mw.loader.implement("ext.math.mathjax.jax.input.TeX",function($,jQuery){(function(TEX,HUB,AJAX){var MML,NBSP="\u00A0";var _=function(id){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",id]].concat([].slice.call(arguments,1)));};var STACK=MathJax.Object.Subclass({Init:function(env,inner){this.global={isInner:inner};this.data=[STACKITEM.start(this.global)];if(env){this.data[0].env=env}this.env=this.data[0].env;},Push:function(){var i,m,item,top;for(i=0,m=arguments.length;i<m;i++){item=arguments[i];if(item instanceof MML.mbase){item=STACKITEM.mml(item)}item.global=this.global;top=(this.data.length?this.Top().checkItem(item):true);if(top instanceof Array){this.Pop();this.Push.apply(this,top)}else if(top instanceof STACKITEM){this.Pop();this.Push(top)}else if(top){this.data.push(item);if(item.env){for(var id in this.env){if(this.env.hasOwnProperty(id)){item.env[id]=this.env[id]}}this.env=item.env;}else{item.env=this.env}}}},Pop:function(){var item=this.data.pop();if(!item.
isOpen){delete item.env}this.env=(this.data.length?this.Top().env:{});return item;},Top:function(n){if(n==null){n=1}if(this.data.length<n){return null}return this.data[this.data.length-n];},Prev:function(noPop){var top=this.Top();if(noPop){return top.data[top.data.length-1]}else{return top.Pop()}},toString:function(){return"stack[\n  "+this.data.join("\n  ")+"\n]"}});var STACKITEM=STACK.Item=MathJax.Object.Subclass({type:"base",endError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],closeError:["ExtraCloseMissingOpen","Extra close brace or missing open brace"],rightError:["MissingLeftExtraRight","Missing \\left or extra \\right"],Init:function(){if(this.isOpen){this.env={}}this.data=[];this.Push.apply(this,arguments);},Push:function(){this.data.push.apply(this.data,arguments)},Pop:function(){return this.data.pop()},mmlData:function(inferred,forceRow){if(inferred==null){inferred=true}if(this.data.length===1&&!forceRow){return this.data[0]}return MML.mrow.apply(MML,
this.data).With((inferred?{inferred:true}:{}));},checkItem:function(item){if(item.type==="over"&&this.isOpen){item.num=this.mmlData(false);this.data=[]}if(item.type==="cell"&&this.isOpen){if(item.linebreak){return false}TEX.Error(["Misplaced","Misplaced %1",item.name]);}if(item.isClose&&this[item.type+"Error"]){TEX.Error(this[item.type+"Error"])}if(!item.isNotStack){return true}this.Push(item.data[0]);return false;},With:function(def){for(var id in def){if(def.hasOwnProperty(id)){this[id]=def[id]}}return this;},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});STACKITEM.start=STACKITEM.Subclass({type:"start",isOpen:true,Init:function(global){this.SUPER(arguments).Init.call(this);this.global=global;},checkItem:function(item){if(item.type==="stop"){return STACKITEM.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,item);}});STACKITEM.stop=STACKITEM.Subclass({type:"stop",isClose:true});STACKITEM.open=STACKITEM.Subclass({type:"open",isOpen:true,
stopError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],checkItem:function(item){if(item.type==="close"){var mml=this.mmlData();return STACKITEM.mml(MML.TeXAtom(mml));}return this.SUPER(arguments).checkItem.call(this,item);}});STACKITEM.close=STACKITEM.Subclass({type:"close",isClose:true});STACKITEM.prime=STACKITEM.Subclass({type:"prime",checkItem:function(item){if(this.data[0].type!=="msubsup"){return[MML.msup(this.data[0],this.data[1]),item]}this.data[0].SetData(this.data[0].sup,this.data[1]);return[this.data[0],item];}});STACKITEM.subsup=STACKITEM.Subclass({type:"subsup",stopError:["MissingScript","Missing superscript or subscript argument"],supError:["MissingOpenForSup","Missing open brace for superscript"],subError:["MissingOpenForSub","Missing open brace for subscript"],checkItem:function(item){if(item.type==="open"||item.type==="left"){return true}if(item.type==="mml"){if(this.primes){if(this.position!==2){this.data[0].SetData(2,this.primes)}else{item.data[
