/*
 *  /MathJax/jax/output/SVG/autoload/multiline.js
 *
 *  Copyright (c) 2009-2014 The MathJax Consortium
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 */

MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var d="2.4.0";var a=MathJax.ElementJax.mml,f=MathJax.OutputJax.SVG,b=f.BBOX;var e={newline:0,nobreak:1000000,goodbreak:[-200],badbreak:[+200],auto:[0],toobig:800,nestfactor:400,spacefactor:-100,spaceoffset:2,spacelimit:1,fence:500,close:500};var c={linebreakstyle:"after"};a.mrow.Augment({SVGmultiline:function(k){var o=this;while(o.inferred||(o.parent&&o.parent.type==="mrow"&&o.parent.data.length===1)){o=o.parent}var n=((o.type==="math"&&o.Get("display")==="block")||o.type==="mtd");o.isMultiline=true;var p=this.getValues("linebreak","linebreakstyle","lineleading","linebreakmultchar","indentalign","indentshift","indentalignfirst","indentshiftfirst","indentalignlast","indentshiftlast");if(p.linebreakstyle===a.LINEBREAKSTYLE.INFIXLINEBREAKSTYLE){p.linebreakstyle=this.Get("infixlinebreakstyle")}p.lineleading=f.length2em(p.lineleading,1,0.5);k=this.SVG();if(n&&o.type!=="mtd"){if(f.linebreakWidth<f.BIGDIMEN){k.w=f.linebreakWidth}else{k.w=f.cwidth/f.em*1000}}var g={n:0,Y:0,scale:this.scale||1,isTop:n,values:{},VALUES:p},m=this.SVGgetAlign(g,{}),i=this.SVGgetShift(g,{},m),h=[],j={index:[],penalty:e.nobreak,w:0,W:i,shift:i,scanW:i,nest:0},l=false;while(this.SVGbetterBreak(j,g)&&(j.scanW>=f.linebreakWidth||j.penalty===e.newline)){this.SVGaddLine(k,h,j.index,g,j.values,l);h=j.index.slice(0);l=true;m=this.SVGgetAlign(g,j.values);i=this.SVGgetShift(g,j.values,m);if(m===a.INDENTALIGN.CENTER){i=0}j.W=j.shift=j.scanW=i;j.penalty=e.nobreak}g.isLast=true;this.SVGaddLine(k,h,[],g,c,l);this.SVGhandleSpace(k);this.SVGhandleColor(k);k.isMultiline=true;this.SVGsaveData(k);return k}});a.mbase.Augment({SVGlinebreakPenalty:e,SVGbetterBreak:function(j,g){if(this.isToken){return false}if(this.isEmbellished()){j.embellished=this;return this.CoreMO().SVGbetterBreak(j,g)}if(this.linebreakContainer){return false}var q=j.index.slice(0),o=j.index.shift(),n=this.data.length,l,r,k,p=(j.index.length>0),h=false;if(o==null){o=-1}if(!p){o++;j.W+=j.w;j.w=0}k=j.scanW=j.W;j.nest++;while(o<n&&j.scanW<1.33*f.linebreakWidth){if(this.data[o]){if(this.data[o].SVGbetterBreak(j,g)){h=true;q=[o].concat(j.index);l=j.W;r=j.w;if(j.penalty===e.newline){j.index=q;if(j.nest){j.nest--}return true}}k=(p?j.scanW:this.SVGaddWidth(o,j,k))}j.index=[];o++;p=false}if(j.nest){j.nest--}j.index=q;if(h){j.W=l}return h},SVGaddWidth:function(h,k,j){if(this.data[h]){var g=this.data[h].SVGdata;j+=g.w+g.x;if(g.X){j+=g.X}k.W=k.scanW=j;k.w=0}return j},SVGaddLine:function(l,h,k,g,p,n){var q=b();g.first=n;g.last=true;this.SVGmoveLine(h,k,q,g,p);q.Clean();var o=this.SVGgetAlign(g,p),i=this.SVGgetShift(g,p,o);if(i){if(o===a.INDENTALIGN.LEFT){q.x=i}else{if(o===a.INDENTALIGN.RIGHT){q.w+=i;q.r=q.w}}}if(g.n>0){var