/* -*- Mode: Javascript; indent-tabs-mode:nil; js-indent-level: 2 -*- */
/* vim: set ts=2 et sw=2 tw=80: */
/*************************************************************
*
* MathJax/extensions/TeX/AMSmath.js
*
* Implements AMS math environments and macros.
*
* ---------------------------------------------------------------------
*
* Copyright (c) 2009-2015 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
MathJax.Extension["TeX/AMSmath"] = {
version: "2.5.1",
number: 0, // current equation number
startNumber: 0, // current starting equation number (for when equation is restarted)
IDs: {}, // IDs used in previous equations
eqIDs: {}, // IDs used in this equation
labels: {}, // the set of labels
eqlabels: {}, // labels in the current equation
refs: [] // array of jax with unresolved references
};
MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () {
var MML = MathJax.ElementJax.mml,
TEX = MathJax.InputJax.TeX,
AMS = MathJax.Extension["TeX/AMSmath"];
var TEXDEF = TEX.Definitions,
STACKITEM = TEX.Stack.Item,
CONFIG = TEX.config.equationNumbers;
var COLS = function (W) {
var WW = [];
for (var i = 0, m = W.length; i < m; i++)
{WW[i] = TEX.Parse.prototype.Em(W[i])}
return WW.join(" ");
};
/******************************************************************************/
TEXDEF.Add({
mathchar0mo: {
iiiint: ['2A0C',{texClass: MML.TEXCLASS.OP}]
},
macros: {
mathring: ['Accent','2DA'], // or 0x30A
nobreakspace: 'Tilde',
negmedspace: ['Spacer',MML.LENGTH.NEGATIVEMEDIUMMATHSPACE],
negthickspace: ['Spacer',MML.LENGTH.NEGATIVETHICKMATHSPACE],
// intI: ['Macro','\\mathchoice{\\!}{}{}{}\\!\\!\\int'],
// iint: ['MultiIntegral','\\int\\intI'], // now in core TeX input jax
// iiint: ['MultiIntegral','\\int\\intI\\intI'], // now in core TeX input jax
// iiiint: ['MultiIntegral','\\int\\intI\\intI\\intI'], // now in mathchar0mo above
idotsint: ['MultiIntegral','\\int\\cdots\\int'],
// dddot: ['Macro','\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}',1],
// ddddot: ['Macro','\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}',1],
dddot: ['Accent','20DB'],
ddddot: ['Accent','20DC'],
sideset: ['Macro','\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}',3],
boxed: ['Macro','\\fbox{$\\displaystyle{#1}$}',1],
tag: 'HandleTag',
notag: 'HandleNoTag',
label: 'HandleLabel',
ref: 'HandleRef',
eqref: ['HandleRef',true],
substack: ['Macro','\\begin{subarray}{c}#1\\end{subarray}',1],
injlim: ['NamedOp','inj lim'],
projlim: ['NamedOp','proj lim'],
varliminf: ['Macro','\\mathop{\\underline{\\mmlToken{mi}{lim}}}'],
varlimsup: ['Macro','\\mathop{\\overline{\\mmlToken{mi}{lim}}}'],
varinjlim: ['Macro','\\mathop{\\underrightarrow{\\mmlToken{mi}{lim}\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}'],
varprojlim: ['Macro','\\mathop{\\underleftarrow{\\mmlToken{mi}{lim}\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}'],
DeclareMathOperator: 'HandleDeclareOp',
operatorname: 'HandleOperatorName',
genfrac: 'Genfrac',
frac: ['Genfrac',"","","",""],
tfrac: ['Genfrac',"","","",1],
dfrac: ['Genfrac',"","","",0],
binom: ['Genfrac',"(",")","0",""],
tbinom: ['Genfrac',"(",")","0",1],
dbinom: ['Genfrac',"(",")","0",0],
cfrac: 'CFrac',
shoveleft: ['HandleShove',MML.ALIGN.LEFT],
shoveright: ['HandleShove',MML.ALIGN.RIGHT],
xrightarrow: ['xArrow',0x2192,5,6],
xleftarrow: ['xArrow',0x2190,7,3]
},
environment: {
align: ['AMSarray',null,true,true, 'rlrlrlrlrlrl',COLS([0,2,0,2,0,2,0,2,0,2,0])],
'align*': ['AMSarray',null,false,true, 'rlrlrlrlrlrl',COLS([0,2,0,2,0,2,0,2,0,2,0])],