0]=MML.mrow(this.primes.With({variantForm:true}),item.data[0])}}this.data[0].SetData(this.position,item.data[0]);return STACKITEM.mml(this.data[0]);}if(this.SUPER(arguments).checkItem.call(this,item)){TEX.Error(this[["","subError","supError"][this.position]])}},Pop:function(){}});STACKITEM.over=STACKITEM.Subclass({type:"over",isClose:true,name:"\\over",checkItem:function(item,stack){if(item.type==="over"){TEX.Error(["AmbiguousUseOf","Ambiguous use of %1",item.name])}if(item.isClose){var mml=MML.mfrac(this.num,this.mmlData(false));if(this.thickness!=null){mml.linethickness=this.thickness}if(this.open||this.close){mml.texClass=MML.TEXCLASS.INNER;mml.texWithDelims=true;mml=TEX.fenced(this.open,mml,this.close);}return[STACKITEM.mml(mml),item];}return this.SUPER(arguments).checkItem.call(this,item);},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});STACKITEM.left=STACKITEM.Subclass({type:"left",isOpen:true,delim:'(',stopError:["ExtraLeftMissingRight",
"Extra \\left or missing \\right"],checkItem:function(item){if(item.type==="right"){return STACKITEM.mml(TEX.fenced(this.delim,this.mmlData(),item.delim))}return this.SUPER(arguments).checkItem.call(this,item);}});STACKITEM.right=STACKITEM.Subclass({type:"right",isClose:true,delim:')'});STACKITEM.begin=STACKITEM.Subclass({type:"begin",isOpen:true,checkItem:function(item){if(item.type==="end"){if(item.name!==this.name){TEX.Error(["EnvBadEnd","\\begin{%1} ended with \\end{%2}",this.name,item.name])}if(!this.end){return STACKITEM.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data);}if(item.type==="stop"){TEX.Error(["EnvMissingEnd","Missing \\end{%1}",this.name])}return this.SUPER(arguments).checkItem.call(this,item);}});STACKITEM.end=STACKITEM.Subclass({type:"end",isClose:true});STACKITEM.style=STACKITEM.Subclass({type:"style",checkItem:function(item){if(!item.isClose){return this.SUPER(arguments).checkItem.call(this,item)}var mml=MML.mstyle.apply(MML,this.data
).With(this.styles);return[STACKITEM.mml(mml),item];}});STACKITEM.position=STACKITEM.Subclass({type:"position",checkItem:function(item){if(item.isClose){TEX.Error(["MissingBoxFor","Missing box for %1",this.name])}if(item.isNotStack){var mml=item.mmlData();switch(this.move){case'vertical':mml=MML.mpadded(mml).With({height:this.dh,depth:this.dd,voffset:this.dh});return[STACKITEM.mml(mml)];case'horizontal':return[STACKITEM.mml(this.left),item,STACKITEM.mml(this.right)];}}return this.SUPER(arguments).checkItem.call(this,item);}});STACKITEM.array=STACKITEM.Subclass({type:"array",isOpen:true,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.frame=[]
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checkItem.call(this,item);},EndEntry:function(){this.row.push(MML.mtd.apply(MML,this.data));this.data=[]},EndRow:function(){this.table.push(MML.mtr.apply(MML,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines();},checkLines:function(){if(this.arraydef.rowlines){var lines=this.arraydef.rowlines.split(/ /);if(lines.length===this.table.length){this.frame.push("bottom");lines.pop();this.arraydef.rowlines=lines.join(' ');}else if(lines.length<this.table.length-1){this.arraydef.rowlines+=" none";}}if(this.rowspacing){var rows=this.arraydef.rowspacing.split(/ /);while(rows.length<this.table.length){rows.push(this.rowspacing+"em")}this.arraydef.rowspacing=rows.join(' ');}},clearEnv:function(){for(var id in this.env){if(this.env.hasOwnProperty(id)){delete this.env[id]}}}});STACKITEM.cell=STACKITEM.Subclass({type:"cell",isClose:true});STACKITEM.mml=STACKITEM.Subclass({type:"mml",isNotStack:true,Add:function(){this.data.
push.apply(this.data,arguments);return this}});STACKITEM.fn=STACKITEM.Subclass({type:"fn",checkItem:function(item){if(this.data[0]){if(item.type!=="mml"||!item.data[0]){return[this.data[0],item]}if(item.data[0].isa(MML.mspace)){return[this.data[0],item]}var mml=item.data[0];if(mml.isEmbellished()){mml=mml.CoreMO()}if([0,0,1,1,0,1,1,0,0,0][mml.Get("texClass")]){return[this.data[0],item]}return[this.data[0],MML.mo(MML.entity("#x2061")).With({texClass:MML.TEXCLASS.NONE}),item];}return this.SUPER(arguments).checkItem.apply(this,arguments);}});STACKITEM.not=STACKITEM.Subclass({type:"not",checkItem:function(item){var mml,c;if(item.type==="open"||item.type==="left"){return true}if(item.type==="mml"&&item.data[0].type.match(/^(mo|mi|mtext)$/)){mml=item.data[0],c=mml.data.join("");if(c.length===1&&!mml.movesupsub){c=STACKITEM.not.remap[c.charCodeAt(0)];if(c){mml.SetData(0,MML.chars(String.fromCharCode(c)))}else{mml.Append(MML.chars("\u0338"))}return item;}}mml=MML.mpadded(MML.mtext("\u29F8")).
