A MathMLの処理
Parsing MathML

A.2.1 完全なMathML
Full MathML

完全なMathMLのRelaxNGスキーマは, 続く節で示す, 言語の様々な部分を説明するスキーマから形成されています. http://www.w3.org/Math/RelaxNG/mathml3/mathml3.rncで見ることができます.

The RelaxNG schema for full MathML builds on the schema describing the various parts of the language which are given in the following sections. It can be found at http://www.w3.org/Math/RelaxNG/mathml3/mathml3.rnc.

#     This is the Mathematical Markup Language (MathML) 3.0, an XML
#     application for describing mathematical notation and capturing
#     both its structure and content.
(注釈:これは数学用マークアップ言語(MathML) 3.0, 数学表記を説明し,
      その構造と内容の両方を捉えるXMLの応用です.)
#
#     Copyright 1998-2010 W3C (MIT, ERCIM, Keio)
# 
#     Use and distribution of this code are permitted under the terms
#     W3C Software Notice and License
(注釈:このコードの利用や配布は, W3Cのソフトウェア告示とライセンスの下で許可されます.)
#     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231


default namespace m = "http://www.w3.org/1998/Math/MathML"

## Content  MathML
(注釈:コンテントMathML)
include "mathml3-content.rnc" 

## Presentation MathML
(注釈:プレゼンテーションMathML)
include "mathml3-presentation.rnc"

## math and semantics common to both Content and Presentation
(注釈:コンテントマークアップとプレゼンテーションマークアップに共通のmathとsemantics)
include "mathml3-common.rnc"

A.2.2 プレゼンテーションMathMLとコンテントMathMLに共通の要素
Elements Common to Presentation and Content MathML

#     This is the Mathematical Markup Language (MathML) 3.0, an XML
#     application for describing mathematical notation and capturing
#     both its structure and content.
(注釈:これは数学用マークアップ言語(MathML) 3.0, 数学表記を説明し,
      その構造と内容の両方を捉えるXMLの応用です.)
#
#     Copyright 1998-2014 W3C (MIT, ERCIM, Keio, Beihang)
# 
#     Use and distribution of this code are permitted under the terms
#     W3C Software Notice and License
(注釈:このコードの利用や配布は, W3Cのソフトウェア告示とライセンスの下で許可されます.)
#     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231


default namespace m = "http://www.w3.org/1998/Math/MathML"
namespace local = ""

start = math

math = element math {math.attributes,MathExpression*}
MathExpression = semantics

NonMathMLAtt = attribute (* - (local:*|m:*)) {xsd:string} 

CommonDeprecatedAtt = attribute other {text}?

CommonAtt = attribute id {xsd:ID}?,
            attribute xref {text}?,
            attribute class {xsd:NMTOKENS}?,
            attribute style {xsd:string}?,
            attribute href {xsd:anyURI}?,
            CommonDeprecatedAtt,
            NonMathMLAtt*


math.attributes = CommonAtt,
               attribute display {"block" | "inline"}?,
               attribute maxwidth {length}?,
               attribute overflow {"linebreak" | "scroll" | "elide" | "truncate" | "scale"}?,
               attribute altimg {xsd:anyURI}?,
               attribute altimg-width {length}?,
               attribute altimg-height {length}?,
               attribute altimg-valign {length | "top" | "middle" | "bottom"}?,
               attribute alttext {text}?,
               attribute cdgroup {xsd:anyURI}?,
               math.deprecatedattributes

# the mathml3-presentation schema  adds additional attributes
# to the math element, all those valid on mstyle
(注釈:mathml3-presentationスキーマが, 追加の属性をmath要素に加えます. これらは全てmstyleで有効.)

math.deprecatedattributes = attribute mode {xsd:string}?,
                            attribute macros {xsd:string}?


name = attribute name {xsd:NCName}
cd = attribute cd {xsd:NCName}

src = attribute src {xsd:anyURI}?

annotation = element annotation {annotation.attributes,text}
                     
annotation-xml.model = (MathExpression|anyElement)*

anyElement =  element (* - m:*) {(attribute * {text}|text| anyElement)*}

annotation-xml = element annotation-xml {annotation.attributes,
                                         annotation-xml.model}
annotation.attributes = CommonAtt,
	                cd?,
                        name?,
                        DefEncAtt,
                        src?

DefEncAtt = attribute encoding {xsd:string}?,
            attribute definitionURL {xsd:anyURI}?

semantics = element semantics {semantics.attributes,
                               MathExpression, 
                              (annotation|annotation-xml)*}
semantics.attributes = CommonAtt,DefEncAtt,cd?,name?



length
# wrapped for display
(注釈:表示のためのパターンの定義)
 = xsd:string {
  pattern = '\s*((-?[0-9]*([0-9]\.?|\.[0-9])[0-9]*(e[mx]|in|cm|mm|p[xtc]|%)?)|(negative)?((very){0,2}thi(n|
         ck)|medium)mathspace)\s*' 
}

A.2.3 プレゼンテーションMathMLの文法
The Grammar for Presentation MathML

#     This is the Mathematical Markup Language (MathML) 3.0, an XML
#     application for describing mathematical notation and capturing
#     both its structure and content.
(注釈:これは数学用マークアップ言語(MathML) 3.0, 数学表記を説明し,
      その構造と内容の両方を捉えるXMLの応用です.)
#
#     Copyright 1998-2014 W3C (MIT, ERCIM, Keio, Beihang)
# 
#     Use and distribution of this code are permitted under the terms
#     W3C Software Notice and License
(注釈:このコードの利用や配布は, W3Cのソフトウェア告示とライセンスの下で許可されます.)
#     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231

default namespace m = "http://www.w3.org/1998/Math/MathML"

MathExpression |= PresentationExpression

ImpliedMrow = MathExpression*

TableRowExpression = mtr|mlabeledtr

TableCellExpression = mtd

MstackExpression = MathExpression|mscarries|msline|msrow|msgroup

MsrowExpression = MathExpression|none

MultiScriptExpression = (MathExpression|none),(MathExpression|none)

mpadded-length
# wrapped for display
(注釈:表示のためのパターンの定義)
 = xsd:string {
  pattern = '\s*([\+\-]?[0-9]*([0-9]\.?|\.[0-9])[0-9]*\s*((%?\s*(height|depth|width)?)|
         e[mx]|in|cm|mm|p[xtc]|((negative)?((very){0,2}thi(n|ck)|medium)mathspace))?)\s*' }

linestyle = "none" | "solid" | "dashed"

verticalalign =
      "top" |
      "bottom" |
      "center" |
      "baseline" |
      "axis"

columnalignstyle = "left" | "center" | "right"

notationstyle =
     "longdiv" |
     "actuarial" |
     "radical" |
     "box" |
     "roundedbox" |
     "circle" |
     "left" |
     "right" |
     "top" |
     "bottom" |
     "updiagonalstrike" |
     "downdiagonalstrike" |
     "verticalstrike" |
     "horizontalstrike" |
     "madruwb"