multline: ['Multline',null,true],
'multline*': ['Multline',null,false],
split: ['AMSarray',null,false,false,'rl',COLS([0])],
gather: ['AMSarray',null,true,true, 'c'],
'gather*': ['AMSarray',null,false,true, 'c'],
alignat: ['AlignAt',null,true,true],
'alignat*': ['AlignAt',null,false,true],
alignedat: ['AlignAt',null,false,false],
aligned: ['AlignedAMSArray',null,null,null,'rlrlrlrlrlrl',COLS([0,2,0,2,0,2,0,2,0,2,0]),".5em",'D'],
gathered: ['AlignedAMSArray',null,null,null,'c',null,".5em",'D'],
subarray: ['Array',null,null,null,null,COLS([0,0,0,0]),"0.1em",'S',1],
smallmatrix: ['Array',null,null,null,'c',COLS([1/3]),".2em",'S',1],
'equation': ['EquationBegin','Equation',true],
'equation*': ['EquationBegin','EquationStar',false],
eqnarray: ['AMSarray',null,true,true, 'rcl',MML.LENGTH.THICKMATHSPACE,".5em"],
'eqnarray*': ['AMSarray',null,false,true,'rcl',MML.LENGTH.THICKMATHSPACE,".5em"]
},
delimiter: {
'\\lvert': ['2223',{texClass:MML.TEXCLASS.OPEN}],
'\\rvert': ['2223',{texClass:MML.TEXCLASS.CLOSE}],
'\\lVert': ['2225',{texClass:MML.TEXCLASS.OPEN}],
'\\rVert': ['2225',{texClass:MML.TEXCLASS.CLOSE}]
}
},null,true);
/******************************************************************************/
TEX.Parse.Augment({
/*
* Add the tag to the environment (to be added to the table row later)
*/
HandleTag: function (name) {
var star = this.GetStar();
var arg = this.trimSpaces(this.GetArgument(name)), tag = arg;
if (!star) {arg = CONFIG.formatTag(arg)}
var global = this.stack.global; global.tagID = tag;
if (global.notags) {
TEX.Error(["CommandNotAllowedInEnv",
"%1 not allowed in %2 environment",
name,global.notags]
);
}
if (global.tag) {TEX.Error(["MultipleCommand","Multiple %1",name])}
global.tag = MML.mtd.apply(MML,this.InternalMath(arg)).With({id:CONFIG.formatID(tag)});
},
HandleNoTag: function (name) {
if (this.stack.global.tag) {delete this.stack.global.tag}
this.stack.global.notag = true; // prevent auto-tagging
},
/*
* Record a label name for a tag
*/
HandleLabel: function (name) {
var global = this.stack.global, label = this.GetArgument(name);
if (label === "") return;
if (!AMS.refUpdate) {
if (global.label) {TEX.Error(["MultipleCommand","Multiple %1",name])}
global.label = label;
if (AMS.labels[label] || AMS.eqlabels[label])
{TEX.Error(["MultipleLabel","Label '%1' multiply defined",label])}
AMS.eqlabels[label] = {tag:"???", id:""}; // will be replaced by tag value later
}
},
/*
* Handle a label reference
*/
HandleRef: function (name,eqref) {
var label = this.GetArgument(name);
var ref = AMS.labels[label] || AMS.eqlabels[label];
if (!ref) {ref = {tag:"???",id:""}; AMS.badref = !AMS.refUpdate}
var tag = ref.tag; if (eqref) {tag = CONFIG.formatTag(tag)}
this.Push(MML.mrow.apply(MML,this.InternalMath(tag)).With({
href:CONFIG.formatURL(ref.id), "class":"MathJax_ref"
}));
},
/*
* Handle \DeclareMathOperator
*/
HandleDeclareOp: function (name) {
var limits = (this.GetStar() ? "" : "\\nolimits");
var cs = this.trimSpaces(this.GetArgument(name));
if (cs.charAt(0) == "\\") {cs = cs.substr(1)}
var op = this.GetArgument(name);
op = op.replace(/\*/g,'\\text{*}').replace(/-/g,'\\text{-}');
TEX.Definitions.macros[cs] = ['Macro','\\mathop{\\rm '+op+'}'+limits];
},
HandleOperatorName: function (name) {
var limits = (this.GetStar() ? "" : "\\nolimits");
var op = this.trimSpaces(this.GetArgument(name));
op = op.replace(/\*/g,'\\text{*}').replace(/-/g,'\\text{-}');