With({width:0});mml=MML.TeXAtom(mml).With({texClass:MML.TEXCLASS.REL});return[mml,item];}});STACKITEM.not.remap={0x2190:0x219A,0x2192:0x219B,0x2194:0x21AE,0x21D0:0x21CD,0x21D2:0x21CF,0x21D4:0x21CE,0x2208:0x2209,0x220B:0x220C,0x2223:0x2224,0x2225:0x2226,0x223C:0x2241,0x007E:0x2241,0x2243:0x2244,0x2245:0x2247,0x2248:0x2249,0x224D:0x226D,0x003D:0x2260,0x2261:0x2262,0x003C:0x226E,0x003E:0x226F,0x2264:0x2270,0x2265:0x2271,0x2272:0x2274,0x2273:0x2275,0x2276:0x2278,0x2277:0x2279,0x227A:0x2280,0x227B:0x2281,0x2282:0x2284,0x2283:0x2285,0x2286:0x2288,0x2287:0x2289,0x22A2:0x22AC,0x22A8:0x22AD,0x22A9:0x22AE,0x22AB:0x22AF,0x227C:0x22E0,0x227D:0x22E1,0x2291:0x22E2,0x2292:0x22E3,0x22B2:0x22EA,0x22B3:0x22EB,0x22B4:0x22EC,0x22B5:0x22ED,0x2203:0x2204};STACKITEM.dots=STACKITEM.Subclass({type:"dots",checkItem:function(item){if(item.type==="open"||item.type==="left"){return true}var dots=this.ldots;if(item.type==="mml"&&item.data[0].isEmbellished()){var tclass=item.data[0].CoreMO().Get("texClass");if(
tclass===MML.TEXCLASS.BIN||tclass===MML.TEXCLASS.REL){dots=this.cdots}}return[dots,item];}});var TEXDEF={Add:function(src,dst,nouser){if(!dst){dst=this}for(var id in src){if(src.hasOwnProperty(id)){if(typeof src[id]==='object'&&!(src[id]instanceof Array)&&(typeof dst[id]==='object'||typeof dst[id]==='function')){this.Add(src[id],dst[id],src[id],nouser)}else if(!dst[id]||!dst[id].isUser||!nouser){dst[id]=src[id]}}}return dst;}};var STARTUP=function(){MML=MathJax.ElementJax.mml;HUB.Insert(TEXDEF,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{'\\':'ControlSequence','{':'Open','}':'Close','~':'Tilde','^':'Superscript','_':'Subscript',' ':'Space',"\t":'Space',"\r":'Space',"\n":'Space',"'":'Prime','%':'Comment','&':'Entry','#':'Hash','\u2019':'Prime'},remap:{'-':'2212','*':'2217','`':'2018'},mathchar0mi:{alpha:'03B1',beta:'03B2',gamma:'03B3',delta:'03B4',epsilon:'03F5',zeta:'03B6',eta:'03B7',theta:'03B8',iota:'03B9',kappa:'03BA',lambda:
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backslash:['2216',{mathvariant:MML.VARIANT.NORMAL,variantForm:true}],forall:['2200',{mathvariant:MML.VARIANT.NORMAL}],exists:['2203',{mathvariant:MML.VARIANT.NORMAL}],neg:['00AC',{mathvariant:MML.VARIANT.NORMAL}],lnot:['00AC',{mathvariant:MML.VARIANT.NORMAL}],flat:['266D',{mathvariant:MML.VARIANT.NORMAL}],natural:['266E',{mathvariant:MML.VARIANT.NORMAL}],sharp:['266F',{mathvariant:MML.VARIANT.NORMAL}],clubsuit:['2663',{mathvariant:MML.VARIANT.NORMAL}],diamondsuit:['2662',{mathvariant:MML.VARIANT.NORMAL}],heartsuit:['2661',{mathvariant:MML.VARIANT.NORMAL}],spadesuit:['2660',{mathvariant:MML.VARIANT.NORMAL}]},mathchar0mo:{surd:'221A',coprod:['2210',{texClass:MML.TEXCLASS.OP,movesupsub:true}],bigvee:['22C1',{texClass:MML.TEXCLASS.OP,movesupsub:true}],bigwedge:['22C0',{texClass:MML.TEXCLASS.OP,movesupsub:true}],biguplus:['2A04',{texClass:MML.TEXCLASS.OP,movesupsub:true}],bigcap:['22C2',{texClass:MML.TEXCLASS.OP,movesupsub:true}],bigcup:['22C3',{texClass:MML.TEXCLASS.OP,movesupsub:true}],
'int':['222B',{texClass:MML.TEXCLASS.OP}],intop:['222B',{texClass:MML.TEXCLASS.OP,movesupsub:true,movablelimits:true}],iint:['222C',{texClass:MML.TEXCLASS.OP}],iiint:['222D',{texClass:MML.TEXCLASS.OP}],prod:['220F',{texClass:MML.TEXCLASS.OP,movesupsub:true}],sum:['2211',{texClass:MML.TEXCLASS.OP,movesupsub:true}],bigotimes:['2A02',{texClass:MML.TEXCLASS.OP,movesupsub:true}],bigoplus:['2A01',{texClass:MML.TEXCLASS.OP,movesupsub:true}],bigodot:['2A00',{texClass:MML.TEXCLASS.OP,movesupsub:true}],oint:['222E',{texClass:MML.TEXCLASS.OP}],bigsqcup:['2A06',{texClass:MML.TEXCLASS.OP,movesupsub:true}],smallint:['222B',{largeop:false}],triangleleft:'25C3',triangleright:'25B9',bigtriangleup:'25B3',bigtriangledown:'25BD',wedge:'2227',land:'2227',vee:'2228',lor:'2228',cap:'2229',cup:'222A',ddagger:'2021',dagger:'2020',sqcap:'2293',sqcup:'2294',uplus:'228E',amalg:'2A3F',diamond:'22C4',bullet:'2219',wr:'2240',div:'00F7',odot:['2299',{largeop:false}],oslash:['2298',{largeop:false}],otimes:['2297',{