idref = text
unsigned-integer = xsd:unsignedLong
integer = xsd:integer
number = xsd:decimal

character = xsd:string {
  pattern = '\s*\S\s*'}

color
# wrapped for display
(注釈:表示のためのパターンの定義)
 =  xsd:string {
  pattern = '\s*((#[0-9a-fA-F]{3}([0-9a-fA-F]{3})?)|[aA][qQ][uU][aA]|[bB][lL][aA][cC][kK]|
         [bB][lL][uU][eE]|[fF][uU][cC][hH][sS][iI][aA]|[gG][rR][aA][yY]|[gG][rR][eE][eE][nN]|
         [lL][iI][mM][eE]|[mM][aA][rR][oO][oO][nN]|[nN][aA][vV][yY]|[oO][lL][iI][vV][eE]|[pP][uU][rR][pP][lL][eE]|
         [rR][eE][dD]|[sS][iI][lL][vV][eE][rR]|[tT][eE][aA][lL]|[wW][hH][iI][tT][eE]|[yY][eE][lL][lL][oO][wW])\s*'}


group-alignment = "left" | "center" | "right" | "decimalpoint"
group-alignment-list = list {group-alignment+}
group-alignment-list-list = xsd:string {
  pattern = '(\s*\{\s*(left|center|right|decimalpoint)(\s+(left|center|right|decimalpoint))*\})*\s*' }
positive-integer = xsd:positiveInteger


TokenExpression = mi|mn|mo|mtext|mspace|ms

token.content = mglyph|malignmark|text

mi = element mi {mi.attributes, token.content*}
mi.attributes = 
  CommonAtt,
  CommonPresAtt,
  TokenAtt


mn = element mn {mn.attributes, token.content*}
mn.attributes = 
  CommonAtt,
  CommonPresAtt,
  TokenAtt


mo = element mo {mo.attributes, token.content*}
mo.attributes = 
  CommonAtt,
  CommonPresAtt,
  TokenAtt,
  attribute form {"prefix" | "infix" | "postfix"}?,
  attribute fence {"true" | "false"}?,
  attribute separator {"true" | "false"}?,
  attribute lspace {length}?,
  attribute rspace {length}?,
  attribute stretchy {"true" | "false"}?,
  attribute symmetric {"true" | "false"}?,
  attribute maxsize {length | "infinity"}?,
  attribute minsize {length}?,
  attribute largeop {"true" | "false"}?,
  attribute movablelimits {"true" | "false"}?,
  attribute accent {"true" | "false"}?,
  attribute linebreak {"auto" | "newline" | "nobreak" | "goodbreak" | "badbreak"}?,
  attribute lineleading {length}?,
  attribute linebreakstyle {"before" | "after" | "duplicate" | "infixlinebreakstyle"}?,
  attribute linebreakmultchar {text}?,
  attribute indentalign {"left" | "center" | "right" | "auto" | "id"}?,
  attribute indentshift {length}?,
  attribute indenttarget {idref}?,
  attribute indentalignfirst {"left" | "center" | "right" | "auto" | "id" | "indentalign"}?,
  attribute indentshiftfirst {length | "indentshift"}?,
  attribute indentalignlast {"left" | "center" | "right" | "auto" | "id" | "indentalign"}?,
  attribute indentshiftlast {length | "indentshift"}?


mtext = element mtext {mtext.attributes, token.content*}
mtext.attributes = 
  CommonAtt,
  CommonPresAtt,
  TokenAtt


mspace = element mspace {mspace.attributes, empty}
mspace.attributes = 
  CommonAtt,
  CommonPresAtt,
  TokenAtt,
  attribute width {length}?,
  attribute height {length}?,
  attribute depth {length}?,
  attribute linebreak {"auto" | "newline" | "nobreak" | "goodbreak" | "badbreak" | "indentingnewline"}?,
  attribute indentalign {"left" | "center" | "right" | "auto" | "id"}?,
  attribute indentshift {length}?,
  attribute indenttarget {idref}?,
  attribute indentalignfirst {"left" | "center" | "right" | "auto" | "id" | "indentalign"}?,
  attribute indentshiftfirst {length | "indentshift"}?,
  attribute indentalignlast {"left" | "center" | "right" | "auto" | "id" | "indentalign"}?,
  attribute indentshiftlast {length | "indentshift"}?


ms = element ms {ms.attributes, token.content*}
ms.attributes = 
  CommonAtt,
  CommonPresAtt,
  TokenAtt,
  attribute lquote {text}?,
  attribute rquote {text}?


mglyph = element mglyph {mglyph.attributes,mglyph.deprecatedattributes,empty}
mglyph.attributes = 
  CommonAtt,  CommonPresAtt,
  attribute src {xsd:anyURI}?,
  attribute width {length}?,
  attribute height {length}?,
  attribute valign {length}?,
  attribute alt {text}?
mglyph.deprecatedattributes =
  attribute index {integer}?,
  attribute mathvariant {"normal" | "bold" | "italic" | "bold-italic" | "double-struck" | "bold-fraktur" |
          "script" | "bold-script" | "fraktur" | "sans-serif" | "bold-sans-serif" | "sans-serif-italic" |
          "sans-serif-bold-italic" | "monospace" | "initial" | "tailed" | "looped" | "stretched"}?,
  attribute mathsize {"small" | "normal" | "big" | length}?,
  DeprecatedTokenAtt

msline = element msline {msline.attributes,empty}
msline.attributes = 
  CommonAtt,  CommonPresAtt,
  attribute position {integer}?,
  attribute length {unsigned-integer}?,
  attribute leftoverhang {length}?,
  attribute rightoverhang {length}?,
  attribute mslinethickness {length | "thin" | "medium" | "thick"}?

none = element none {none.attributes,empty}
none.attributes = 
  CommonAtt,
  CommonPresAtt

mprescripts = element mprescripts {mprescripts.attributes,empty}
mprescripts.attributes = 
  CommonAtt,
  CommonPresAtt


CommonPresAtt = 
  attribute mathcolor {color}?,
  attribute mathbackground {color | "transparent"}?

TokenAtt = 
  attribute mathvariant {"normal" | "bold" | "italic" | "bold-italic" | "double-struck" | "bold-fraktur" |
          "script" | "bold-script" | "fraktur" | "sans-serif" | "bold-sans-serif" | "sans-serif-italic" |
          "sans-serif-bold-italic" | "monospace" | "initial" | "tailed" | "looped" | "stretched"}?,
  attribute mathsize {"small" | "normal" | "big" | length}?,
  attribute dir {"ltr" | "rtl"}?,
  DeprecatedTokenAtt

DeprecatedTokenAtt = 
  attribute fontfamily {text}?,
  attribute fontweight {"normal" | "bold"}?,
  attribute fontstyle {"normal" | "italic"}?,
  attribute fontsize {length}?,
  attribute color {color}?,
  attribute background {color | "transparent"}?