m=f.FONTDATA.baselineskip*g.scale;var j=(g.values.lineleading==null?g.VALUES:g.values).lineleading*g.scale;g.Y-=Math.max(m,g.d+q.h+j)}l.Align(q,o,0,g.Y);g.d=q.d;g.values=p;g.n++},SVGgetAlign:function(j,g){var k=g,h=j.values,i=j.VALUES,l;if(j.n===0){l=k.indentalignfirst||h.indentalignfirst||i.indentalignfirst}else{if(j.isLast){l=h.indentalignlast||i.indentalignlast}else{l=h.indentalign||i.indentalign}}if(l===a.INDENTALIGN.INDENTALIGN){l=h.indentalign||i.indentalign}if(l===a.INDENTALIGN.AUTO){l=(j.isTop?this.displayAlign:a.INDENTALIGN.LEFT)}return l},SVGgetShift:function(k,h,m){if(m===a.INDENTALIGN.CENTER){return 0}var l=h,i=k.values,j=k.VALUES,g;if(k.n===0){g=l.indentshiftfirst||i.indentshiftfirst||j.indentshiftfirst}else{if(k.isLast){g=i.indentshiftlast||j.indentshiftlast}else{g=i.indentshift||j.indentshift}}if(g===a.INDENTSHIFT.INDENTSHIFT){g=i.indentshift||j.indentshift}if(g==="auto"||g===""){g=(k.isTSop?this.displayIndent:"0")}return f.length2em(g,0)},SVGmoveLine:function(p,g,k,o,h){var m=p[0],l=g[0];if(m==null){m=-1}if(l==null){l=this.data.length-1}if(m===l&&p.length>1){this.data[m].SVGmoveSlice(p.slice(1),g.slice(1),k,o,h,"paddingLeft")}else{var n=o.last;o.last=false;while(m<l){if(this.data[m]){if(p.length<=1){this.data[m].SVGmove(k,o,h)}else{this.data[m].SVGmoveSlice(p.slice(1),[],k,o,h,"paddingLeft")}}m++;o.first=false;p=[]}o.last=n;if(this.data[m]){if(g.length<=1){this.data[m].SVGmove(k,o,h)}else{this.data[m].SVGmoveSlice([],g.slice(1),k,o,h,"paddingRight")}}}},SVGmoveSlice:function(m,g,i,j,h,k){var l=b();this.SVGmoveLine(m,g,l,j,h);l.Clean();this.SVGhandleColor(l);i.Add(l,i.w,0,true);return l},SVGmove:function(g,j,i){if(!(j.first||j.last)||(j.first&&j.values.linebreakstyle===a.LINEBREAKSTYLE.BEFORE)||(j.last&&i.linebreakstyle===a.LINEBREAKSTYLE.AFTER)){var h=this.toSVG(this.SVGdata.HW,this.SVGdata.D);if(j.first||j.nextIsFirst){h.x=0}if(j.last&&h.X){h.X=0}g.Add(h,g.w,0,true)}if(j.first&&h&&h.w===0){j.nextIsFirst=true}else{delete j.nextIsFirst}}});a.mfenced.Augment({SVGbetterBreak:function(l,g){var u=l.index.slice(0),s=l.index.shift(),p=this.data.length,o,v,n,t=(l.index.length>0),h=false;if(s==null){s=-1}if(!t){s++;l.W+=l.w;l.w=0}n=l.scanW=l.W;l.nest++;if(!this.dataI){this.dataI=[];if(this.data.open){this.dataI.push("open")}if(p){this.dataI.push(0)}for(var r=1;r<p;r++){if(this.data["sep"+r]){this.dataI.push("sep"+r)}this.dataI.push(r)}if(this.data.close){this.dataI.push("close")}}p=this.dataI.length;while(s<p&&l.scanW<1.33*f.linebreakWidth){var q=this.dataI[s];if(this.data[q]){if(this.data[q].SVGbetterBreak(l,g)){h=true;u=[s].concat(l.index);o=l.W;v=l.w;if(l.penalty===e.newline){l.index=u;if(l.nest){l.nest--}return true}}n=(t?l.scanW:this.SVGaddWidth(s,l,n))}l.index=[];s++;t=false}if(l.nest){l.nest--}l.index=u;if(h){l.W=o;l.w=v}return