this.string = '\\mathop{\\rm '+op+'}'+limits+" "+this.string.slice(this.i);
this.i = 0;
},
/*
* Record presence of \shoveleft and \shoveright
*/
HandleShove: function (name,shove) {
var top = this.stack.Top();
if (top.type !== "multline" || top.data.length) {
TEX.Error(["CommandAtTheBeginingOfLine",
"%1 must come at the beginning of the line",name]);
}
top.data.shove = shove;
},
/*
* Handle \cfrac
*/
CFrac: function (name) {
var lr = this.trimSpaces(this.GetBrackets(name,"")),
num = this.GetArgument(name),
den = this.GetArgument(name);
var frac = MML.mfrac(TEX.Parse('\\strut\\textstyle{'+num+'}',this.stack.env).mml(),
TEX.Parse('\\strut\\textstyle{'+den+'}',this.stack.env).mml());
lr = ({l:MML.ALIGN.LEFT, r:MML.ALIGN.RIGHT,"":""})[lr];
if (lr == null)
{TEX.Error(["IllegalAlign","Illegal alignment specified in %1",name])}
if (lr) {frac.numalign = frac.denomalign = lr}
this.Push(frac);
},
/*
* Implement AMS generalized fraction
*/
Genfrac: function (name,left,right,thick,style) {
if (left == null) {left = this.GetDelimiterArg(name)}
if (right == null) {right = this.GetDelimiterArg(name)}
if (thick == null) {thick = this.GetArgument(name)}
if (style == null) {style = this.trimSpaces(this.GetArgument(name))}
var num = this.ParseArg(name);
var den = this.ParseArg(name);
var frac = MML.mfrac(num,den);
if (thick !== "") {frac.linethickness = thick}
if (left || right) {frac = TEX.fixedFence(left,frac.With({texWithDelims:true}),right)}
if (style !== "") {
var STYLE = (["D","T","S","SS"])[style];
if (STYLE == null)
{TEX.Error(["BadMathStyleFor","Bad math style for %1",name])}
frac = MML.mstyle(frac);
if (STYLE === "D") {frac.displaystyle = true; frac.scriptlevel = 0}
else {frac.displaystyle = false; frac.scriptlevel = style - 1}
}
this.Push(frac);
},
/*
* Implements multline environment (mostly handled through STACKITEM below)
*/
Multline: function (begin,numbered) {
this.Push(begin); this.checkEqnEnv();
return STACKITEM.multline(numbered,this.stack).With({
arraydef: {
displaystyle: true,
rowspacing: ".5em",
width: TEX.config.MultLineWidth, columnwidth:"100%",
side: TEX.config.TagSide,
minlabelspacing: TEX.config.TagIndent
}
});
},
/*
* Handle AMS aligned environments
*/
AMSarray: function (begin,numbered,taggable,align,spacing) {
this.Push(begin); if (taggable) {this.checkEqnEnv()}
align = align.replace(/[^clr]/g,'').split('').join(' ');
align = align.replace(/l/g,'left').replace(/r/g,'right').replace(/c/g,'center');
return STACKITEM.AMSarray(begin.name,numbered,taggable,this.stack).With({
arraydef: {
displaystyle: true,
rowspacing: ".5em",
columnalign: align,
columnspacing: (spacing||"1em"),
rowspacing: "3pt",
side: TEX.config.TagSide,
minlabelspacing: TEX.config.TagIndent
}
});
},
AlignedAMSArray: function (begin) {
var align = this.GetBrackets("\\begin{"+begin.name+"}");
return this.setArrayAlign(this.AMSarray.apply(this,arguments),align);
},
/*
* Handle alignat environments
*/
AlignAt: function (begin,numbered,taggable) {
var n, valign, align = "", spacing = [];
if (!taggable) {valign = this.GetBrackets("\\begin{"+begin.name+"}")}
n = this.GetArgument("\\begin{"+begin.name+"}");
if (n.match(/[^0-9]/)) {
TEX.Error(["PositiveIntegerArg","Argument to %1 must me a positive integer",
"\\begin{"+begin.name+"}"]);
}
while (n > 0) {align += "rl"; spacing.push("0em 0em"); n--}
spacing = spacing.join(" ");
if (taggable) {return this.AMSarray(begin,numbered,taggable,align,spacing)}
var array = this.Array.call(this,begin,null,null,align,spacing,".5em",'D');