MalignExpression = maligngroup|malignmark

malignmark = element malignmark {malignmark.attributes, empty}
malignmark.attributes = 
  CommonAtt, CommonPresAtt,
  attribute edge {"left" | "right"}?


maligngroup = element maligngroup {maligngroup.attributes, empty}
maligngroup.attributes = 
  CommonAtt, CommonPresAtt,
  attribute groupalign {"left" | "center" | "right" | "decimalpoint"}?


PresentationExpression = TokenExpression|MalignExpression|
                         mrow|mfrac|msqrt|mroot|mstyle|merror|mpadded|mphantom|
                         mfenced|menclose|msub|msup|msubsup|munder|mover|munderover|
                         mmultiscripts|mtable|mstack|mlongdiv|maction



mrow = element mrow {mrow.attributes, MathExpression*}
mrow.attributes = 
  CommonAtt, CommonPresAtt,
  attribute dir {"ltr" | "rtl"}?


mfrac = element mfrac {mfrac.attributes, MathExpression, MathExpression}
mfrac.attributes = 
  CommonAtt, CommonPresAtt,
  attribute linethickness {length | "thin" | "medium" | "thick"}?,
  attribute numalign {"left" | "center" | "right"}?,
  attribute denomalign {"left" | "center" | "right"}?,
  attribute bevelled {"true" | "false"}?


msqrt = element msqrt {msqrt.attributes, ImpliedMrow}
msqrt.attributes = 
  CommonAtt, CommonPresAtt


mroot = element mroot {mroot.attributes, MathExpression, MathExpression}
mroot.attributes = 
  CommonAtt, CommonPresAtt


mstyle = element mstyle {mstyle.attributes, ImpliedMrow}
mstyle.attributes = 
  CommonAtt, CommonPresAtt,
  mstyle.specificattributes,
  mstyle.generalattributes,
  mstyle.deprecatedattributes

mstyle.specificattributes =
  attribute scriptlevel {integer}?,
  attribute displaystyle {"true" | "false"}?,
  attribute scriptsizemultiplier {number}?,
  attribute scriptminsize {length}?,
  attribute infixlinebreakstyle {"before" | "after" | "duplicate"}?,
  attribute decimalpoint {character}?

mstyle.generalattributes =
  attribute accent {"true" | "false"}?,
  attribute accentunder {"true" | "false"}?,
  attribute align {"left" | "right" | "center"}?,
  attribute alignmentscope {list {("true" | "false") +}}?,
  attribute bevelled {"true" | "false"}?,
  attribute charalign {"left" | "center" | "right"}?,
  attribute charspacing {length | "loose" | "medium" | "tight"}?,
  attribute close {text}?,
  attribute columnalign {list {columnalignstyle+} }?,
  attribute columnlines {list {linestyle +}}?,
  attribute columnspacing {list {(length) +}}?,
  attribute columnspan {positive-integer}?,
  attribute columnwidth {list {("auto" | length | "fit") +}}?,
  attribute crossout {list {("none" | "updiagonalstrike" | "downdiagonalstrike" | "verticalstrike" | "horizontalstrike")*}}?,
  attribute denomalign {"left" | "center" | "right"}?,
  attribute depth {length}?,
  attribute dir {"ltr" | "rtl"}?,
  attribute edge {"left" | "right"}?,
  attribute equalcolumns {"true" | "false"}?,
  attribute equalrows {"true" | "false"}?,
  attribute fence {"true" | "false"}?,
  attribute form {"prefix" | "infix" | "postfix"}?,
  attribute frame {linestyle}?,
  attribute framespacing {list {length, length}}?,
  attribute groupalign {group-alignment-list-list}?,
  attribute height {length}?,
  attribute indentalign {"left" | "center" | "right" | "auto" | "id"}?,
  attribute indentalignfirst {"left" | "center" | "right" | "auto" | "id" | "indentalign"}?,
  attribute indentalignlast {"left" | "center" | "right" | "auto" | "id" | "indentalign"}?,
  attribute indentshift {length}?,
  attribute indentshiftfirst {length | "indentshift"}?,
  attribute indentshiftlast {length | "indentshift"}?,
  attribute indenttarget {idref}?,
  attribute largeop {"true" | "false"}?,
  attribute leftoverhang {length}?,
  attribute length {unsigned-integer}?,
  attribute linebreak {"auto" | "newline" | "nobreak" | "goodbreak" | "badbreak"}?,
  attribute linebreakmultchar {text}?,
  attribute linebreakstyle {"before" | "after" | "duplicate" | "infixlinebreakstyle"}?,
  attribute lineleading {length}?,
  attribute linethickness {length | "thin" | "medium" | "thick"}?,
  attribute location {"w" | "nw" | "n" | "ne" | "e" | "se" | "s" | "sw"}?,
  attribute longdivstyle {"lefttop" | "stackedrightright" | "mediumstackedrightright" | "shortstackedrightright" |
          "righttop" | "left/\right" | "left)(right" | ":right=right" | "stackedleftleft" |
          "stackedleftlinetop"}?,
  attribute lquote {text}?,
  attribute lspace {length}?,
  attribute mathsize {"small" | "normal" | "big" | length}?,
  attribute mathvariant {"normal" | "bold" | "italic" | "bold-italic" | "double-struck" | "bold-fraktur" |
          "script" | "bold-script" | "fraktur" | "sans-serif" | "bold-sans-serif" | "sans-serif-italic" |
          "sans-serif-bold-italic" | "monospace" | "initial" | "tailed" | "looped" | "stretched"}?,
  attribute maxsize {length | "infinity"}?,
  attribute minlabelspacing {length}?,
  attribute minsize {length}?,
  attribute movablelimits {"true" | "false"}?,
  attribute mslinethickness {length | "thin" | "medium" | "thick"}?,
  attribute notation {text}?,
  attribute numalign {"left" | "center" | "right"}?,
  attribute open {text}?,
  attribute position {integer}?,
  attribute rightoverhang {length}?,
  attribute rowalign {list {verticalalign+} }?,
  attribute rowlines {list {linestyle +}}?,
  attribute rowspacing {list {(length) +}}?,
  attribute rowspan {positive-integer}?,
  attribute rquote {text}?,
  attribute rspace {length}?,
  attribute selection {positive-integer}?,
  attribute separator {"true" | "false"}?,
  attribute separators {text}?,
  attribute shift {integer}?,
  attribute side {"left" | "right" | "leftoverlap" | "rightoverlap"}?,
  attribute stackalign {"left" | "center" | "right" | "decimalpoint"}?,
  attribute stretchy {"true" | "false"}?,
  attribute subscriptshift {length}?,
  attribute superscriptshift {length}?,
  attribute symmetric {"true" | "false"}?,
  attribute valign {length}?,
  attribute width {length}?

