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782 lines
25 KiB
782 lines
25 KiB
5 years ago
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/* -*- Mode: Javascript; indent-tabs-mode:nil; js-indent-level: 2 -*- */
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/* vim: set ts=2 et sw=2 tw=80: */
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/*************************************************************
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*
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* MathJax/jax/input/MathML/jax.js
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*
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* Implements the MathML InputJax that reads mathematics in
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* MathML format and converts it to the MML ElementJax
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* internal format.
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*
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* ---------------------------------------------------------------------
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*
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* Copyright (c) 2010-2018 The MathJax Consortium
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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(function (MATHML,BROWSER) {
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var MML;
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var _ = function (id) {
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return MathJax.Localization._.apply(MathJax.Localization,
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[["MathML",id]].concat([].slice.call(arguments,1)))
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};
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MATHML.Parse = MathJax.Object.Subclass({
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Init: function (string,script) {this.Parse(string,script)},
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//
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// Parse the MathML and check for errors
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//
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Parse: function (math,script) {
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var doc;
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if (typeof math !== "string") {doc = math.parentNode} else {
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doc = MATHML.ParseXML(this.preProcessMath.call(this,math));
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if (doc == null) {MATHML.Error(["ErrorParsingMathML","Error parsing MathML"])}
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}
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var err = doc.getElementsByTagName("parsererror")[0];
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if (err) MATHML.Error(["ParsingError","Error parsing MathML: %1",
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err.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")]);
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if (doc.childNodes.length !== 1)
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{MATHML.Error(["MathMLSingleElement","MathML must be formed by a single element"])}
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if (doc.firstChild.nodeName.toLowerCase() === "html") {
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var h1 = doc.getElementsByTagName("h1")[0];
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if (h1 && h1.textContent === "XML parsing error" && h1.nextSibling)
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MATHML.Error(["ParsingError","Error parsing MathML: %1",
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String(h1.nextSibling.nodeValue).replace(/fatal parsing error: /,"")]);
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}
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if (doc.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"") !== "math") {
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MATHML.Error(["MathMLRootElement",
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"MathML must be formed by a <math> element, not %1",
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"<"+doc.firstChild.nodeName+">"]);
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}
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var data = {math:doc.firstChild, script:script};
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MATHML.DOMfilterHooks.Execute(data);
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this.mml = this.MakeMML(data.math);
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},
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//
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// Convert the MathML structure to the MathJax Element jax structure
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//
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MakeMML: function (node) {
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var CLASS = String(node.getAttribute("class")||""); // make sure CLASS is a string
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var mml, type = node.nodeName.toLowerCase().replace(/^[a-z]+:/,"");
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var match = (CLASS.match(/(^| )MJX-TeXAtom-([^ ]*)/));
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if (match) {
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mml = this.TeXAtom(match[2],match[2] === "OP" && !CLASS.match(/MJX-fixedlimits/));
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} else if (!(MML[type] && MML[type].isa && MML[type].isa(MML.mbase))) {
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MathJax.Hub.signal.Post(["MathML Jax - unknown node type",type]);
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return MML.Error(_("UnknownNodeType","Unknown node type: %1",type));
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} else {
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mml = MML[type]();
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}
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this.AddAttributes(mml,node); this.CheckClass(mml,mml["class"]);
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this.AddChildren(mml,node);
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if (MATHML.config.useMathMLspacing) {mml.useMMLspacing = 0x08}
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return mml;
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},
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TeXAtom: function (mclass,movablelimits) {
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var mml = MML.TeXAtom().With({texClass:MML.TEXCLASS[mclass]});
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if (movablelimits) {mml.movesupsub = mml.movablelimits = true}
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return mml;
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},
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CheckClass: function (mml,CLASS) {
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CLASS = (CLASS||"").split(/ /); var NCLASS = [];
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for (var i = 0, m = CLASS.length; i < m; i++) {
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if (CLASS[i].substr(0,4) === "MJX-") {
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if (CLASS[i] === "MJX-arrow") {
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// This class was used in former versions of MathJax to attach an
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// arrow to the updiagonalstrike notation. For backward
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// compatibility, let's continue to accept this case. See issue 481.