return this.setArrayAlign(array,valign);
},
/*
* Handle equation environment
*/
EquationBegin: function (begin,force) {
this.checkEqnEnv();
this.stack.global.forcetag = (force && CONFIG.autoNumber !== "none");
return begin;
},
EquationStar: function (begin,row) {
this.stack.global.tagged = true; // prevent automatic tagging
return row;
},
/*
* Check for bad nesting of equation environments
*/
checkEqnEnv: function () {
if (this.stack.global.eqnenv)
{TEX.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}
this.stack.global.eqnenv = true;
},
/*
* Handle multiple integrals (make a mathop if followed by limits)
*/
MultiIntegral: function (name,integral) {
var next = this.GetNext();
if (next === "\\") {
var i = this.i; next = this.GetArgument(name); this.i = i;
if (next === "\\limits") {
if (name === "\\idotsint") {integral = "\\!\\!\\mathop{\\,\\,"+integral+"}"}
else {integral = "\\!\\!\\!\\mathop{\\,\\,\\,"+integral+"}"}
}
}
this.string = integral + " " + this.string.slice(this.i);
this.i = 0;
},
/*
* Handle stretchable arrows
*/
xArrow: function (name,chr,l,r) {
var def = {width: "+"+(l+r)+"mu", lspace: l+"mu"};
var bot = this.GetBrackets(name),
top = this.ParseArg(name);
var arrow = MML.mo(MML.chars(String.fromCharCode(chr))).With({
stretchy: true, texClass: MML.TEXCLASS.REL
});
var mml = MML.munderover(arrow);
mml.SetData(mml.over,MML.mpadded(top).With(def).With({voffset:".15em"}));
if (bot) {
bot = TEX.Parse(bot,this.stack.env).mml()
mml.SetData(mml.under,MML.mpadded(bot).With(def).With({voffset:"-.24em"}));
}
this.Push(mml.With({subsupOK:true}));
},
/*
* Get a delimiter or empty argument
*/
GetDelimiterArg: function (name) {
var c = this.trimSpaces(this.GetArgument(name));
if (c == "") return null;
if (TEXDEF.delimiter[c]) return c;
TEX.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",name]);
},
/*
* Get a star following a control sequence name, if any
*/
GetStar: function () {
var star = (this.GetNext() === "*");
if (star) {this.i++}
return star;
}
});
/******************************************************************************/
STACKITEM.Augment({
/*
* Increment equation number and form tag mtd element
*/
autoTag: function () {
var global = this.global;
if (!global.notag) {
AMS.number++; global.tagID = CONFIG.formatNumber(AMS.number.toString());
var mml = TEX.Parse("\\text{"+CONFIG.formatTag(global.tagID)+"}",{}).mml();
global.tag = MML.mtd(mml).With({id:CONFIG.formatID(global.tagID)});
}
},
/*
* Get the tag and record the label, if any
*/
getTag: function () {
var global = this.global, tag = global.tag; global.tagged = true;
if (global.label) {
if (CONFIG.useLabelIds) {tag.id = CONFIG.formatID(global.label)}
AMS.eqlabels[global.label] = {tag:global.tagID, id:tag.id};
}
//
// Check for repeated ID's (either in the document or as
// a previous tag) and find a unique related one. (#240)
//
if (document.getElementById(tag.id) || AMS.IDs[tag.id] || AMS.eqIDs[tag.id]) {
var i = 0, ID;
do {i++; ID = tag.id+"_"+i}
while (document.getElementById(ID) || AMS.IDs[ID] || AMS.eqIDs[ID]);
tag.id = ID; if (global.label) {AMS.eqlabels[global.label].id = ID}
}
AMS.eqIDs[tag.id] = 1;
this.clearTag();
return tag;
},
clearTag: function () {
var global = this.global;
delete global.tag; delete global.tagID; delete global.label;
},
/*
* If the initial child, skipping any initial space or
* empty braces (TeXAtom with child being an empty inferred row),
* is an <mo>, preceed it by an empty <mi> to force the <mo> to
* be infix.