mstyle.deprecatedattributes =
  DeprecatedTokenAtt,
  attribute veryverythinmathspace {length}?,
  attribute verythinmathspace {length}?,
  attribute thinmathspace {length}?,
  attribute mediummathspace {length}?,
  attribute thickmathspace {length}?,
  attribute verythickmathspace {length}?,
  attribute veryverythickmathspace {length}?

math.attributes &= CommonPresAtt
math.attributes &= mstyle.specificattributes
math.attributes &= mstyle.generalattributes




merror = element merror {merror.attributes, ImpliedMrow}
merror.attributes = 
  CommonAtt, CommonPresAtt


mpadded = element mpadded {mpadded.attributes, ImpliedMrow}
mpadded.attributes = 
  CommonAtt, CommonPresAtt,
  attribute height {mpadded-length}?,
  attribute depth {mpadded-length}?,
  attribute width {mpadded-length}?,
  attribute lspace {mpadded-length}?,
  attribute voffset {mpadded-length}?


mphantom = element mphantom {mphantom.attributes, ImpliedMrow}
mphantom.attributes = 
  CommonAtt, CommonPresAtt


mfenced = element mfenced {mfenced.attributes, MathExpression*}
mfenced.attributes = 
  CommonAtt, CommonPresAtt,
  attribute open {text}?,
  attribute close {text}?,
  attribute separators {text}?


menclose = element menclose {menclose.attributes, ImpliedMrow}
menclose.attributes = 
  CommonAtt, CommonPresAtt,
  attribute notation {text}?


msub = element msub {msub.attributes, MathExpression, MathExpression}
msub.attributes = 
  CommonAtt, CommonPresAtt,
  attribute subscriptshift {length}?


msup = element msup {msup.attributes, MathExpression, MathExpression}
msup.attributes = 
  CommonAtt, CommonPresAtt,
  attribute superscriptshift {length}?


msubsup = element msubsup {msubsup.attributes, MathExpression, MathExpression, MathExpression}
msubsup.attributes = 
  CommonAtt, CommonPresAtt,
  attribute subscriptshift {length}?,
  attribute superscriptshift {length}?


munder = element munder {munder.attributes, MathExpression, MathExpression}
munder.attributes = 
  CommonAtt, CommonPresAtt,
  attribute accentunder {"true" | "false"}?,
  attribute align {"left" | "right" | "center"}?


mover = element mover {mover.attributes, MathExpression, MathExpression}
mover.attributes = 
  CommonAtt, CommonPresAtt,
  attribute accent {"true" | "false"}?,
  attribute align {"left" | "right" | "center"}?


munderover = element munderover {munderover.attributes, MathExpression, MathExpression, MathExpression}
munderover.attributes = 
  CommonAtt, CommonPresAtt,
  attribute accent {"true" | "false"}?,
  attribute accentunder {"true" | "false"}?,
  attribute align {"left" | "right" | "center"}?


mmultiscripts = element mmultiscripts {mmultiscripts.attributes, MathExpression,MultiScriptExpression*,(mprescripts,MultiScriptExpression*)?}
mmultiscripts.attributes = 
  msubsup.attributes


mtable = element mtable {mtable.attributes, TableRowExpression*}
mtable.attributes = 
  CommonAtt, CommonPresAtt,
  attribute align {xsd:string {
    pattern ='\s*(top|bottom|center|baseline|axis)(\s+-?[0-9]+)?\s*'}}?,
  attribute rowalign {list {verticalalign+} }?,
  attribute columnalign {list {columnalignstyle+} }?,
  attribute groupalign {group-alignment-list-list}?,
  attribute alignmentscope {list {("true" | "false") +}}?,
  attribute columnwidth {list {("auto" | length | "fit") +}}?,
  attribute width {"auto" | length}?,
  attribute rowspacing {list {(length) +}}?,
  attribute columnspacing {list {(length) +}}?,
  attribute rowlines {list {linestyle +}}?,
  attribute columnlines {list {linestyle +}}?,
  attribute frame {linestyle}?,
  attribute framespacing {list {length, length}}?,
  attribute equalrows {"true" | "false"}?,
  attribute equalcolumns {"true" | "false"}?,
  attribute displaystyle {"true" | "false"}?,
  attribute side {"left" | "right" | "leftoverlap" | "rightoverlap"}?,
  attribute minlabelspacing {length}?


mlabeledtr = element mlabeledtr {mlabeledtr.attributes, TableCellExpression+}
mlabeledtr.attributes = 
  mtr.attributes


mtr = element mtr {mtr.attributes, TableCellExpression*}
mtr.attributes = 
  CommonAtt, CommonPresAtt,
  attribute rowalign {"top" | "bottom" | "center" | "baseline" | "axis"}?,
  attribute columnalign {list {columnalignstyle+} }?,
  attribute groupalign {group-alignment-list-list}?


mtd = element mtd {mtd.attributes, ImpliedMrow}
mtd.attributes = 
  CommonAtt, CommonPresAtt,
  attribute rowspan {positive-integer}?,
  attribute columnspan {positive-integer}?,
  attribute rowalign {"top" | "bottom" | "center" | "baseline" | "axis"}?,
  attribute columnalign {columnalignstyle}?,
  attribute groupalign {group-alignment-list}?


mstack = element mstack {mstack.attributes, MstackExpression*}
mstack.attributes = 
  CommonAtt, CommonPresAtt,
  attribute align {xsd:string {
    pattern ='\s*(top|bottom|center|baseline|axis)(\s+-?[0-9]+)?\s*'}}?,
  attribute stackalign {"left" | "center" | "right" | "decimalpoint"}?,
  attribute charalign {"left" | "center" | "right"}?,
  attribute charspacing {length | "loose" | "medium" | "tight"}?


mlongdiv = element mlongdiv {mlongdiv.attributes, MstackExpression,MstackExpression,MstackExpression+}
mlongdiv.attributes = 
  msgroup.attributes,
  attribute longdivstyle {"lefttop" | "stackedrightright" | "mediumstackedrightright" | "shortstackedrightright" |
          "righttop" | "left/\right" | "left)(right" | ":right=right" | "stackedleftleft" |
          "stackedleftlinetop"}?


msgroup = element msgroup {msgroup.attributes, MstackExpression*}
msgroup.attributes = 
  CommonAtt, CommonPresAtt,
  attribute position {integer}?,
  attribute shift {integer}?


msrow = element msrow {msrow.attributes, MsrowExpression*}
msrow.attributes = 
  CommonAtt, CommonPresAtt,
  attribute position {integer}?


mscarries = element mscarries {mscarries.attributes, (MsrowExpression|mscarry)*}
mscarries.attributes = 
  CommonAtt, CommonPresAtt,
  attribute position {integer}?,
  attribute location {"w" | "nw" | "n" | "ne" | "e" | "se" | "s" | "sw"}?,
  attribute crossout {list {("none" | "updiagonalstrike" | "downdiagonalstrike" | "verticalstrike" | "horizontalstrike")*}}?,
  attribute scriptsizemultiplier {number}?


mscarry = element mscarry {mscarry.attributes, MsrowExpression*}
mscarry.attributes = 
  CommonAtt, CommonPresAtt,
  attribute location {"w" | "nw" | "n" | "ne" | "e" | "se" | "s" | "sw"}?,
  attribute crossout {list {("none" | "updiagonalstrike" | "downdiagonalstrike" | "verticalstrike" | "horizontalstrike")*}}?


maction = element maction {maction.attributes, MathExpression+}
maction.attributes = 
  CommonAtt, CommonPresAtt,
  attribute actiontype {text},
  attribute selection {positive-integer}?

