/* -*- Mode: Javascript; indent-tabs-mode:nil; js-indent-level: 2 -*- */
/* vim: set ts=2 et sw=2 tw=80: */
/*************************************************************
*
* MathJax/jax/input/MathML/jax.js
*
* Implements the MathML InputJax that reads mathematics in
* MathML format and converts it to the MML ElementJax
* internal format.
*
* ---------------------------------------------------------------------
*
* Copyright (c) 2010-2015 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.
*/
(function (MATHML,BROWSER) {
var MML;
var _ = function (id) {
return MathJax.Localization._.apply(MathJax.Localization,
[["MathML",id]].concat([].slice.call(arguments,1)))
};
MATHML.Parse = MathJax.Object.Subclass({
Init: function (string,script) {this.Parse(string,script)},
//
// Parse the MathML and check for errors
//
Parse: function (math,script) {
var doc;
if (typeof math !== "string") {doc = math.parentNode} else {
doc = MATHML.ParseXML(this.preProcessMath.call(this,math));
if (doc == null) {MATHML.Error(["ErrorParsingMathML","Error parsing MathML"])}
}
var err = doc.getElementsByTagName("parsererror")[0];
if (err) MATHML.Error(["ParsingError","Error parsing MathML: %1",
err.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")]);
if (doc.childNodes.length !== 1)
{MATHML.Error(["MathMLSingleElement","MathML must be formed by a single element"])}
if (doc.firstChild.nodeName.toLowerCase() === "html") {
var h1 = doc.getElementsByTagName("h1")[0];
if (h1 && h1.textContent === "XML parsing error" && h1.nextSibling)
MATHML.Error(["ParsingError","Error parsing MathML: %1",
String(h1.nextSibling.nodeValue).replace(/fatal parsing error: /,"")]);
}
if (doc.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"") !== "math") {
MATHML.Error(["MathMLRootElement",
"MathML must be formed by a <math> element, not %1",
"<"+doc.firstChild.nodeName+">"]);
}
var data = {math:doc.firstChild, script:script};
MATHML.DOMfilterHooks.Execute(data);
this.mml = this.MakeMML(data.math);
},
//
// Convert the MathML structure to the MathJax Element jax structure
//
MakeMML: function (node) {
var CLASS = String(node.getAttribute("class")||""); // make sure CLASS is a string
var mml, type = node.nodeName.toLowerCase().replace(/^[a-z]+:/,"");
var match = (CLASS.match(/(^| )MJX-TeXAtom-([^ ]*)/));
if (match) {
mml = this.TeXAtom(match[2]);
} else if (!(MML[type] && MML[type].isa && MML[type].isa(MML.mbase))) {
MathJax.Hub.signal.Post(["MathML Jax - unknown node type",type]);
return MML.Error(_("UnknownNodeType","Unknown node type: %1",type));
} else {
mml = MML[type]();
}
this.AddAttributes(mml,node); this.CheckClass(mml,mml["class"]);
this.AddChildren(mml,node);
if (MATHML.config.useMathMLspacing) {mml.useMMLspacing = 0x08}
return mml;
},
TeXAtom: function (mclass) {
var mml = MML.TeXAtom().With({texClass:MML.TEXCLASS[mclass]});
if (mml.texClass === MML.TEXCLASS.OP) {mml.movesupsub = mml.movablelimits = true}
return mml;
},
CheckClass: function (mml,CLASS) {
CLASS = (CLASS||"").split(/ /); var NCLASS = [];
for (var i = 0, m = CLASS.length; i < m; i++) {
if (CLASS[i].substr(0,4) === "MJX-") {
if (CLASS[i] === "MJX-arrow") {
// This class was used in former versions of MathJax to attach an
// arrow to the updiagonalstrike notation. For backward
// compatibility, let's continue to accept this case. See issue 481.
if (!mml.notation.match("/"+MML.NOTATION.UPDIAGONALARROW+"/"))
mml.notation += " "+MML.NOTATION.UPDIAGONALARROW;
} else if (CLASS[i] === "MJX-variant") {
mml.variantForm = true;
//
// Variant forms come from AMSsymbols, and it sets up the
// character mappings, so load that if needed.
//
if (!MathJax.Extension["TeX/AMSsymbols"])
{MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/AMSsymbols.js"))}
} else if (CLASS[i].substr(0,11) !== "MJX-TeXAtom") {
mml.mathvariant = CLASS[i].substr(3);
//
// Caligraphic and oldstyle bold are set up in the boldsymbol
// extension, so load it if it isn't already loaded.