h},SVGmoveLine:function(h,m,p,g,r){var o=h[0],n=m[0];if(o==null){o=-1}if(n==null){n=this.dataI.length-1}if(o===n&&h.length>1){this.data[this.dataI[o]].SVGmoveSlice(h.slice(1),m.slice(1),p,g,r,"paddingLeft")}else{var q=g.last;g.last=false;var l=this.dataI[o];while(o<n){if(this.data[l]){if(h.length<=1){this.data[l].SVGmove(p,g,r)}else{this.data[l].SVGmoveSlice(h.slice(1),[],p,g,r,"paddingLeft")}}o++;l=this.dataI[o];g.first=false;h=[]}g.last=q;if(this.data[l]){if(m.length<=1){this.data[l].SVGmove(p,g,r)}else{this.data[l].SVGmoveSlice([],m.slice(1),p,g,r,"paddingRight")}}}}});a.msubsup.Augment({SVGbetterBreak:function(j,g){if(!this.data[this.base]){return false}var o=j.index.slice(0),m=j.index.shift(),l,p,k,n=(j.index.length>0),h=false;if(!n){j.W+=j.w;j.w=0}k=j.scanW=j.W;if(m==null){this.SVGdata.dw=this.SVGdata.w-this.data[this.base].SVGdata.w}if(this.data[this.base].SVGbetterBreak(j,g)){h=true;o=[this.base].concat(j.index);l=j.W;p=j.w;if(j.penalty===e.newline){h=n=true}}if(!n){this.SVGaddWidth(this.base,j,k)}j.scanW+=this.SVGdata.dw;j.W=j.scanW;j.index=[];if(h){j.W=l;j.w=p;j.index=o}return h},SVGmoveLine:function(i,j,m,h,o){if(this.data[this.base]){if(i.length>1){this.data[this.base].SVGmoveSlice(i.slice(1),j.slice(1),m,h,o,"paddingLeft")}else{if(j.length<=1){this.data[this.base].SVGmove(m,h,o)}else{this.data[this.base].SVGmoveSlice([],j.slice(1),m,h,o,"paddingRight")}}}if(j.length===0){var l=this.data[this.sup],g=this.data[this.sub],n=m.w,k;if(l){k=l.SVGdata;m.Add(l.toSVG(),n+(k.dx||0),k.dy)}if(g){k=g.SVGdata;m.Add(g.toSVG(),n+(k.dx||0),k.dy)}}}});a.mmultiscripts.Augment({SVGbetterBreak:function(k,h){if(!this.data[this.base]){return false}var p=k.index.slice(0),n=k.index.shift(),m,q,l,o=(k.index.length>0),j=false;if(!o){k.W+=k.w;k.w=0}k.scanW=k.W;var g=this.SVGdata.w-this.data[this.base].SVGdata.w-this.SVGdata.dx;k.scanW+=this.SVGdata.dx;l=k.scanW;if(this.data[this.base].SVGbetterBreak(k,h)){j=true;p=[this.base].concat(k.index);m=k.W;q=k.w;if(k.penalty===e.newline){j=o=true}}if(!o){this.SVGaddWidth(this.base,k,l)}k.scanW+=g;k.W=k.scanW;k.index=[];if(j){k.W=m;k.w=q;k.index=p}return j},SVGmoveLine:function(i,k,n,h,p){var q,m=this.SVGdata;if(i.length<1){this.scriptBox=this.SVGgetScripts(this.SVGdata.s);var j=this.scriptBox[2],o=this.scriptBox[3];q=n.w+m.dx;if(o){n.Add(o,q+m.delta-o.w,m.u)}if(j){n.Add(j,q-j.w,-m.v)}}if(this.data[this.base]){if(i.length>1){this.data[this.base].SVGmoveSlice(i.slice(1),k.slice(1),n,h,p,"paddingLeft")}else{if(k.length<=1){this.data[this.base].SVGmove(n,h,p)}else{this.data[this.base].SVGmoveSlice([],k.slice(1),n,h,p,"paddingRight")}}}if(k.length===0){var g=this.scriptBox[0],l=this.scriptBox[1];q=n.w+m.s;if(l){n.Add(l,q,m.u)}if(g){n.Add(g,q-m.delta,-m.v)}delete this.scriptBox}}});a.mo.Augment({SVGbetterBreak:function(i,g){if(i.values&&i.values.last===this){return