A.2.4 厳格なコンテントMathMLの文法
The Grammar for Strict Content MathML3

厳格なコンテントMathML3の文法は, http://www.w3.org/Math/RelaxNG/mathml3/mathml3-strict-content.rncで見ることができます.

The grammar for Strict Content MathML3 can be found at http://www.w3.org/Math/RelaxNG/mathml3/mathml3-strict-content.rnc.

#     This is the Mathematical Markup Language (MathML) 3.0, an XML
#     application for describing mathematical notation and capturing
#     both its structure and content.
(注釈:これは数学用マークアップ言語(MathML) 3.0, 数学表記を説明し,
      その構造と内容の両方を捉えるXMLの応用です.)
#
#     Copyright 1998-2014 W3C (MIT, ERCIM, Keio, Beihang)
# 
#     Use and distribution of this code are permitted under the terms
#     W3C Software Notice and License
(注釈:このコードの利用や配布は, W3Cのソフトウェア告示とライセンスの下で許可されます.)
#     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231


default namespace m = "http://www.w3.org/1998/Math/MathML"

ContExp = semantics-contexp | cn | ci | csymbol | apply | bind | share | cerror | cbytes | cs

cn = element cn {cn.attributes,cn.content}
cn.content = text
cn.attributes = CommonAtt, attribute type {"integer" | "real" | "double" | "hexdouble"}

semantics-ci = element semantics {semantics.attributes,(ci|semantics-ci), 
  (annotation|annotation-xml)*}

semantics-contexp = element semantics {semantics.attributes,ContExp, 
  (annotation|annotation-xml)*}

ci = element ci {ci.attributes, ci.content}
ci.attributes = CommonAtt, ci.type?
ci.type = attribute type {"integer" | "rational" | "real" | "complex" | "complex-polar" | "complex-cartesian" |
          "constant" | "function" | "vector" | "list" | "set" | "matrix"}
ci.content = text


csymbol = element csymbol {csymbol.attributes,csymbol.content}

SymbolName = xsd:NCName
csymbol.attributes = CommonAtt, cd
csymbol.content = SymbolName

BvarQ = bvar*
bvar = element bvar {CommonAtt, (ci | semantics-ci)}

apply = element apply {CommonAtt,apply.content}
apply.content = ContExp+


bind = element bind {CommonAtt,bind.content}
bind.content = ContExp,bvar*,ContExp

share = element share {CommonAtt, src, empty}

cerror = element cerror {cerror.attributes, csymbol, ContExp*}
cerror.attributes = CommonAtt

cbytes = element cbytes {cbytes.attributes, base64}
cbytes.attributes = CommonAtt
base64 = xsd:base64Binary

cs = element cs {cs.attributes, text}
cs.attributes = CommonAtt

MathExpression |= ContExp

A.2.5 コンテントMathMLの文法
The Grammar for Content MathML

コンテントMathML3の文法は, 厳格なコンテントMathMLの文法から形成されており, http://www.w3.org/Math/RelaxNG/mathml3/mathml3-content.rncで見ることができます.

The grammar for Content MathML3 builds on the grammar for the Strict Content MathML subset, and can be found at http://www.w3.org/Math/RelaxNG/mathml3/mathml3-content.rnc.

#     This is the Mathematical Markup Language (MathML) 3.0, an XML
#     application for describing mathematical notation and capturing
#     both its structure and content.
(注釈:これは数学用マークアップ言語(MathML) 3.0, 数学表記を説明し,
      その構造と内容の両方を捉えるXMLの応用です.)
#
#     Copyright 1998-2014 W3C (MIT, ERCIM, Keio, Beihang)
# 
#     Use and distribution of this code are permitted under the terms
#     W3C Software Notice and License
(注釈:このコードの利用や配布は, W3Cのソフトウェア告示とライセンスの下で許可されます.)
#     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231

include "mathml3-strict-content.rnc"{
  cn.content = (text | mglyph | sep | PresentationExpression)* 
  cn.attributes = CommonAtt, DefEncAtt, attribute type {text}?, base?

  ci.attributes = CommonAtt, DefEncAtt, ci.type?
  ci.type = attribute type {text}
  ci.content = (text | mglyph | PresentationExpression)* 

  csymbol.attributes = CommonAtt, DefEncAtt, attribute type {text}?,cd?
  csymbol.content = (text | mglyph | PresentationExpression)* 

  bvar = element bvar {CommonAtt, ((ci | semantics-ci) & degree?)}

  cbytes.attributes = CommonAtt, DefEncAtt

  cs.attributes = CommonAtt, DefEncAtt

  apply.content = ContExp+ | (ContExp, BvarQ, Qualifier*, ContExp*)

  bind.content = apply.content
}

base = attribute base {text}


sep = element sep {empty}
PresentationExpression |= notAllowed


DomainQ = (domainofapplication|condition|interval|(lowlimit,uplimit?))*
domainofapplication = element domainofapplication {ContExp}
condition = element condition {ContExp}
uplimit = element uplimit {ContExp}
lowlimit = element lowlimit {ContExp}

Qualifier = DomainQ|degree|momentabout|logbase
degree = element degree {ContExp}
momentabout = element momentabout {ContExp}
logbase = element logbase {ContExp}

type = attribute type {text}
order = attribute order {"numeric" | "lexicographic"}
closure = attribute closure {text}