//
if (mml.mathvariant === "-tex-caligraphic-bold" ||
mml.mathvariant === "-tex-oldstyle-bold") {
if (!MathJax.Extension["TeX/boldsymbol"])
{MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/boldsymbol.js"))}
}
}
} else {NCLASS.push(CLASS[i])}
}
if (NCLASS.length) {mml["class"] = NCLASS.join(" ")} else {delete mml["class"]}
},
//
// Add the attributes to the mml node
//
AddAttributes: function (mml,node) {
mml.attr = {}; mml.attrNames = [];
for (var i = 0, m = node.attributes.length; i < m; i++) {
var name = node.attributes[i].name;
if (name == "xlink:href") {name = "href"}
if (name.match(/:/)) continue;
if (name.match(/^_moz-math-((column|row)(align|line)|font-style)$/)) continue;
var value = node.attributes[i].value;
value = this.filterAttribute(name,value);
var defaults = (mml.type === "mstyle" ? MML.math.prototype.defaults : mml.defaults);
if (value != null) {
if (value.toLowerCase() === "true") {value = true}
else if (value.toLowerCase() === "false") {value = false}
if (defaults[name] != null || MML.copyAttributes[name])
{mml[name] = value} else {mml.attr[name] = value}
mml.attrNames.push(name);
}
}
},
filterAttribute: function (name,value) {return value}, // safe mode overrides this
//
// Create the children for the mml node
//
AddChildren: function (mml,node) {
for (var i = 0, m = node.childNodes.length; i < m; i++) {
var child = node.childNodes[i];
if (child.nodeName === "#comment") continue;
if (child.nodeName === "#text") {
if ((mml.isToken || mml.isChars) && !mml.mmlSelfClosing) {
var text = child.nodeValue;
if (mml.isToken) {
text = text.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);
text = this.trimSpace(text);
}
mml.Append(MML.chars(text));
} else if (child.nodeValue.match(/\S/)) {
MATHML.Error(["UnexpectedTextNode",
"Unexpected text node: %1","'"+child.nodeValue+"'"]);
}
} else if (mml.type === "annotation-xml") {
mml.Append(MML.xml(child));
} else {
var cmml = this.MakeMML(child); mml.Append(cmml);
if (cmml.mmlSelfClosing && cmml.data.length)
{mml.Append.apply(mml,cmml.data); cmml.data = []}
}
}
if (mml.type === "mrow" && mml.data.length >= 2) {
var first = mml.data[0], last = mml.data[mml.data.length-1];
if (first.type === "mo" && first.Get("fence") &&
last.type === "mo" && last.Get("fence")) {
if (first.data[0]) {mml.open = first.data.join("")}
if (last.data[0]) {mml.close = last.data.join("")}
}
}
},
//
// Clean Up the <math> source to prepare for XML parsing
//
preProcessMath: function (math) {
if (math.match(/^<[a-z]+:/i) && !math.match(/^<[^<>]* xmlns:/)) {
math = math.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')
}
// HTML5 removes xmlns: namespaces, so put them back for XML
var match = math.match(/^(<math( ('.*?'|".*?"|[^>])+)>)/i);
if (match && match[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)) {
math = match[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1") +
math.substr(match[0].length);
}
if (math.match(/^<math/i) && !math.match(/^<[^<>]* xmlns=/)) {
// append the MathML namespace
math = math.replace(/^<(math)/i,'<math xmlns="http://www.w3.org/1998/Math/MathML"')
}
math = math.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");
return math.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);
},
//
// Remove attribute whitespace
//
trimSpace: function (string) {
return string.replace(/[\t\n\r]/g," ") // whitespace to spaces
.replace(/^ +/,"") // initial whitespace
.replace(/ +$/,"") // trailing whitespace
.replace(/ +/g," "); // internal multiple whitespace
},
//
// Replace a named entity by its value
// (look up from external files if necessary)
//
replaceEntity: function (match,entity) {
if (entity.match(/^(lt|amp|quot)$/)) {return match} // these mess up attribute parsing
if (MATHML.Parse.Entity[entity]) {return MATHML.Parse.Entity[entity]}
var file = entity.charAt(0).toLowerCase();
var font = entity.match(/^[a-zA-Z](fr|scr|opf)$/);
if (font) {file = font[1]}
if (!MATHML.Parse.loaded[file]) {
MATHML.Parse.loaded[file] = true;
MathJax.Hub.RestartAfter(MathJax.Ajax.Require(MATHML.entityDir+"/"+file+".js"));
}
return match;
}
}, {
loaded: [] // the entity files that are loaded
});
/************************************************************************/
