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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

3.4 Script and Limit Schemata

3.4.7 Prescripts and Tensor Indices <mmultiscripts>

3.4.7.1 Description

Presubscripts and tensor notations are represented by a single element, mmultiscripts, using the syntax:

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

This element allows the representation of any number of vertically-aligned pairs of subscripts and superscripts, attached to one base expression. It supports both postscripts and prescripts. Missing scripts can be represented by the empty element none.

The prescripts are optional, and when present are given after the postscripts, because prescripts are relatively rare compared to tensor notation.

The argument sequence consists of the base followed by zero or more pairs of vertically-aligned subscripts and superscripts (in that order) that represent all of the postscripts. This list is optionally followed by an empty element mprescripts and a list of zero or more pairs of vertically-aligned presubscripts and presuperscripts that represent all of the prescripts. The pair lists for postscripts and prescripts are displayed in the same order as the directional context (ie. left-to-right order in LTR context). If no subscript or superscript should be rendered in a given position, then the empty element none should be used in that position.

The base, subscripts, superscripts, the optional separator element mprescripts, the presubscripts, and the presuperscripts, are all direct sub-expressions of the mmultiscripts element, i.e. they are all at the same level of the expression tree. Whether a script argument is a subscript or a superscript, or whether it is a presubscript or a presuperscript is determined by whether it occurs in an even-numbered or odd-numbered argument position, respectively, ignoring the empty element mprescripts itself when determining the position. The first argument, the base, is considered to be in position 1. The total number of arguments must be odd, if mprescripts is not given, or even, if it is.

The empty element mprescripts is only allowed as direct sub-expression of mmultiscripts.

3.4.7.2 Attributes

Same as the attributes of msubsup. See Section 3.4.3.2 Attributes.

The mmultiscripts element increments scriptlevel by 1, and sets displaystyle to "false", within each of its arguments except base, but leaves both attributes unchanged within base.

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