ContExp |= piecewise


piecewise = element piecewise {CommonAtt, DefEncAtt,(piece* & otherwise?)}

piece = element piece {CommonAtt, DefEncAtt, ContExp, ContExp}

otherwise = element otherwise {CommonAtt, DefEncAtt, ContExp}


DeprecatedContExp = reln | fn | declare
ContExp |= DeprecatedContExp

reln = element reln {ContExp*}
fn = element fn {ContExp}
declare = element declare {attribute type {xsd:string}?,
                           attribute scope {xsd:string}?,
                           attribute nargs {xsd:nonNegativeInteger}?,
                           attribute occurrence {"prefix"|"infix"|"function-model"}?,
                           DefEncAtt, 
                           ContExp+}


interval.class = interval
ContExp |= interval.class


interval = element interval { CommonAtt, DefEncAtt,closure?, ContExp,ContExp}

unary-functional.class = inverse | ident | domain | codomain | image | ln | log | moment
ContExp |= unary-functional.class


inverse = element inverse { CommonAtt, DefEncAtt, empty}
ident = element ident { CommonAtt, DefEncAtt, empty}
domain = element domain { CommonAtt, DefEncAtt, empty}
codomain = element codomain { CommonAtt, DefEncAtt, empty}
image = element image { CommonAtt, DefEncAtt, empty}
ln = element ln { CommonAtt, DefEncAtt, empty}
log = element log { CommonAtt, DefEncAtt, empty}
moment = element moment { CommonAtt, DefEncAtt, empty}

lambda.class = lambda
ContExp |= lambda.class


lambda = element lambda { CommonAtt, DefEncAtt, BvarQ, DomainQ, ContExp}

nary-functional.class = compose
ContExp |= nary-functional.class


compose = element compose { CommonAtt, DefEncAtt, empty}

binary-arith.class = quotient | divide | minus | power | rem | root
ContExp |= binary-arith.class


quotient = element quotient { CommonAtt, DefEncAtt, empty}
divide = element divide { CommonAtt, DefEncAtt, empty}
minus = element minus { CommonAtt, DefEncAtt, empty}
power = element power { CommonAtt, DefEncAtt, empty}
rem = element rem { CommonAtt, DefEncAtt, empty}
root = element root { CommonAtt, DefEncAtt, empty}

unary-arith.class = factorial | minus | root | abs | conjugate | arg | real | imaginary | floor | ceiling | exp
ContExp |= unary-arith.class


factorial = element factorial { CommonAtt, DefEncAtt, empty}
abs = element abs { CommonAtt, DefEncAtt, empty}
conjugate = element conjugate { CommonAtt, DefEncAtt, empty}
arg = element arg { CommonAtt, DefEncAtt, empty}
real = element real { CommonAtt, DefEncAtt, empty}
imaginary = element imaginary { CommonAtt, DefEncAtt, empty}
floor = element floor { CommonAtt, DefEncAtt, empty}
ceiling = element ceiling { CommonAtt, DefEncAtt, empty}
exp = element exp { CommonAtt, DefEncAtt, empty}

nary-minmax.class = max | min
ContExp |= nary-minmax.class


max = element max { CommonAtt, DefEncAtt, empty}
min = element min { CommonAtt, DefEncAtt, empty}

nary-arith.class = plus | times | gcd | lcm
ContExp |= nary-arith.class


plus = element plus { CommonAtt, DefEncAtt, empty}
times = element times { CommonAtt, DefEncAtt, empty}
gcd = element gcd { CommonAtt, DefEncAtt, empty}
lcm = element lcm { CommonAtt, DefEncAtt, empty}

nary-logical.class = and | or | xor
ContExp |= nary-logical.class


and = element and { CommonAtt, DefEncAtt, empty}
or = element or { CommonAtt, DefEncAtt, empty}
xor = element xor { CommonAtt, DefEncAtt, empty}

unary-logical.class = not
ContExp |= unary-logical.class


not = element not { CommonAtt, DefEncAtt, empty}

binary-logical.class = implies | equivalent
ContExp |= binary-logical.class


implies = element implies { CommonAtt, DefEncAtt, empty}
equivalent = element equivalent { CommonAtt, DefEncAtt, empty}

quantifier.class = forall | exists
ContExp |= quantifier.class


forall = element forall { CommonAtt, DefEncAtt, empty}
exists = element exists { CommonAtt, DefEncAtt, empty}

nary-reln.class = eq | gt | lt | geq | leq
ContExp |= nary-reln.class


eq = element eq { CommonAtt, DefEncAtt, empty}
gt = element gt { CommonAtt, DefEncAtt, empty}
lt = element lt { CommonAtt, DefEncAtt, empty}
geq = element geq { CommonAtt, DefEncAtt, empty}
leq = element leq { CommonAtt, DefEncAtt, empty}

binary-reln.class = neq | approx | factorof | tendsto
ContExp |= binary-reln.class


neq = element neq { CommonAtt, DefEncAtt, empty}
approx = element approx { CommonAtt, DefEncAtt, empty}
factorof = element factorof { CommonAtt, DefEncAtt, empty}
tendsto = element tendsto { CommonAtt, DefEncAtt, type?, empty}

int.class = int
ContExp |= int.class


int = element int { CommonAtt, DefEncAtt, empty}

Differential-Operator.class = diff
ContExp |= Differential-Operator.class


diff = element diff { CommonAtt, DefEncAtt, empty}

partialdiff.class = partialdiff
ContExp |= partialdiff.class


partialdiff = element partialdiff { CommonAtt, DefEncAtt, empty}

unary-veccalc.class = divergence | grad | curl | laplacian
ContExp |= unary-veccalc.class


divergence = element divergence { CommonAtt, DefEncAtt, empty}
grad = element grad { CommonAtt, DefEncAtt, empty}
curl = element curl { CommonAtt, DefEncAtt, empty}
laplacian = element laplacian { CommonAtt, DefEncAtt, empty}

nary-setlist-constructor.class = set | \list
ContExp |= nary-setlist-constructor.class


set = element set { CommonAtt, DefEncAtt, type?, BvarQ*, DomainQ*, ContExp*}
\list = element \list { CommonAtt, DefEncAtt, order?, BvarQ*, DomainQ*, ContExp*}

nary-set.class = union | intersect | cartesianproduct
ContExp |= nary-set.class


union = element union { CommonAtt, DefEncAtt, empty}
intersect = element intersect { CommonAtt, DefEncAtt, empty}
cartesianproduct = element cartesianproduct { CommonAtt, DefEncAtt, empty}

binary-set.class = in | notin | notsubset | notprsubset | setdiff
ContExp |= binary-set.class


in = element in { CommonAtt, DefEncAtt, empty}
notin = element notin { CommonAtt, DefEncAtt, empty}
notsubset = element notsubset { CommonAtt, DefEncAtt, empty}
notprsubset = element notprsubset { CommonAtt, DefEncAtt, empty}
setdiff = element setdiff { CommonAtt, DefEncAtt, empty}

nary-set-reln.class = subset | prsubset
ContExp |= nary-set-reln.class


subset = element subset { CommonAtt, DefEncAtt, empty}
prsubset = element prsubset { CommonAtt, DefEncAtt, empty}

unary-set.class = card
ContExp |= unary-set.class


card = element card { CommonAtt, DefEncAtt, empty}

sum.class = sum
ContExp |= sum.class


sum = element sum { CommonAtt, DefEncAtt, empty}

product.class = product
ContExp |= product.class


product = element product { CommonAtt, DefEncAtt, empty}

limit.class = limit
ContExp |= limit.class


limit = element limit { CommonAtt, DefEncAtt, empty}

unary-elementary.class = sin | cos | tan | sec | csc | cot | sinh | cosh | tanh | sech | csch | coth | arcsin | arccos | arctan | arccosh | arccot | arccoth | arccsc | arccsch | arcsec | arcsech | arcsinh | arctanh
ContExp |= unary-elementary.class