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if (!mml.notation.match("/"+MML.NOTATION.UPDIAGONALARROW+"/"))
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mml.notation += " "+MML.NOTATION.UPDIAGONALARROW;
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} else if (CLASS[i] === "MJX-variant") {
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mml.variantForm = true;
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//
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// Variant forms come from AMSsymbols, and it sets up the
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// character mappings, so load that if needed.
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//
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if (!MathJax.Extension["TeX/AMSsymbols"])
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{MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/AMSsymbols.js"))}
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} else if (CLASS[i].substr(0,11) !== "MJX-TeXAtom") {
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mml.mathvariant = CLASS[i].substr(3);
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//
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// Caligraphic and oldstyle bold are set up in the boldsymbol
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// extension, so load it if it isn't already loaded.
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//
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if (mml.mathvariant === "-tex-caligraphic-bold" ||
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mml.mathvariant === "-tex-oldstyle-bold") {
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if (!MathJax.Extension["TeX/boldsymbol"])
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{MathJax.Hub.RestartAfter(MathJax.Ajax.Require("[MathJax]/extensions/TeX/boldsymbol.js"))}
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}
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}
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} else {NCLASS.push(CLASS[i])}
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}
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if (NCLASS.length) {mml["class"] = NCLASS.join(" ")} else {delete mml["class"]}
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},
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//
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// Add the attributes to the mml node
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//
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AddAttributes: function (mml,node) {
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mml.attr = {}; mml.attrNames = [];
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for (var i = 0, m = node.attributes.length; i < m; i++) {
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var name = node.attributes[i].name;
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if (name == "xlink:href") {name = "href"}
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if (name.match(/:/)) continue;
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if (name.match(/^_moz-math-((column|row)(align|line)|font-style)$/)) continue;
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var value = node.attributes[i].value;
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value = this.filterAttribute(name,value);
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var defaults = (mml.type === "mstyle" ? MML.math.prototype.defaults : mml.defaults);
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if (value != null) {
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var val = value.toLowerCase();
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if (val === "true" || val === "false") {
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if (typeof (defaults[name]) === "boolean" || defaults[name] === MML.INHERIT ||
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mml.type === "math" || mml.type === "mstyle" ||
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(defaults[name] === MML.AUTO &&
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(mml.defaultDef == null || typeof(mml.defaultDef[name]) === "boolean"))) {
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value = (val === "true");
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}
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}
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if (defaults[name] != null || MML.copyAttributes[name])
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{mml[name] = value} else {mml.attr[name] = value}
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mml.attrNames.push(name);
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}
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}
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},
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filterAttribute: function (name,value) {return value}, // safe mode overrides this
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//
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// Create the children for the mml node
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//
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AddChildren: function (mml,node) {
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for (var i = 0, m = node.childNodes.length; i < m; i++) {
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var child = node.childNodes[i];
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if (child.nodeName === "#comment") continue;
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if (child.nodeName === "#text") {
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if ((mml.isToken || mml.isChars) && !mml.mmlSelfClosing) {
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var text = child.nodeValue;
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if (mml.isToken) {
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text = text.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);
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text = this.trimSpace(text);
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}
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mml.Append(MML.chars(text));
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} else if (child.nodeValue.match(/\S/)) {
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MATHML.Error(["UnexpectedTextNode",
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"Unexpected text node: %1","'"+child.nodeValue+"'"]);
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}
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} else if (mml.type === "annotation-xml") {
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mml.Append(MML.xml(child));
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} else {
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var cmml = this.MakeMML(child); mml.Append(cmml);
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if (cmml.mmlSelfClosing && cmml.data.length)
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{mml.Append.apply(mml,cmml.data); cmml.data = []}
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}
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}
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if (mml.type === "mrow" && mml.data.length >= 2) {
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var first = mml.data[0], last = mml.data[mml.data.length-1];
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if (first.type === "mo" && first.Get("fence") &&
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last.type === "mo" && last.Get("fence")) {
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if (first.data[0]) {mml.open = first.data.join("")}
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if (last.data[0]) {mml.close = last.data.join("")}
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}
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}
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},
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//
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// Clean Up the <math> source to prepare for XML parsing
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//
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preProcessMath: function (math) {
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if (math.match(/^<[a-z]+:/i) && !math.match(/^<[^<>]* xmlns:/)) {
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math = math.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')
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}
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// HTML5 removes xmlns: namespaces, so put them back for XML
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var match = math.match(/^(<math( ('.*?'|".*?"|[^>])+)>)/i);
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if (match && match[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)) {