largeop:false}],ominus:['2296',{largeop:false}],oplus:['2295',{largeop:false}],mp:'2213',pm:'00B1',circ:'2218',bigcirc:'25EF',setminus:['2216',{variantForm:true}],cdot:'22C5',ast:'2217',times:'00D7',star:'22C6',propto:'221D',sqsubseteq:'2291',sqsupseteq:'2292',parallel:'2225',mid:'2223',dashv:'22A3',vdash:'22A2',leq:'2264',le:'2264',geq:'2265',ge:'2265',lt:'003C',gt:'003E',succ:'227B',prec:'227A',approx:'2248',succeq:'2AB0',preceq:'2AAF',supset:'2283',subset:'2282',supseteq:'2287',subseteq:'2286','in':'2208',ni:'220B',notin:'2209',owns:'220B',gg:'226B',ll:'226A',sim:'223C',simeq:'2243',perp:'22A5',equiv:'2261',asymp:'224D',smile:'2323',frown:'2322',ne:'2260',neq:'2260',cong:'2245',doteq:'2250',bowtie:'22C8',models:'22A8',notChar:'29F8',Leftrightarrow:'21D4',Leftarrow:'21D0',Rightarrow:'21D2',leftrightarrow:'2194',leftarrow:'2190',gets:'2190',rightarrow:'2192',to:'2192',mapsto:'21A6',leftharpoonup:'21BC',leftharpoondown:'21BD',rightharpoonup:'21C0',rightharpoondown:'21C1',nearrow:'2197'
,searrow:'2198',nwarrow:'2196',swarrow:'2199',rightleftharpoons:'21CC',hookrightarrow:'21AA',hookleftarrow:'21A9',longleftarrow:'27F5',Longleftarrow:'27F8',longrightarrow:'27F6',Longrightarrow:'27F9',Longleftrightarrow:'27FA',longleftrightarrow:'27F7',longmapsto:'27FC',ldots:'2026',cdots:'22EF',vdots:'22EE',ddots:'22F1',dotsc:'2026',dotsb:'22EF',dotsm:'22EF',dotsi:'22EF',dotso:'2026',ldotp:['002E',{texClass:MML.TEXCLASS.PUNCT}],cdotp:['22C5',{texClass:MML.TEXCLASS.PUNCT}],colon:['003A',{texClass:MML.TEXCLASS.PUNCT}]},mathchar7:{Gamma:'0393',Delta:'0394',Theta:'0398',Lambda:'039B',Xi:'039E',Pi:'03A0',Sigma:'03A3',Upsilon:'03A5',Phi:'03A6',Psi:'03A8',Omega:'03A9','_':'005F','#':'0023','$':'0024','%':'0025','&':'0026',And:'0026'},delimiter:{'(':'(',')':')','[':'[',']':']','<':'27E8','>':'27E9','\\lt':'27E8','\\gt':'27E9','/':'/','|':['|',{texClass:MML.TEXCLASS.ORD}],'.':'','\\\\':'\\','\\lmoustache':'23B0','\\rmoustache':'23B1','\\lgroup':'27EE','\\rgroup':'27EF','\\arrowvert':'23D0',
'\\Arrowvert':'2016','\\bracevert':'23AA','\\Vert':['2225',{texClass:MML.TEXCLASS.ORD}],'\\|':['2225',{texClass:MML.TEXCLASS.ORD}],'\\vert':['|',{texClass:MML.TEXCLASS.ORD}],'\\uparrow':'2191','\\downarrow':'2193','\\updownarrow':'2195','\\Uparrow':'21D1','\\Downarrow':'21D3','\\Updownarrow':'21D5','\\backslash':'\\','\\rangle':'27E9','\\langle':'27E8','\\rbrace':'}','\\lbrace':'{','\\}':'}','\\{':'{','\\rceil':'2309','\\lceil':'2308','\\rfloor':'230B','\\lfloor':'230A','\\lbrack':'[','\\rbrack':']'},macros:{displaystyle:['SetStyle','D',true,0],textstyle:['SetStyle','T',false,0],scriptstyle:['SetStyle','S',false,1],scriptscriptstyle:['SetStyle','SS',false,2],rm:['SetFont',MML.VARIANT.NORMAL],mit:['SetFont',MML.VARIANT.ITALIC],oldstyle:['SetFont',MML.VARIANT.OLDSTYLE],cal:['SetFont',MML.VARIANT.CALIGRAPHIC],it:['SetFont',"-tex-mathit"],bf:['SetFont',MML.VARIANT.BOLD],bbFont:['SetFont',MML.VARIANT.DOUBLESTRUCK],scr:['SetFont',MML.VARIANT.SCRIPT],frak:['SetFont',MML.VARIANT.FRAKTUR],sf:[
'SetFont',MML.VARIANT.SANSSERIF],tt:['SetFont',MML.VARIANT.MONOSPACE],tiny:['SetSize',0.5],Tiny:['SetSize',0.6],scriptsize:['SetSize',0.7],small:['SetSize',0.85],normalsize:['SetSize',1.0],large:['SetSize',1.2],Large:['SetSize',1.44],LARGE:['SetSize',1.73],huge:['SetSize',2.07],Huge:['SetSize',2.49],arcsin:['NamedFn'],arccos:['NamedFn'],arctan:['NamedFn'],arg:['NamedFn'],cos:['NamedFn'],cosh:['NamedFn'],cot:['NamedFn'],coth:['NamedFn'],csc:['NamedFn'],deg:['NamedFn'],det:'NamedOp',dim:['NamedFn'],exp:['NamedFn'],gcd:'NamedOp',hom:['NamedFn'],inf:'NamedOp',ker:['NamedFn'],lg:['NamedFn'],lim:'NamedOp',liminf:['NamedOp','lim&thinsp;inf'],limsup:['NamedOp','lim&thinsp;sup'],ln:['NamedFn'],log:['NamedFn'],max:'NamedOp',min:'NamedOp',Pr:'NamedOp',sec:['NamedFn'],sin:['NamedFn'],sinh:['NamedFn'],sup:'NamedOp',tan:['NamedFn'],tanh:['NamedFn'],limits:['Limits',1],nolimits:['Limits',0],overline:['UnderOver','00AF'],underline:['UnderOver','005F'],overbrace:['UnderOver','23DE',1],underbrace:[
