing space appearing after the operator;
stretchy "true" | "false" set by dictionary (false)
Specifies whether the operator should stretch to the size of adjacent material;
symmetric "true" | "false" set by dictionary (false)
Specifies whether the operator should be kept symmetric around the math axis when stretchy.
maxsize length | "infinity" set by dictionary (infinity)
Specifies the maximum size of the operator when stretchy;
minsize length set by dictionary (1em)
Specifies the minimum size of the operator when stretchy;
largeop "true" | "false" set by dictionary (false)
Specifies whether the operator is considered a Large operator, that is, whether it should be drawn larger than normal when displaystyle="true" (similar to using TEX's \displaystyle). Examples of large operators include &int; and &prod;.
movablelimits "true" | "false" set by dictionary (false)
Specifies whether under- and overscripts attached to this operator "move" to the more compact sub- and superscript positions when displaystyle is false. Examples of operators that typically have movablelimits="true" are &sum;, &prod;, and lim.
accent "true" | "false" set by dictionary (false)
Specifies whether this operator should be treated as an accent (diacritical mark) when used as an underscript or overscript;
3.2.5.2.2 Linebreaking attributes

The following attributes affect when a linebreak does or does not occur, and the appearance of the linebreak when it does occur.

Name values default
linebreak "newline" auto
Specifies the desirability of a linebreak occurring at this operator:
lineleading length inherited (100%)
Specifies the amount of vertical space to use after a linebreak.
linebreakstyle "before" | "after" | "duplicate" | "infixlinebreakstyle" set by dictionary (before)
Specifies whether a linebreak occurs "before" or "after" the operator when a linebreaks occur on this operator; or whether the operator is duplicated. "before" causes the operator to appears at the beginning of the new line (but possibly indented); "after" causes it to appear at the end of the line before the break. "duplicate" places the operator at both positions. "infixlinebreakstyle" uses the value that has been specified for infix operators;
linebreakmultchar string inherited (&InvisibleTimes;)
Specifies the character used to make an &InvisibleTimes; operator visible at a linebreak. For example, linebreakmultchar="&#xB7;" would make the multiplication visible as a center dot.

linebreak values on adjacent mo and mspaceelements do not interact; linebreak="nobreak" on a mo does not, in itself, inhibit a break on a preceding or following (possibly nested) mo or mspace element and does not interact with the linebreakstyle attribute value of the preceding or following mo element. It does prevent breaks from occurring on either side of the mo element in all other situations.

3.2.5.2.3 Indentation attributes

The following attributes affect indentation of the lines making up a formula.

Name values default
indentalign "left" | "center" | "right" | "auto" | "id" inherited (auto)
Specifies the positioning of lines when linebreaking takes place within an mrow; see below for discussion of the attribute values.
indentshift length inherited (0)
Specifies an additional indentation offset relative to the position determined by indentalign.
indenttarget idref inherited (none)
Specifies the id of another element whose horizontal position determines the position of indented lines when indentalign="id".
indentalignfirst "left" | "center" | "right" | "auto" | "id" | "indentalign" inherited (indentalign)
Specifies the indentation style to use for the first line of a formula; the value "indentalign" (the default) means to indent the same way as used for the general line.
indentshiftfirst length | "indentshift" inherited (indentshift)
Specifies the offset to use for the first line of a formula; the value "indentshift" (the default) means to use the same offset as used for the general line.
indentalignlast "left" | "center" | "right" | "auto" | "id" | "indentalign" inherited (indentalign)
Specifies the indentation style to use for the last line when a linebreak occurs within a given mrow; the value "indentalign" (the default) means to indent the same way as used for the general line.
indentshiftlast length | "indentshift" inherited (indentshift)
Specifies the offset to use for the last line when a linebreak occurs within a given mrow; the value "indentshift" (the default) means to indent the same way as used for the general line.

The legal values of indentalign are:

Value Meaning
left Align the left side of the next line to the left side of the line wrapping width
center Align the center of the next line to the center of the line wrapping width
right Align the right side of the next line to the right side of the line wrapping width
auto (default) is left
id Align the left side of the next line to the left side of the element referenced by the idref (given by indenttarget);

FMath Component Test

MathML Display in:

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