MATHML.Augment({
sourceMenuTitle: /*_(MathMenu)*/ ["OriginalMathML","Original MathML"],
prefilterHooks: MathJax.Callback.Hooks(true), // hooks to run on MathML string before processing MathML
DOMfilterHooks: MathJax.Callback.Hooks(true), // hooks to run on MathML DOM before processing
postfilterHooks: MathJax.Callback.Hooks(true), // hooks to run on internal jax format after processing MathML
Translate: function (script) {
if (!this.ParseXML) {this.ParseXML = this.createParser()}
var mml, math, data = {script:script};
if (script.firstChild &&
script.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"") === "math") {
data.math = script.firstChild;
} else {
math = MathJax.HTML.getScript(script);
if (BROWSER.isMSIE) {math = math.replace(/( )+$/,"")}
data.math = math;
}
var callback = this.prefilterHooks.Execute(data); if (callback) return callback;
math = data.math;
try {
mml = MATHML.Parse(math,script).mml;
} catch(err) {
if (!err.mathmlError) {throw err}
mml = this.formatError(err,math,script);
}
data.math = MML(mml);
return this.postfilterHooks.Execute(data) || data.math;
},
prefilterMath: function (math,script) {return math},
prefilterMathML: function (math,script) {return math},
formatError: function (err,math,script) {
var message = err.message.replace(/\n.*/,"");
MathJax.Hub.signal.Post(["MathML Jax - parse error",message,math,script]);
return MML.Error(message);
},
Error: function (message) {
//
// Translate message if it is ["id","message",args]
//
if (message instanceof Array) {message = _.apply(_,message)}
throw MathJax.Hub.Insert(Error(message),{mathmlError: true});
},
//
// Parsers for various forms (DOMParser, Windows ActiveX object, other)
//
parseDOM: function (string) {return this.parser.parseFromString(string,"text/xml")},
parseMS: function (string) {return (this.parser.loadXML(string) ? this.parser : null)},
parseDIV: function (string) {
this.div.innerHTML =
"<div>"+string.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>")+"</div>";
var doc = this.div.firstChild;
this.div.innerHTML = "";
return doc;
},
parseError: function (string) {return null},
createMSParser: function() {
var parser = null;
var xml = ["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0",
"MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0",
"MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];
for (var i = 0, m = xml.length; i < m && !parser; i++) {
try {
parser = new ActiveXObject(xml[i])
} catch (err) {}
}
return parser;
},
//
// Create the parser using a DOMParser, or other fallback method
//
createParser: function () {
if (window.DOMParser) {
this.parser = new DOMParser();
return(this.parseDOM);
} else if (window.ActiveXObject) {
this.parser = this.createMSParser();
if (!this.parser) {
MathJax.Localization.Try(this.parserCreationError);
return(this.parseError);
}
this.parser.async = false;
return(this.parseMS);
}
this.div = MathJax.Hub.Insert(document.createElement("div"),{
style:{visibility:"hidden", overflow:"hidden", height:"1px",
position:"absolute", top:0}
});
if (!document.body.firstChild) {document.body.appendChild(this.div)}
else {document.body.insertBefore(this.div,document.body.firstChild)}
return(this.parseDIV);
},
parserCreationError: function () {
alert(_("CantCreateXMLParser",
"MathJax can't create an XML parser for MathML. Check that\n"+
"the 'Script ActiveX controls marked safe for scripting' security\n"+
"setting is enabled (use the Internet Options item in the Tools\n"+
"menu, and select the Security panel, then press the Custom Level\n"+
"button to check this).\n\n"+
"MathML equations will not be able to be processed by MathJax."));
},
//
// Initialize the parser object (whichever type is used)
//
Startup: function () {
MML = MathJax.ElementJax.mml;
MML.mspace.Augment({mmlSelfClosing: true});
MML.none.Augment({mmlSelfClosing: true});
MML.mprescripts.Augment({mmlSelfClosing:true});
MML.maligngroup.Augment({mmlSelfClosing:true});
MML.malignmark.Augment({mmlSelfClosing:true});
}
});
//
// Add the default pre-filter (for backward compatibility)
//
MATHML.prefilterHooks.Add(function (data) {
data.math = (typeof(data.math) === "string" ?