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['Spacer',".5em"],quad:['Spacer',"1em"],qquad:['Spacer',"2em"],thinspace:['Spacer',MML.LENGTH.THINMATHSPACE],negthinspace:['Spacer',MML.LENGTH.NEGATIVETHINMATHSPACE],hskip:'Hskip',hspace:'Hskip',kern:'Hskip',mskip:'Hskip',mspace:'Hskip',mkern:'Hskip',Rule:['Rule'],Space:['Rule','blank'],big:['MakeBig',MML.TEXCLASS.ORD,0.85],Big:['MakeBig',MML.TEXCLASS.ORD,1.15],bigg:['MakeBig',MML.TEXCLASS.ORD,1.45],Bigg:['MakeBig',MML.TEXCLASS.ORD,1.75],bigl:['MakeBig',MML.TEXCLASS.OPEN,0.85],Bigl:['MakeBig',MML.TEXCLASS.OPEN,1.15],biggl:['MakeBig',MML.TEXCLASS.OPEN,1.45],Biggl:['MakeBig',MML.TEXCLASS.OPEN,1.75],bigr:['MakeBig',MML.TEXCLASS.CLOSE,0.85],Bigr:['MakeBig',MML.TEXCLASS.CLOSE,1.15],biggr:['MakeBig',MML.TEXCLASS.CLOSE,1.45],Biggr:['MakeBig',MML.TEXCLASS.CLOSE,1.75],bigm:['MakeBig',MML.TEXCLASS.REL,0.85],Bigm:['MakeBig',MML.TEXCLASS.REL,1.15],biggm:['MakeBig',MML.TEXCLASS.REL,1.45],Biggm:['MakeBig',MML.TEXCLASS.REL,1.75],mathord:['TeXAtom',MML.TEXCLASS.ORD],mathop:['TeXAtom',MML.TEXCLASS.OP],
mathopen:['TeXAtom',MML.TEXCLASS.OPEN],mathclose:['TeXAtom',MML.TEXCLASS.CLOSE],mathbin:['TeXAtom',MML.TEXCLASS.BIN],mathrel:['TeXAtom',MML.TEXCLASS.REL],mathpunct:['TeXAtom',MML.TEXCLASS.PUNCT],mathinner:['TeXAtom',MML.TEXCLASS.INNER],vcenter:['TeXAtom',MML.TEXCLASS.VCENTER],mathchoice:['Extension','mathchoice'],buildrel:'BuildRel',hbox:['HBox',0],text:'HBox',mbox:['HBox',0],fbox:'FBox',strut:'Strut',mathstrut:['Macro','\\vphantom{(}'],phantom:'Phantom',vphantom:['Phantom',1,0],hphantom:['Phantom',0,1],smash:'Smash',acute:['Accent',"00B4"],grave:['Accent',"0060"],ddot:['Accent',"00A8"],tilde:['Accent',"007E"],bar:['Accent',"00AF"],breve:['Accent',"02D8"],check:['Accent',"02C7"],hat:['Accent',"005E"],vec:['Accent',"2192"],dot:['Accent',"02D9"],widetilde:['Accent',"007E",1],widehat:['Accent',"005E",1],matrix:'Matrix',array:'Matrix',pmatrix:['Matrix','(',')'],cases:['Matrix','{','',"left left",null,".1em",null,true],eqalign:['Matrix',null,null,"right left",MML.LENGTH.THICKMATHSPACE,
".5em",'D'],displaylines:['Matrix',null,null,"center",null,".5em",'D'],cr:'Cr','\\':'CrLaTeX',newline:'Cr',hline:['HLine','solid'],hdashline:['HLine','dashed'],eqalignno:['Matrix',null,null,"right left right",MML.LENGTH.THICKMATHSPACE+" 3em",".5em",'D'],leqalignno:['Matrix',null,null,"right left right",MML.LENGTH.THICKMATHSPACE+" 3em",".5em",'D'],bmod:['Macro','\\mathbin{\\mmlToken{mo}{mod}}'],pmod:['Macro','\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}',1],mod:['Macro','\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1',1],pod:['Macro','\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)',1],iff:['Macro','\\;\\Longleftrightarrow\\;'],skew:['Macro','{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}',3],mathcal:['Macro','{\\cal #1}',1],mathscr:['Macro','{\\scr #1}',1],mathrm:['Macro','{\\rm #1}',1],mathbf:['Macro','{\\bf #1}',1],mathbb:['Macro','{\\bbFont #1}',1],Bbb:['Macro','{\\bbFont #1}',1],mathit:['Macro','{\\it #1}',1],mathfrak:['Macro','{\\frak #1}',1]
,mathsf:['Macro','{\\sf #1}',1],mathtt:['Macro','{\\tt #1}',1],textrm:['Macro','\\mathord{\\rm\\text{#1}}',1],textit:['Macro','\\mathord{\\it{\\text{#1}}}',1],textbf:['Macro','\\mathord{\\bf{\\text{#1}}}',1],pmb:['Macro','\\rlap{#1}\\kern1px{#1}',1],TeX:['Macro','T\\kern-.14em\\lower.5ex{E}\\kern-.115em X'],LaTeX:['Macro','L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX'],' ':['Macro','\\text{ }'],not:'Not',dots:'Dots',space:'Tilde',begin:'Begin',end:'End',newcommand:['Extension','newcommand'],renewcommand:['Extension','newcommand'],newenvironment:['Extension','newcommand'],renewenvironment:['Extension','newcommand'],def:['Extension','newcommand'],let:['Extension','newcommand'],verb:['Extension','verb'],boldsymbol:['Extension','boldsymbol'],tag:['Extension','AMSmath'],notag:['Extension','AMSmath'],label:['Extension','AMSmath'],ref:['Extension','AMSmath'],eqref:['Extension','AMSmath'],nonumber:['Macro','\\notag'],unicode:['Extension','unicode'],color:'Color',href:[