*/
fixInitialMO: function (data) {
for (var i = 0, m = data.length; i < m; i++) {
if (data[i] && (data[i].type !== "mspace" &&
(data[i].type !== "texatom" || (data[i].data[0] && data[i].data[0].data.length)))) {
if (data[i].isEmbellished()) data.unshift(MML.mi());
break;
}
}
}
});
/*
* Implement multline environment via a STACKITEM
*/
STACKITEM.multline = STACKITEM.array.Subclass({
type: "multline",
Init: function (numbered,stack) {
this.SUPER(arguments).Init.apply(this);
this.numbered = (numbered && CONFIG.autoNumber !== "none");
this.save = {notag: stack.global.notag};
stack.global.tagged = !numbered && !stack.global.forcetag; // prevent automatic tagging in starred environments
},
EndEntry: function () {
if (this.table.length) {this.fixInitialMO(this.data)}
var mtd = MML.mtd.apply(MML,this.data);
if (this.data.shove) {mtd.columnalign = this.data.shove}
this.row.push(mtd);
this.data = [];
},
EndRow: function () {
if (this.row.length != 1) {
TEX.Error(["MultlineRowsOneCol",
"The rows within the %1 environment must have exactly one column",
"multline"]);
}
this.table.push(this.row); this.row = [];
},
EndTable: function () {
this.SUPER(arguments).EndTable.call(this);
if (this.table.length) {
var m = this.table.length-1, i, label = -1;
if (!this.table[0][0].columnalign) {this.table[0][0].columnalign = MML.ALIGN.LEFT}
if (!this.table[m][0].columnalign) {this.table[m][0].columnalign = MML.ALIGN.RIGHT}
if (!this.global.tag && this.numbered) {this.autoTag()}
if (this.global.tag && !this.global.notags) {
label = (this.arraydef.side === "left" ? 0 : this.table.length - 1);
this.table[label] = [this.getTag()].concat(this.table[label]);
}
for (i = 0, m = this.table.length; i < m; i++) {
var mtr = (i === label ? MML.mlabeledtr : MML.mtr);
this.table[i] = mtr.apply(MML,this.table[i]);
}
}
this.global.notag = this.save.notag;
}
});
/*
* Save data about numbering and taging equations, and add
* tags at the ends of rows.