MATHML.prefilterMath(data.math,data.script) :
MATHML.prefilterMathML(data.math,data.script));
});
MATHML.Parse.Entity = {
ApplyFunction: '\u2061',
Backslash: '\u2216',
Because: '\u2235',
Breve: '\u02D8',
Cap: '\u22D2',
CenterDot: '\u00B7',
CircleDot: '\u2299',
CircleMinus: '\u2296',
CirclePlus: '\u2295',
CircleTimes: '\u2297',
Congruent: '\u2261',
ContourIntegral: '\u222E',
Coproduct: '\u2210',
Cross: '\u2A2F',
Cup: '\u22D3',
CupCap: '\u224D',
Dagger: '\u2021',
Del: '\u2207',
Delta: '\u0394',
Diamond: '\u22C4',
DifferentialD: '\u2146',
DotEqual: '\u2250',
DoubleDot: '\u00A8',
DoubleRightTee: '\u22A8',
DoubleVerticalBar: '\u2225',
DownArrow: '\u2193',
DownLeftVector: '\u21BD',
DownRightVector: '\u21C1',
DownTee: '\u22A4',
Downarrow: '\u21D3',
Element: '\u2208',
EqualTilde: '\u2242',
Equilibrium: '\u21CC',
Exists: '\u2203',
ExponentialE: '\u2147',
FilledVerySmallSquare: '\u25AA',
ForAll: '\u2200',
Gamma: '\u0393',
Gg: '\u22D9',
GreaterEqual: '\u2265',
GreaterEqualLess: '\u22DB',
GreaterFullEqual: '\u2267',
GreaterLess: '\u2277',
GreaterSlantEqual: '\u2A7E',
GreaterTilde: '\u2273',
Hacek: '\u02C7',
Hat: '\u005E',
HumpDownHump: '\u224E',
HumpEqual: '\u224F',
Im: '\u2111',
ImaginaryI: '\u2148',
Integral: '\u222B',
Intersection: '\u22C2',
InvisibleComma: '\u2063',
InvisibleTimes: '\u2062',
Lambda: '\u039B',
Larr: '\u219E',
LeftAngleBracket: '\u27E8',
LeftArrow: '\u2190',
LeftArrowRightArrow: '\u21C6',
LeftCeiling: '\u2308',
LeftDownVector: '\u21C3',
LeftFloor: '\u230A',
LeftRightArrow: '\u2194',
LeftTee: '\u22A3',
LeftTriangle: '\u22B2',
LeftTriangleEqual: '\u22B4',
LeftUpVector: '\u21BF',
LeftVector: '\u21BC',
Leftarrow: '\u21D0',
Leftrightarrow: '\u21D4',
LessEqualGreater: '\u22DA',
LessFullEqual: '\u2266',
LessGreater: '\u2276',
LessSlantEqual: '\u2A7D',
LessTilde: '\u2272',
Ll: '\u22D8',
Lleftarrow: '\u21DA',
LongLeftArrow: '\u27F5',
LongLeftRightArrow: '\u27F7',
LongRightArrow: '\u27F6',
Longleftarrow: '\u27F8',
Longleftrightarrow: '\u27FA',
Longrightarrow: '\u27F9',
Lsh: '\u21B0',
MinusPlus: '\u2213',
NestedGreaterGreater: '\u226B',
NestedLessLess: '\u226A',
NotDoubleVerticalBar: '\u2226',
NotElement: '\u2209',
NotEqual: '\u2260',
NotExists: '\u2204',
NotGreater: '\u226F',
NotGreaterEqual: '\u2271',
NotLeftTriangle: '\u22EA',
NotLeftTriangleEqual: '\u22EC',
NotLess: '\u226E',
NotLessEqual: '\u2270',
NotPrecedes: '\u2280',
NotPrecedesSlantEqual: '\u22E0',
NotRightTriangle: '\u22EB',
NotRightTriangleEqual: '\u22ED',
NotSubsetEqual: '\u2288',
NotSucceeds: '\u2281',
NotSucceedsSlantEqual: '\u22E1',
NotSupersetEqual: '\u2289',
NotTilde: '\u2241',
NotVerticalBar: '\u2224',
Omega: '\u03A9',
OverBar: '\u203E',
OverBrace: '\u23DE',
PartialD: '\u2202',
Phi: '\u03A6',
Pi: '\u03A0',
PlusMinus: '\u00B1',