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math = match[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1") +
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math.substr(match[0].length);
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}
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if (math.match(/^<math[ >]/i) && !math.match(/^<[^<>]* xmlns=/)) {
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// append the MathML namespace
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math = math.replace(/^<(math)/i,'<math xmlns="http://www.w3.org/1998/Math/MathML"')
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}
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math = math.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");
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return math.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);
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},
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//
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// Remove attribute whitespace
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//
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trimSpace: function (string) {
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return string.replace(/[\t\n\r]/g," ") // whitespace to spaces
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.replace(/^ +/,"") // initial whitespace
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.replace(/ +$/,"") // trailing whitespace
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.replace(/ +/g," "); // internal multiple whitespace
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},
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//
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// Replace a named entity by its value
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// (look up from external files if necessary)
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//
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replaceEntity: function (match,entity) {
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if (entity.match(/^(lt|amp|quot)$/)) {return match} // these mess up attribute parsing
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if (MATHML.Parse.Entity[entity]) {return MATHML.Parse.Entity[entity]}
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var file = entity.charAt(0).toLowerCase();
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var font = entity.match(/^[a-zA-Z](fr|scr|opf)$/);
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if (font) {file = font[1]}
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if (!MATHML.Parse.loaded[file]) {
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MATHML.Parse.loaded[file] = true;
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MathJax.Hub.RestartAfter(MathJax.Ajax.Require(MATHML.entityDir+"/"+file+".js"));
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}
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return match;
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}
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}, {
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loaded: [] // the entity files that are loaded
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});
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/************************************************************************/
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MATHML.Augment({
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sourceMenuTitle: /*_(MathMenu)*/ ["OriginalMathML","Original MathML"],
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prefilterHooks: MathJax.Callback.Hooks(true), // hooks to run on MathML string before processing MathML
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DOMfilterHooks: MathJax.Callback.Hooks(true), // hooks to run on MathML DOM before processing
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postfilterHooks: MathJax.Callback.Hooks(true), // hooks to run on internal jax format after processing MathML
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Translate: function (script) {
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if (!this.ParseXML) {this.ParseXML = this.createParser()}
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var mml, math, data = {script:script};
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if (script.firstChild &&
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script.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"") === "math") {
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data.math = script.firstChild;
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} else {
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math = MathJax.HTML.getScript(script);
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if (BROWSER.isMSIE) {math = math.replace(/( )+$/,"")}
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data.math = math;
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}
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var callback = this.prefilterHooks.Execute(data); if (callback) return callback;
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math = data.math;
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try {
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mml = MATHML.Parse(math,script).mml;
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} catch(err) {
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if (!err.mathmlError) {throw err}
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mml = this.formatError(err,math,script);
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}
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data.math = MML(mml);
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return this.postfilterHooks.Execute(data) || data.math;
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},
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prefilterMath: function (math,script) {return math},
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prefilterMathML: function (math,script) {return math},
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formatError: function (err,math,script) {
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var message = err.message.replace(/\n.*/,"");
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MathJax.Hub.signal.Post(["MathML Jax - parse error",message,math,script]);
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return MML.Error(message);
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},
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Error: function (message) {
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//
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// Translate message if it is ["id","message",args]
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//
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if (MathJax.Object.isArray(message)) {message = _.apply(_,message)}
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throw MathJax.Hub.Insert(Error(message),{mathmlError: true});
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},
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//
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// Parsers for various forms (DOMParser, Windows ActiveX object, other)
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//
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parseDOM: function (string) {return this.parser.parseFromString(string,"text/xml")},
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parseMS: function (string) {return (this.parser.loadXML(string) ? this.parser : null)},
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parseDIV: function (string) {
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this.div.innerHTML =
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"<div>"+string.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>")+"</div>";
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var doc = this.div.firstChild;
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this.div.innerHTML = "";
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return doc;
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},
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parseError: function (string) {return null},
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createMSParser: function() {
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var parser = null;
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var xml = ["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0",
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"MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0",
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"MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];
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for (var i = 0, m = xml.length; i < m && !parser; i++) {
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|
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);
|