*/
STACKITEM.AMSarray = STACKITEM.array.Subclass({
type: "AMSarray",
Init: function (name,numbered,taggable,stack) {
this.SUPER(arguments).Init.apply(this);
this.numbered = (numbered && CONFIG.autoNumber !== "none");
this.save = {notags: stack.global.notags, notag: stack.global.notag};
stack.global.notags = (taggable ? null : name);
stack.global.tagged = !numbered && !stack.global.forcetag; // prevent automatic tagging in starred environments
},
EndEntry: function () {
if (this.row.length) {this.fixInitialMO(this.data)}
this.row.push(MML.mtd.apply(MML,this.data));
this.data = [];
},
EndRow: function () {
var mtr = MML.mtr;
if (!this.global.tag && this.numbered) {this.autoTag()}
if (this.global.tag && !this.global.notags) {
this.row = [this.getTag()].concat(this.row);
mtr = MML.mlabeledtr;
} else {this.clearTag()}
if (this.numbered) {delete this.global.notag}
this.table.push(mtr.apply(MML,this.row)); this.row = [];
},
EndTable: function () {
this.SUPER(arguments).EndTable.call(this);
this.global.notags = this.save.notags;
this.global.notag = this.save.notag;
}
});
//
// Look for \tag on a formula and make an mtable to include it
//
STACKITEM.start.Augment({
oldCheckItem: STACKITEM.start.prototype.checkItem,
checkItem: function (item) {
if (item.type === "stop") {
var mml = this.mmlData(), global = this.global;
if (AMS.display && !global.tag && !global.tagged && !global.isInner &&
(CONFIG.autoNumber === "all" || global.forcetag)) {this.autoTag()}
if (global.tag) {
var row = [this.getTag(),MML.mtd(mml)];
var def = {
side: TEX.config.TagSide,
minlabelspacing: TEX.config.TagIndent,
columnalign: mml.displayAlign,
displaystyle: "inherit" // replaced by TeX input jax Translate() function with actual value
};
if (mml.displayAlign === MML.INDENTALIGN.LEFT) {
def.width = "100%";
if (mml.displayIndent !== "0") {
def.columnwidth = mml.displayIndent + " fit"; def.columnspacing = "0"
row = [row[0],MML.mtd(),row[1]];
}
} else if (mml.displayAlign === MML.INDENTALIGN.RIGHT) {
def.width = "100%";
if (mml.displayIndent !== "0") {
def.columnwidth = "fit "+mml.displayIndent; def.columnspacing = "0"
row[2] = MML.mtd();
}
}
mml = MML.mtable(MML.mlabeledtr.apply(MML,row)).With(def);
}
return STACKITEM.mml(mml);
}
return this.oldCheckItem.call(this,item);
}
});
/******************************************************************************/
/*
* Add pre- and post-filters to handle the equation number maintainance.
*/
TEX.prefilterHooks.Add(function (data) {
AMS.display = data.display;
AMS.number = AMS.startNumber; // reset equation numbers (in case the equation restarted)
AMS.eqlabels = AMS.eqIDs = {}; AMS.badref = false;
if (AMS.refUpdate) {AMS.number = data.script.MathJax.startNumber}
});
TEX.postfilterHooks.Add(function (data) {
data.script.MathJax.startNumber = AMS.startNumber;
AMS.startNumber = AMS.number; // equation numbers for next equation
MathJax.Hub.Insert(AMS.IDs,AMS.eqIDs); // save IDs from this equation
MathJax.Hub.Insert(AMS.labels,AMS.eqlabels); // save labels from this equation
if (AMS.badref && !data.math.texError) {AMS.refs.push(data.script)} // reprocess later
},100);
MathJax.Hub.Register.MessageHook("Begin Math Input",function () {
AMS.refs = []; // array of jax with bad references
AMS.refUpdate = false;
});
MathJax.Hub.Register.MessageHook("End Math Input",function (message) {
if (AMS.refs.length) {
AMS.refUpdate = true;
for (var i = 0, m = AMS.refs.length; i < m; i++)
{AMS.refs[i].MathJax.state = MathJax.ElementJax.STATE.UPDATE}
return MathJax.Hub.processInput({
scripts:AMS.refs,
start: new Date().getTime(),
i:0, j:0, jax:{}, jaxIDs:[]
});
}
return null;
});
//
// Clear the equation numbers and labels
//
TEX.resetEquationNumbers = function (n,keepLabels) {
AMS.startNumber = (n || 0);
if (!keepLabels) {AMS.labels = AMS.IDs = {}}
}
/******************************************************************************/
MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready");
});
MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js");