Precedes: '\u227A',
PrecedesEqual: '\u2AAF',
PrecedesSlantEqual: '\u227C',
PrecedesTilde: '\u227E',
Product: '\u220F',
Proportional: '\u221D',
Psi: '\u03A8',
Rarr: '\u21A0',
Re: '\u211C',
ReverseEquilibrium: '\u21CB',
RightAngleBracket: '\u27E9',
RightArrow: '\u2192',
RightArrowLeftArrow: '\u21C4',
RightCeiling: '\u2309',
RightDownVector: '\u21C2',
RightFloor: '\u230B',
RightTee: '\u22A2',
RightTeeArrow: '\u21A6',
RightTriangle: '\u22B3',
RightTriangleEqual: '\u22B5',
RightUpVector: '\u21BE',
RightVector: '\u21C0',
Rightarrow: '\u21D2',
Rrightarrow: '\u21DB',
Rsh: '\u21B1',
Sigma: '\u03A3',
SmallCircle: '\u2218',
Sqrt: '\u221A',
Square: '\u25A1',
SquareIntersection: '\u2293',
SquareSubset: '\u228F',
SquareSubsetEqual: '\u2291',
SquareSuperset: '\u2290',
SquareSupersetEqual: '\u2292',
SquareUnion: '\u2294',
Star: '\u22C6',
Subset: '\u22D0',
SubsetEqual: '\u2286',
Succeeds: '\u227B',
SucceedsEqual: '\u2AB0',
SucceedsSlantEqual: '\u227D',
SucceedsTilde: '\u227F',
SuchThat: '\u220B',
Sum: '\u2211',
Superset: '\u2283',
SupersetEqual: '\u2287',
Supset: '\u22D1',
Therefore: '\u2234',
Theta: '\u0398',
Tilde: '\u223C',
TildeEqual: '\u2243',
TildeFullEqual: '\u2245',
TildeTilde: '\u2248',
UnderBar: '\u005F',
UnderBrace: '\u23DF',
Union: '\u22C3',
UnionPlus: '\u228E',
UpArrow: '\u2191',
UpDownArrow: '\u2195',
UpTee: '\u22A5',
Uparrow: '\u21D1',
Updownarrow: '\u21D5',
Upsilon: '\u03A5',
Vdash: '\u22A9',
Vee: '\u22C1',
VerticalBar: '\u2223',
VerticalTilde: '\u2240',
Vvdash: '\u22AA',
Wedge: '\u22C0',
Xi: '\u039E',
acute: '\u00B4',
aleph: '\u2135',
alpha: '\u03B1',
amalg: '\u2A3F',
and: '\u2227',
ang: '\u2220',
angmsd: '\u2221',
angsph: '\u2222',
ape: '\u224A',
backprime: '\u2035',
backsim: '\u223D',
backsimeq: '\u22CD',
beta: '\u03B2',
beth: '\u2136',
between: '\u226C',
bigcirc: '\u25EF',
bigodot: '\u2A00',
bigoplus: '\u2A01',
bigotimes: '\u2A02',
bigsqcup: '\u2A06',
bigstar: '\u2605',
bigtriangledown: '\u25BD',
bigtriangleup: '\u25B3',
biguplus: '\u2A04',
blacklozenge: '\u29EB',
blacktriangle: '\u25B4',
blacktriangledown: '\u25BE',
blacktriangleleft: '\u25C2',
bowtie: '\u22C8',
boxdl: '\u2510',
boxdr: '\u250C',
boxminus: '\u229F',
boxplus: '\u229E',
boxtimes: '\u22A0',
boxul: '\u2518',
boxur: '\u2514',
bsol: '\u005C',
bull: '\u2022',
cap: '\u2229',
check: '\u2713',
chi: '\u03C7',
circ: '\u02C6',
circeq: '\u2257',
circlearrowleft: '\u21BA',
circlearrowright: '\u21BB',
circledR: '\u00AE',
circledS: '\u24C8',
circledast: '\u229B',
circledcirc: '\u229A',
circleddash: '\u229D',
clubs: '\u2663',
colon: '\u003A',
comp: '\u2201',
ctdot: '\u22EF',
cuepr: '\u22DE',
cuesc: '\u22DF',
cularr: '\u21B6',
cup: '\u222A',
curarr: '\u21B7',
curlyvee: '\u22CE',
curlywedge: '\u22CF',
dagger: '\u2020',
daleth: '\u2138',
ddarr: '\u21CA',