sin = element sin { CommonAtt, DefEncAtt, empty}
cos = element cos { CommonAtt, DefEncAtt, empty}
tan = element tan { CommonAtt, DefEncAtt, empty}
sec = element sec { CommonAtt, DefEncAtt, empty}
csc = element csc { CommonAtt, DefEncAtt, empty}
cot = element cot { CommonAtt, DefEncAtt, empty}
sinh = element sinh { CommonAtt, DefEncAtt, empty}
cosh = element cosh { CommonAtt, DefEncAtt, empty}
tanh = element tanh { CommonAtt, DefEncAtt, empty}
sech = element sech { CommonAtt, DefEncAtt, empty}
csch = element csch { CommonAtt, DefEncAtt, empty}
coth = element coth { CommonAtt, DefEncAtt, empty}
arcsin = element arcsin { CommonAtt, DefEncAtt, empty}
arccos = element arccos { CommonAtt, DefEncAtt, empty}
arctan = element arctan { CommonAtt, DefEncAtt, empty}
arccosh = element arccosh { CommonAtt, DefEncAtt, empty}
arccot = element arccot { CommonAtt, DefEncAtt, empty}
arccoth = element arccoth { CommonAtt, DefEncAtt, empty}
arccsc = element arccsc { CommonAtt, DefEncAtt, empty}
arccsch = element arccsch { CommonAtt, DefEncAtt, empty}
arcsec = element arcsec { CommonAtt, DefEncAtt, empty}
arcsech = element arcsech { CommonAtt, DefEncAtt, empty}
arcsinh = element arcsinh { CommonAtt, DefEncAtt, empty}
arctanh = element arctanh { CommonAtt, DefEncAtt, empty}

nary-stats.class = mean | sdev | variance | median | mode
ContExp |= nary-stats.class


mean = element mean { CommonAtt, DefEncAtt, empty}
sdev = element sdev { CommonAtt, DefEncAtt, empty}
variance = element variance { CommonAtt, DefEncAtt, empty}
median = element median { CommonAtt, DefEncAtt, empty}
mode = element mode { CommonAtt, DefEncAtt, empty}

nary-constructor.class = vector | matrix | matrixrow
ContExp |= nary-constructor.class


vector = element vector { CommonAtt, DefEncAtt, BvarQ, DomainQ, ContExp*}
matrix = element matrix { CommonAtt, DefEncAtt, BvarQ, DomainQ, ContExp*}
matrixrow = element matrixrow { CommonAtt, DefEncAtt, BvarQ, DomainQ, ContExp*}

unary-linalg.class = determinant | transpose
ContExp |= unary-linalg.class


determinant = element determinant { CommonAtt, DefEncAtt, empty}
transpose = element transpose { CommonAtt, DefEncAtt, empty}

nary-linalg.class = selector
ContExp |= nary-linalg.class


selector = element selector { CommonAtt, DefEncAtt, empty}

binary-linalg.class = vectorproduct | scalarproduct | outerproduct
ContExp |= binary-linalg.class


vectorproduct = element vectorproduct { CommonAtt, DefEncAtt, empty}
scalarproduct = element scalarproduct { CommonAtt, DefEncAtt, empty}
outerproduct = element outerproduct { CommonAtt, DefEncAtt, empty}

constant-set.class = integers | reals | rationals | naturalnumbers | complexes | primes | emptyset
ContExp |= constant-set.class


integers = element integers { CommonAtt, DefEncAtt, empty}
reals = element reals { CommonAtt, DefEncAtt, empty}
rationals = element rationals { CommonAtt, DefEncAtt, empty}
naturalnumbers = element naturalnumbers { CommonAtt, DefEncAtt, empty}
complexes = element complexes { CommonAtt, DefEncAtt, empty}
primes = element primes { CommonAtt, DefEncAtt, empty}
emptyset = element emptyset { CommonAtt, DefEncAtt, empty}

constant-arith.class = exponentiale | imaginaryi | notanumber | true | false | pi | eulergamma | infinity
ContExp |= constant-arith.class


exponentiale = element exponentiale { CommonAtt, DefEncAtt, empty}
imaginaryi = element imaginaryi { CommonAtt, DefEncAtt, empty}
notanumber = element notanumber { CommonAtt, DefEncAtt, empty}
true = element true { CommonAtt, DefEncAtt, empty}
false = element false { CommonAtt, DefEncAtt, empty}
pi = element pi { CommonAtt, DefEncAtt, empty}
eulergamma = element eulergamma { CommonAtt, DefEncAtt, empty}
infinity = element infinity { CommonAtt, DefEncAtt, empty}

A.2.6 RelaxNGスキーマにおける部品としてのMathML
MathML as a module in a RelaxNG Schema

通常, MathMLの式は, 完全なXML文書を構成しません. MathMLは, 大きなマークアップ言語の中の数学の部分として使われるように設計されています. 特に, XHTMLに関係するマークアップ言語と一緒に記述される文書の中で, 部品として使われるように設計されています. RelaxNGは直接, 部品の開発に対応しており, その利用は通常とても簡単です. XHTML+MathMLスキーマは, 単純に次のように指定されます.

Normally, a MathML expression does not constitute an entire XML document. MathML is designed to be used as the mathematics fragment of larger markup languages. In particular it is designed to be used as a module in documents marked up with the XHTML family of markup languages. As RelaxNG directly supports modular development, this is usually very easy: an XHTML+MathML schema can be specified as simply as

# A RelaxNG Schema for  XHTML+MathML
(注釈:XHTML+MathMLのRelaxNGスキーマ)
include "xhtml.rnc"
math = external "mathml3.rnc"
Inline.class |= math
Block.class |= math

この構文はXHTMLにおける, 行の一部である要素と領域要素に対する中身の部品を種類ごとに構成するInline.classとBlock.classを利用するRelaxNGスキーマの部分を利用できることを想定しています.

assuming that we have access to a modular RelaxNG schema for XHTML that uses Inline.class and Block.class to collect the the content models for inline and block-level elements.

annotation-xml要素の内容を限定できるようMathML3スキーマを変更することは, 同じように単純で, 例えば, 次のようにです.

Customizing the MathML3 schema so that we can restrict the content of annotation-xml elements is similarly simple, for example:

# A RelaxNG Schema for MathML with OpenMath3 annotations
(注釈:OpenMath3付加情報付きのMathMLのRelaxNGスキーマ)
omobj = external "openmath3.rnc" 
include "mathml3.rnc" {anotation-xml.model = omobj}

MathML3スキーマは体系づけられているので, ここで指定された派生した言語の一部を決定することは簡単です. スキーマに厳格なコンテントMathML3を含めるには, include mathml3.rncの代わりに, 単に次のようにします.