false}var q=this.getValues("linebreak","linebreakstyle","lineleading","linebreakmultchar","indentalign","indentshift","indentalignfirst","indentshiftfirst","indentalignlast","indentshiftlast","texClass","fence");if(q.linebreakstyle===a.LINEBREAKSTYLE.INFIXLINEBREAKSTYLE){q.linebreakstyle=this.Get("infixlinebreakstyle")}if(q.texClass===a.TEXCLASS.OPEN){i.nest++}if(q.texClass===a.TEXCLASS.CLOSE&&i.nest){i.nest--}var j=i.scanW,k=i.embellished;delete i.embellished;if(!k||!k.SVGdata){k=this}var m=k.SVGdata,p=m.w+m.x;if(q.linebreakstyle===a.LINEBREAKSTYLE.AFTER){j+=p;p=0}if(j-i.shift===0&&q.linebreak!==a.LINEBREAK.NEWLINE){return false}var l=f.linebreakWidth-j;if(g.n===0&&(q.indentshiftfirst!==g.VALUES.indentshiftfirst||q.indentalignfirst!==g.VALUES.indentalignfirst)){var n=this.SVGgetAlign(g,q),h=this.SVGgetShift(g,q,n);l+=(i.shift-h)}var o=Math.floor(l/f.linebreakWidth*1000);if(o<0){o=e.toobig-3*o}if(q.fence){o+=e.fence}if((q.linebreakstyle===a.LINEBREAKSTYLE.AFTER&&q.texClass===a.TEXCLASS.OPEN)||q.texClass===a.TEXCLASS.CLOSE){o+=e.close}o+=i.nest*e.nestfactor;var r=e[q.linebreak||a.LINEBREAK.AUTO];if(!(r instanceof Array)){if(l>=0){o=r*i.nest}}else{o=Math.max(1,o+r[0]*i.nest)}if(o>=i.penalty){return false}i.penalty=o;i.values=q;i.W=j;i.w=p;q.lineleading=f.length2em(q.lineleading,g.VALUES.lineleading);q.last=this;return true}});a.mspace.Augment({SVGbetterBreak:function(h,g){if(h.values&&h.values.last===this){return false}var o=this.getValues("linebreak");var m=o.linebreak;if(!m||this.hasDimAttr()){m=a.LINEBREAK.AUTO}var i=h.scanW,k=this.SVGdata,n=k.w+k.x;if(i-h.shift===0){return false}var j=f.linebreakWidth-i;var l=Math.floor(j/f.linebreakWidth*1000);if(l<0){l=e.toobig-3*l}l+=h.nest*e.nestfactor;var p=e[m];if(m===a.LINEBREAK.AUTO&&n>=e.spacelimit*1000&&!this.mathbackground&&!this.backrgound){p=[(n/1000+e.spaceoffset)*e.spacefactor]}if(!(p instanceof Array)){if(j>=0){l=p*h.nest}}else{l=Math.max(1,l+p[0]*h.nest)}if(l>=h.penalty){return false}h.penalty=l;h.values=o;h.W=i;h.w=n;o.lineleading=g.VALUES.lineleading;o.linebreakstyle="before";o.last=this;return true}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({SVGbetterBreak:function(h,g){return this.Core().SVGbetterBreak(h,g)},SVGmoveLine:function(k,g,i,j,h){return this.Core().SVGmoveSlice(k,g,i,j,h)}})});a.maction.Augment({SVGbetterBreak:function(h,g){return this.Core().SVGbetterBreak(h,g)},SVGmoveLine:function(k,g,i,j,h){return this.Core().SVGmoveSlice(k,g,i,j,h)},});a.semantics.Augment({SVGbetterBreak:function(h,g){return(this.data[0]?this.data[0].SVGbetterBreak(h,g):false)},SVGmoveLine:function(k,g,i,j,h){return(this.data[0]?this.data[0].SVGmoveSlice(k,g,i,j,h):null)}});MathJax.Hub.Startup.signal.Post("SVG multiline Ready");MathJax.Ajax.loadComplete(f.autoloadDir+"/multiline.js")});