deg: '\u00B0',
delta: '\u03B4',
digamma: '\u03DD',
div: '\u00F7',
divideontimes: '\u22C7',
dot: '\u02D9',
doteqdot: '\u2251',
dotplus: '\u2214',
dotsquare: '\u22A1',
dtdot: '\u22F1',
ecir: '\u2256',
efDot: '\u2252',
egs: '\u2A96',
ell: '\u2113',
els: '\u2A95',
empty: '\u2205',
epsi: '\u03B5',
epsiv: '\u03F5',
erDot: '\u2253',
eta: '\u03B7',
eth: '\u00F0',
flat: '\u266D',
fork: '\u22D4',
frown: '\u2322',
gEl: '\u2A8C',
gamma: '\u03B3',
gap: '\u2A86',
gimel: '\u2137',
gnE: '\u2269',
gnap: '\u2A8A',
gne: '\u2A88',
gnsim: '\u22E7',
gt: '\u003E',
gtdot: '\u22D7',
harrw: '\u21AD',
hbar: '\u210F',
hellip: '\u2026',
hookleftarrow: '\u21A9',
hookrightarrow: '\u21AA',
imath: '\u0131',
infin: '\u221E',
intcal: '\u22BA',
iota: '\u03B9',
jmath: '\u0237',
kappa: '\u03BA',
kappav: '\u03F0',
lEg: '\u2A8B',
lambda: '\u03BB',
lap: '\u2A85',
larrlp: '\u21AB',
larrtl: '\u21A2',
lbrace: '\u007B',
lbrack: '\u005B',
le: '\u2264',
leftleftarrows: '\u21C7',
leftthreetimes: '\u22CB',
lessdot: '\u22D6',
lmoust: '\u23B0',
lnE: '\u2268',
lnap: '\u2A89',
lne: '\u2A87',
lnsim: '\u22E6',
longmapsto: '\u27FC',
looparrowright: '\u21AC',
lowast: '\u2217',
loz: '\u25CA',
lt: '\u003C',
ltimes: '\u22C9',
ltri: '\u25C3',
macr: '\u00AF',
malt: '\u2720',
mho: '\u2127',
mu: '\u03BC',
multimap: '\u22B8',
nLeftarrow: '\u21CD',
nLeftrightarrow: '\u21CE',
nRightarrow: '\u21CF',
nVDash: '\u22AF',
nVdash: '\u22AE',
natur: '\u266E',
nearr: '\u2197',
nharr: '\u21AE',
nlarr: '\u219A',
not: '\u00AC',
nrarr: '\u219B',
nu: '\u03BD',
nvDash: '\u22AD',
nvdash: '\u22AC',
nwarr: '\u2196',
omega: '\u03C9',
omicron: '\u03BF',
or: '\u2228',
osol: '\u2298',
period: '\u002E',
phi: '\u03C6',
phiv: '\u03D5',
pi: '\u03C0',
piv: '\u03D6',
prap: '\u2AB7',
precnapprox: '\u2AB9',
precneqq: '\u2AB5',
precnsim: '\u22E8',
prime: '\u2032',
psi: '\u03C8',
rarrtl: '\u21A3',
rbrace: '\u007D',
rbrack: '\u005D',
rho: '\u03C1',
rhov: '\u03F1',
rightrightarrows: '\u21C9',
rightthreetimes: '\u22CC',
ring: '\u02DA',
rmoust: '\u23B1',
rtimes: '\u22CA',
rtri: '\u25B9',
scap: '\u2AB8',
scnE: '\u2AB6',
scnap: '\u2ABA',
scnsim: '\u22E9',
sdot: '\u22C5',
searr: '\u2198',
sect: '\u00A7',
sharp: '\u266F',
sigma: '\u03C3',
sigmav: '\u03C2',
simne: '\u2246',
smile: '\u2323',
spades: '\u2660',
sub: '\u2282',
subE: '\u2AC5',
subnE: '\u2ACB',
subne: '\u228A',
supE: '\u2AC6',
supnE: '\u2ACC',
supne: '\u228B',
swarr: '\u2199',
tau: '\u03C4',
theta: '\u03B8',
thetav: '\u03D1',
tilde: '\u02DC',
times: '\u00D7',
triangle: '\u25B5',
triangleq: '\u225C',
upsi: '\u03C5',
upuparrows: '\u21C8',
veebar: '\u22BB',
vellip: '\u22EE',
weierp: '\u2118',
xi: '\u03BE',
yen: '\u00A5',
zeta: '\u03B6',
zigrarr: '\u21DD'
};
MATHML.loadComplete("jax.js");
})(MathJax.InputJax.MathML,MathJax.Hub.Browser);