'Extension','HTML'],'class':['Extension','HTML'],style:['Extension','HTML'],cssId:['Extension','HTML'],bbox:['Extension','bbox'],mmlToken:'MmlToken',require:'Require'},environment:{array:['AlignedArray'],matrix:['Array',null,null,null,'c'],pmatrix:['Array',null,'(',')','c'],bmatrix:['Array',null,'[',']','c'],Bmatrix:['Array',null,'\\{','\\}','c'],vmatrix:['Array',null,'\\vert','\\vert','c'],Vmatrix:['Array',null,'\\Vert','\\Vert','c'],cases:['Array',null,'\\{','.','ll',null,".2em",'T'],equation:[null,'Equation'],'equation*':[null,'Equation'],eqnarray:['ExtensionEnv',null,'AMSmath'],'eqnarray*':['ExtensionEnv',null,'AMSmath'],align:['ExtensionEnv',null,'AMSmath'],'align*':['ExtensionEnv',null,'AMSmath'],aligned:['ExtensionEnv',null,'AMSmath'],multline:['ExtensionEnv',null,'AMSmath'],'multline*':['ExtensionEnv',null,'AMSmath'],split:['ExtensionEnv',null,'AMSmath'],gather:['ExtensionEnv',null,'AMSmath'],'gather*':['ExtensionEnv',null,'AMSmath'],gathered:['ExtensionEnv',null,'AMSmath'],
alignat:['ExtensionEnv',null,'AMSmath'],'alignat*':['ExtensionEnv',null,'AMSmath'],alignedat:['ExtensionEnv',null,'AMSmath']},p_height:1.2/.85});if(this.config.Macros){var MACROS=this.config.Macros;for(var id in MACROS){if(MACROS.hasOwnProperty(id)){if(typeof(MACROS[id])==="string"){TEXDEF.macros[id]=['Macro',MACROS[id]]}else{TEXDEF.macros[id]=["Macro"].concat(MACROS[id])}TEXDEF.macros[id].isUser=true;}}}};var PARSE=MathJax.Object.Subclass({Init:function(string,env){this.string=string;this.i=0;this.macroCount=0;var ENV;if(env){ENV={};for(var id in env){if(env.hasOwnProperty(id)){ENV[id]=env[id]}}}this.stack=TEX.Stack(ENV,!!env);this.Parse();this.Push(STACKITEM.stop());},Parse:function(){var c,n;while(this.i<this.string.length){c=this.string.charAt(this.i++);n=c.charCodeAt(0);if(n>=0xD800&&n<0xDC00){c+=this.string.charAt(this.i++)}if(TEXDEF.special[c]){this[TEXDEF.special[c]](c)}else if(TEXDEF.letter.test(c)){this.Variable(c)}else if(TEXDEF.digit.test(c)){this.Number(c)}else{this.Other(
c)}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0];},mmlToken:function(token){return token},ControlSequence:function(c){var name=this.GetCS(),macro=this.csFindMacro(name);if(macro){if(!(macro instanceof Array)){macro=[macro]}var fn=macro[0];if(!(fn instanceof Function)){fn=this[fn]}fn.apply(this,[c+name].concat(macro.slice(1)));}else if(TEXDEF.mathchar0mi[name]){this.csMathchar0mi(name,TEXDEF.mathchar0mi[name])}else if(TEXDEF.mathchar0mo[name]){this.csMathchar0mo(name,TEXDEF.mathchar0mo[name])}else if(TEXDEF.mathchar7[name]){this.csMathchar7(name,TEXDEF.mathchar7[name])}else if(TEXDEF.delimiter["\\"+name]!=null){this.csDelimiter(name,TEXDEF.delimiter["\\"+name])}else{this.csUndefined(c+name)}},csFindMacro:function(name){return TEXDEF.macros[name]},csMathchar0mi:function(name,mchar){var def={mathvariant:MML.VARIANT.ITALIC};if(mchar instanceof Array){def=mchar[1];mchar=mchar[0]}
this.Push(this.mmlToken(MML.mi(MML.entity("#x"+mchar)).With(def)));},csMathchar0mo:function(name,mchar){var def={stretchy:false};if(mchar instanceof Array){def=mchar[1];def.stretchy=false;mchar=mchar[0]}this.Push(this.mmlToken(MML.mo(MML.entity("#x"+mchar)).With(def)));},csMathchar7:function(name,mchar){var def={mathvariant:MML.VARIANT.NORMAL};if(mchar instanceof Array){def=mchar[1];mchar=mchar[0]}if(this.stack.env.font){def.mathvariant=this.stack.env.font}this.Push(this.mmlToken(MML.mi(MML.entity("#x"+mchar)).With(def)));},csDelimiter:function(name,delim){var def={};if(delim instanceof Array){def=delim[1];delim=delim[0]}if(delim.length===4){delim=MML.entity('#x'+delim)}else{delim=MML.chars(delim)}this.Push(this.mmlToken(MML.mo(delim).With({fence:false,stretchy:false}).With(def)));},csUndefined:function(name){TEX.Error(["UndefinedControlSequence","Undefined control sequence %1",name]);},Variable:function(c){var def={};if(this.stack.env.font){def.mathvariant=this.stack.env.font}this.