The MathML3 schema is organized so that subsetting to one of the sublanguages specified here is easy. To include strict content MathML3 in a schema just include

include "mathml3-common.rnc"
include "mathml3-strict-content.rnc"

instead of include mathml3.rnc.

RelaxNGの文法と部品化の詳細については詳しくは, [RELAX-NG]または[RelaxNGBook]を参照して下さい.

For details about RelaxNG grammars and modularization see [RELAX-NG] or [RelaxNGBook].

A.3.1 文書の有効性の問題
Document Validation Issues

名前空間の接頭辞の利用は, MathMLを埋め込んでいる文書のDTDの検証に対し, 問題を生じさせます. DTDの検証は, 文書の中の要素の名前の(頭に付けられたであろう)文字列を知っていることが必要です. しかしながら, XML勧告の名前空間 [名前空間]は, 名前空間の接頭辞がどの要素でも宣言できるように, 文書の任意の場所で接頭辞を変えることを認めています.

The use of namespace prefixes creates an issue for DTD validation of documents embedding MathML. DTD validation requires knowing the literal (possibly prefixed) element names used in the document. However, the Namespaces in XML Recommendation [Namespaces] allows the prefix to be changed at arbitrary points in the document, since namespace prefixes may be declared on any element.

MathML DTDは, DTDの中にある全ての要素の名前を実体参照で参照するという[モジュール化]で要素を述べる戦略を使用しています. このことは, DTDが読み込まれる前に, 接頭辞を指定する実体の組を宣言することによって, 接頭辞を文書の著者が選べることを意味します. また, 様々な部品を含む複合したDTDが, DTDの部品を変えることなく, 衝突を避けるように各部品に固有の接頭辞を指定することを意味します.

The MathML DTD uses the strategy outlined in [Modularization] of making every element name in the DTD be accessed by an entity reference. This means that by declaring a couple of entities to specify the prefix before the DTD is loaded, the prefix can be chosen by a document author, and compound DTDs that include several modules can, without changing the module DTDs, specify unique prefixes for each module to avoid clashes.

A.3.2 MathML DTDでの属性値
Attribute values in the MathML DTD

DTDは, RelaxNGスキーマよりはるかに寛大で, 属性値の多くの制限がDTD構文を用いて強制できないことに注意して下さい. 例えば, 多くの属性は, 数値または特定の構文を期待していますが, DTDではCDATA(任意の文字列)として宣言することしかできません. ただし, DTDで必要なことを強制できないことは, その必要なことがMathML言語自体の一部でないことや, 特定のMathML描画ソフトウェアによって強制されないであろうことを意味する訳ではありません. (MathML描画ソフトウェアがMathMLエラーにどう対処すべきかの説明については, 第2.3.2節 エラーの扱いを参照して下さい.)

Note that the DTD is far more permissive than the Relax NG schema, many constraints on attribute values may not be enforced using DTD syntax. For example, many attributes expect numerical values or specific micro-syntax, but are declared as CDATA (arbitrary string) in the DTD. However, lack of enforcement of a requirement in the DTD does not imply that the requirement is not part of the MathML language itself, or that it will not be enforced by a particular MathML renderer. (See Section 2.3.2 Handling of Errors for a description of how MathML renderers should respond to MathML errors.)

その上で, MathML DTDは便利さのために提供されています. 仕様書の文章と完全に互換性があることを意図しているにも関わらず, 矛盾があるかもしれないことが決定的であると受け取るべきです. (この文書の様々な章の間で存在するかもしれない矛盾は, まず, 第7章 文字, 実体, 書式を優先し, 第3章 プレゼンテーションマークアップ, 第4章 コンテントマークアップ, 第2.1節 MathML構文と文法, この文書の他の部分の順に優先していくことで解決されるべきです.

Furthermore, the MathML DTD is provided for convenience; although it is intended to be fully compatible with the text of the specification, the text should be taken as definitive if there is a contradiction. (Any contradictions which may exist between various chapters of the text should be resolved by favoring Chapter 7 Characters, Entities and Fonts first, then Chapter 3 Presentation Markup, Chapter 4 Content Markup, then Section 2.1 MathML Syntax and Grammar, and then other parts of the text.)

A.3.3 MathMLのDOCTYPE宣言
DOCTYPE declaration for MathML

MathML文書は, MathMLのXML DTD, http://www.w3.org/Math/DTD/mathml3/mathml3.dtdを利用して処理されるべきです.

MathML documents should be validated using the XML DTD for MathML, http://www.w3.org/Math/DTD/mathml3/mathml3.dtd.

DTDを使用する文書は, 次の形式のDOCTYPE宣言を含むべきです.

Documents using this DTD should contain a DOCTYPE declaration of the form:

<!DOCTYPE math 
    PUBLIC "-//W3C//DTD MathML 3.0//EN"
           "http://www.w3.org/Math/DTD/mathml3/mathml3.dtd">

上のURIは, 必要に応じてDTDのローカル環境のコピーに変更されるでしょう.

The URI may be changed to that of a local copy of the DTD if required.

A.4.1 MathMLデータにMathMLスキーマを結び付ける
Associating the MathML schema with MathML fragments

文書の中で利用されるDOCTYPE宣言と同様に, MathMLデータにXMLスキーマを下に示すようにリンクすることができます.

Similarly to the DOCTYPE declaration used in documents, it is possible to link a MathML fragment to the XML Schema, as shown below.

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"
          xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
          xsi:schemaLocation="http://www.w3.org/1998/Math/MathML
            http://www.w3.org/Math/XMLSchema/mathml3/mathml3.xsd">
...
</mml:math>

xsi:schemaLocation属性は, XMLスキーマインスタンス名前空間に属しています. 属性値はURIの組です. 1つ目がMathML名前空間URIで, 2つ目がその名前空間に対するスキーマの場所です. 2つ目のURIは, 必要に応じてローカル環境のコピーに変更されるでしょう.

The xsi:schemaLocation attribute belongs to the XML Schema instance namespace, defined in [XMLSchemas]. The value of the attribute is a pair of URIs: the first is the MathML namespace URI and the second is the location of the schema for that namespace. The second URI may be changed to that of a local copy if required.

XMLスキーマ仕様書が示すように, schemaLocation属性の利用は, スキーマ処理ソフトウェアへの助言を与えているのみです. MathMLに配慮した処理プログラムによる検証は, schemaLocation属性が実際のデータで宣言されていることを必要とせずに動作します. さらに, 処理プログラムは, 割当てられているならば, 指定されたスキーマのURLを無視したり上書きしたりできます.

As the XML Schema specification indicates, the use of the schemaLocation attribute is only a hint for schema processors: validation by a MathML-aware processor can be performed without requiring that the schemaLocation attribute be declared in the instance. Moreover, a processor can even ignore or override the specified schema URI, if it is directed to.