Push(this.mmlToken(MML.mi(MML.chars(c)).With(def)));},Number:function(c){var mml,n=this.string.slice(this.i-1).match(TEXDEF.number);if(n){mml=MML.mn(n[0].replace(/[{}]/g,""));this.i+=n[0].length-1}else{mml=MML.mo(MML.chars(c))}if(this.stack.env.font){mml.mathvariant=this.stack.env.font}this.Push(this.mmlToken(mml));},Open:function(c){this.Push(STACKITEM.open())},Close:function(c){this.Push(STACKITEM.close())},Tilde:function(c){this.Push(MML.mtext(MML.chars(NBSP)))},Space:function(c){},Superscript:function(c){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var position,primes,base,top=this.stack.Top();if(top.type==="prime"){base=top.data[0];primes=top.data[1];this.stack.Pop()}else{base=this.stack.Prev();if(!base){base=MML.mi("")}}if(base.isEmbellishedWrapper){base=base.data[0].data[0]}if(base.type==="msubsup"){if(base.data[base.sup]){TEX.Error(["DoubleExponent","Double exponent: use braces to clarify"])}position=base.sup;}else if
(base.movesupsub){if(base.type!=="munderover"||base.data[base.over]){if(base.movablelimits&&base.isa(MML.mi)){base=this.mi2mo(base)}base=MML.munderover(base,null,null).With({movesupsub:true})}position=base.over;}else{base=MML.msubsup(base,null,null);position=base.sup;}this.Push(STACKITEM.subsup(base).With({position:position,primes:primes}));},Subscript:function(c){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var position,primes,base,top=this.stack.Top();if(top.type==="prime"){base=top.data[0];primes=top.data[1];this.stack.Pop()}else{base=this.stack.Prev();if(!base){base=MML.mi("")}}if(base.isEmbellishedWrapper){base=base.data[0].data[0]}if(base.type==="msubsup"){if(base.data[base.sub]){TEX.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}position=base.sub;}else if(base.movesupsub){if(base.type!=="munderover"||base.data[base.under]){if(base.movablelimits&&base.isa(MML.mi)){base=this.mi2mo(base)}base=MML.
munderover(base,null,null).With({movesupsub:true})}position=base.under;}else{base=MML.msubsup(base,null,null);position=base.sub;}this.Push(STACKITEM.subsup(base).With({position:position,primes:primes}));},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(c){var base=this.stack.Prev();if(!base){base=MML.mi()}if(base.type==="msubsup"&&base.data[base.sup]){TEX.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"]);}var sup="";this.i--;do{sup+=this.PRIME;this.i++,c=this.GetNext()}while(c==="'"||c===this.SMARTQUOTE);sup=["","\u2032","\u2033","\u2034","\u2057"][sup.length]||sup;this.Push(STACKITEM.prime(base,this.mmlToken(MML.mo(sup))));},mi2mo:function(mi){var mo=MML.mo();mo.Append.apply(mo,mi.data);var id;for(id in mo.defaults){if(mo.defaults.hasOwnProperty(id)&&mi[id]!=null){mo[id]=mi[id]}}for(id in MML.copyAttributes){if(MML.copyAttributes.hasOwnProperty(id)&&mi[id]!=null){mo[id]=mi[id]}}return mo;},Comment:function(c){while(this.i<this.string.length&&this.
string.charAt(this.i)!="\n"){this.i++}},Hash:function(c){TEX.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"]);},Other:function(c){var def={stretchy:false},mo;if(this.stack.env.font){def.mathvariant=this.stack.env.font}if(TEXDEF.remap[c]){c=TEXDEF.remap[c];if(c instanceof Array){def=c[1];c=c[0]}mo=MML.mo(MML.entity('#x'+c)).With(def);}else{mo=MML.mo(c).With(def);}if(mo.autoDefault("texClass",true)==""){mo=MML.TeXAtom(mo)}this.Push(this.mmlToken(mo));},SetFont:function(name,font){this.stack.env.font=font},SetStyle:function(name,texStyle,style,level){this.stack.env.style=texStyle;this.stack.env.level=level;this.Push(STACKITEM.style().With({styles:{displaystyle:style,scriptlevel:level}}));},SetSize:function(name,size){this.stack.env.size=size;this.Push(STACKITEM.style().With({styles:{mathsize:size+"em"}}));},Color:function(name){var color=this.GetArgument(name);var old=this.stack.env.color;this.stack.env.color=color;var math=this.ParseArg(name);if(old){
this.stack.env.color}else{delete this.stack.env.color}this.Push(MML.mstyle(math).With({mathcolor:color}));},Spacer:function(name,space){this.Push(MML.mspace().With({width:space,mathsize:MML.SIZE.NORMAL,scriptlevel:0}));},LeftRight:function(name){this.Push(STACKITEM[name.substr(1)]().With({delim:this.GetDelimiter(name)}));},Middle:function(name){var delim=this.GetDelimiter(name);if(this.stack.Top().type!=="left"){TEX.Error(["MisplacedMiddle","%1 must be within \\left and \\right",name])}this.Push(MML.mo(delim).With({stretchy:true}));},NamedFn:function(name,id){if(!id){id=name.substr(1)};var mml=MML.mi(id).With({texClass:MML.TEXCLASS.OP});this.Push(STACKITEM.fn(this.mmlToken(mml)));},NamedOp:function(name,id){if(!id){id=name.substr(1)};id=id.replace(/&thinsp;/,"\u2006");var mml=MML.mo(id).With({movablelimits:true,movesupsub:true,form:MML.FORM.PREFIX,texClass:MML.TEXCLASS.OP});mml.useMMLspacing&=~mml.SPACE_ATTR.form;this.Push(this.mmlToken(mml));},Limits:function(name,limits){var op=this.
stack.Prev("nopop");if(!op||op.texClass!==MML.TEXCLASS.OP){TEX.Error(["MisplacedLimits","%1 is allowed only on operators",name])}op.movesupsub=(limits?true:false);op.movablelimits=false;},Over:function(name,open,close){var mml=STACKITEM.over().With({name:name});if(open||close){mml.open=open;mml.close=close;}else if(name.match(/withdelims$/)){mml.open=this.GetDelimiter(name);mml.close=this.GetDelimiter(name);}if(name.match(/^\\above/)){mml.thickness=this.GetDimen(name)}else if(name.match(/^\\atop/)||open||close){mml.thickness=0}this.Push(mml);},Frac:function(name){var num=this.ParseArg(name);var den=this.ParseArg(name);this.Push(MML.mfrac(num,den));},Sqrt:function(name){var n=this.GetBrackets(name),arg=this.GetArgument(name);if(arg==="\\frac"){arg+="{"+this.GetArgument(arg)+"}{"+this.GetArgument(arg)+"}"}var mml=TEX.Parse(arg,this.stack.env).mml();if(!n){mml=MML.msqrt.apply(MML,mml.array())}else{mml=MML.mroot(mml,this.parseRoot(n))}this.Push(mml);},Root:function(name){var n=this.GetUpTo
(name,"\\of");var arg=this.ParseArg(name);this.Push(MML.mroot(arg,this.parseRoot(n)));},parseRoot:function(n){var env=this.stack.env,inRoot=env.inRoot;env.inRoot=true;var parser=TEX.Parse(n,env);n=parser.mml();var global=parser.stack.global;if(global.leftRoot||global.upRoot){n=MML.mpadded(n);if(global.leftRoot){n.width=global.leftRoot}if(global.upRoot){n.voffset=global.upRoot;n.height=global.upRoot}}env.inRoot=inRoot;return n;},MoveRoot:function(name,id){if(!this.stack.env.inRoot){TEX.Error(["MisplacedMoveRoot","%1 can appear only within a root",name])}if(this.stack.global[id]){TEX.Error(["MultipleMoveRoot","Multiple use of %1",name])}var n=this.GetArgument(name);if(!n.match(/-?[0-9]+/)){TEX.Error(["IntegerArg","The argument to %1 must be an integer",name])}n=(n/15)+"em";if(n.substr(0,1)!=="-"){n="+"+n}this.stack.global[id]=n;},Accent:function(name,accent,stretchy){var c=this.ParseArg(name);var def={accent:true};if(this.stack.env.font){def.mathvariant=this.stack.env.font}var mml=this.
mmlToken(MML.mo(MML.entity("#x"+accent)).With(def));mml.stretchy=(stretchy?true:false);this.Push(MML.TeXAtom(MML.munderover(c,null,mml).With({accent:true})));},UnderOver:function(name,c,stack){var pos={o:"over",u:"under"}[name.charAt(1)];var base=this.ParseArg(name);if(base.Get("movablelimits")){base.movablelimits=false}var mml=MML.munderover(base,null,null);if(stack){mml.movesupsub=true}mml.data[mml[pos]]=this.mmlToken(MML.mo(MML.entity("#x"+c)).With({stretchy:true,accent:(pos=="under")}));this.Push(mml);},Overset:function(name){var top=this.ParseArg(name),base=this.ParseArg(name);this.Push(MML.mover(base,top));},Underset:function(name){var bot=this.ParseArg(name),base=this.ParseArg(name);this.Push(MML.munder(base,bot));},TeXAtom:function(name,mclass){var def={texClass:mclass},mml;if(mclass==MML.TEXCLASS.OP){def.movesupsub=def.movablelimits=true;var arg=this.GetArgument(name);var match=arg.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(match){def.mathvariant=MML.VARIANT.NORMAL;mml=STACKITEM.
fn(this.mmlToken(MML.mi(match[1]).With(def)));}else{mml=STACKITEM.fn(MML.TeXAtom(TEX.Parse(arg,this.stack.env).mml()).With(def));}}else{mml=MML.TeXAtom(this.ParseArg(name)).With(def)}this.Push(mml);},MmlToken:function(name){var type=this.GetArgument(name),attr=this.GetBrackets(name,"").replace(/^\s+/,""),data=this.GetArgument(name),def={attrNames:[]},match;if(!MML[type]||!MML[type].prototype.isToken){TEX.Error(["NotMathMLToken","%1 is not a token element",type])}while(attr!==""){match=attr.match(/^([a-z]+)\s*=\s*(\'[^']*'|"[^"]*"|[^ ]*)\s*/i);if(!match){TEX.Error(["InvalidMathMLAttr","Invalid MathML attribute: %1",attr])}if(!MML[type].prototype.defaults[match[1]]&&!this.MmlTokenAllow[match[1]]){TEX.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",match[1],type]);}var value=this.MmlFilterAttribute(match[1],match[2].replace(/^(['"])(.*)\1$/,"$2"));if(value){if(value.toLowerCase()==="true"){value=true}else if(value.toLowerCase()==="false"){value=false}def[match[1]]
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