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/*
THIS IS A GENERATED/BUNDLED FILE BY ESBUILD
if you want to view the source, please visit the github repository of this plugin
*/
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je=ie(c.symbols),Q=t.Utils.arrayMin(je),c=t.PARSER.divide(c,t.PARSER.parse(c.value+"^"+Q));for(var le=ie(c.symbols).sort().pop(),ye=c.group===t.groups.PL?c.symbols:c.symbols[le],Ae=ye.group,je=Ae===l?[ye.power.toDecimal()]:ie(ye.symbols),it=[],yt=t.Utils.arrayMax(je),me=1;me<=yt;me++){var Ue=0;je.indexOf(me+"")!==-1&&(Ae===l?Ue=ye.multiplier:Ue=ye.symbols[me].multiplier),it.unshift(Ue)}return it.push(c.symbols[Te].multiplier),ye.group===l&&(it[0]=ye.multiplier),I(it,je,yt)}else if(t.Utils.isArray(c)){for(var Le=c,it=[],je=[],Ve=0,me=0;me<Le.length;me++){for(var lt=Le[me][0],Nt=Le[me][1],Ct=Nt-Ve-1,Xe=0;Xe<Ct;Xe++)it.unshift(0);it.unshift(lt),Nt!==0&&je.push(Nt),Ve=Nt}var yt=Math.max.apply(void 0,je);return I(it,je,yt)}else throw new t.exceptions.NerdamerTypeError("Cannot calculate roots. Symbol must be a polynomial!");function he(et,Lt,H){var P=100,B=et.slice(0);if(et.unshift(H),H>P)throw new t.exceptions.ValueLimitExceededError("This utility accepts polynomials of degree up to "+P+". ");var fe=[],pe={};for(pe.Degree=H,me=0;me<H;me++)fe.push(0);var ue=fe.slice(0);function st(He,ge,Je,gt,ne,Se){ne[0]=Se.b=gt[0],ne[1]=Se.a=-(ge*Se.b)+gt[1];for(var qe=2;qe<He;qe++)ne[qe]=-(ge*Se.a+Je*Se.b)+gt[qe],Se.b=Se.a,Se.a=ne[qe]}function se(He,ge,Je,gt,ne,Se,qe,Be,ct){var wt=new Object,Mt=3;return wt.b=wt.a=0,st(ge,qe,Be,Se,ct,wt),ne.c=wt.a,ne.d=wt.b,Math.abs(ne.c)<=100*He*Math.abs(Se[ge-1])&&Math.abs(ne.d)<=100*He*Math.abs(Se[ge-2])||(ne.h=Be*gt,Math.abs(ne.d)>=Math.abs(ne.c)?(Mt=2,ne.e=Je/ne.d,ne.f=ne.c/ne.d,ne.g=qe*gt,ne.a3=ne.e*(ne.g+Je)+ne.h*(gt/ne.d),ne.a1=-Je+ne.f*gt,ne.a7=ne.h+(ne.f+qe)*Je):(Mt=1,ne.e=Je/ne.c,ne.f=ne.d/ne.c,ne.g=ne.e*qe,ne.a3=ne.e*Je+(ne.g+ne.h/ne.c)*gt,ne.a1=-(Je*(ne.d/ne.c))+gt,ne.a7=ne.g*ne.d+ne.h*ne.f+Je)),Mt}function te(He,ge,Je,gt,ne,Se,qe,Be,ct){var wt;if(Je==3){qe[1]=qe[0]=0;for(var Mt=2;Mt<ge;Mt++)qe[Mt]=Be[Mt-2];return}if(wt=Je==1?ne:gt,Math.abs(Se.a1)>10*He*Math.abs(wt)){Se.a7/=Se.a1,Se.a3/=Se.a1,qe[0]=ct[0],qe[1]=-(ct[0]*Se.a7)+ct[1];for(var Mt=2;Mt<ge;Mt++)qe[Mt]=-(ct[Mt-1]*Se.a7)+Be[Mt-2]*Se.a3+ct[Mt]}else{qe[0]=0,qe[1]=-(ct[0]*Se.a7);for(var Mt=2;Mt<ge;Mt++)qe[Mt]=-(ct[Mt-1]*Se.a7)+Be[Mt-2]*Se.a3}}function D(He,ge,Je,gt,ne,Se,qe,Be,ct,wt,Mt,qt,Ft,Tt,Ze,ht,Et){var Pt,Ye,nt,O,Z,g,E,T,s;ge.b=ge.a=0,He!=3&&(He!=2?(Pt=Je+Ft*qe+qt*wt,Ye=Be+(Ft+Tt*wt)*ct):(Pt=(Je+Mt)*wt+qt,Ye=(wt+Ft)*Be+Tt*ct),nt=-(Ze[ht-1]/Et[ht]),O=-(Ze[ht-2]+nt*Et[ht-1])/Et[ht],Z=Tt*O*gt,g=nt*Se,E=nt*nt*ne,T=-(g+E)+Z,s=-T+Ye+nt*Pt,s!=0&&(ge.a=-((Ft*(E+g)+Tt*(nt*gt+O*Se))/s)+Ft,ge.b=Tt*(1+T/s)))}function re(He,ge,Je,gt){var ne,Se,qe;if(gt.sr=gt.si=gt.lr=gt.li=0,He==0){gt.sr=ge!=0?-(Je/ge):gt.sr;return}if(Je==0){gt.lr=-(ge/He);return}ne=ge/2,Math.abs(ne)<Math.abs(Je)?(qe=Je>=0?He:-He,qe=-qe+ne*(ne/Math.abs(Je)),Se=Math.sqrt(Math.abs(qe))*Math.sqrt(Math.abs(Je))):(qe=-(He/ne*(Je/ne))+1,Se=Math.sqrt(Math.abs(qe))*Math.abs(ne)),qe>=0?(Se=ne>=0?-Se:Se,gt.lr=(-ne+Se)/He,gt.sr=gt.lr!=0?Je/gt.lr/He:gt.sr):(gt.lr=gt.sr=-(ne/He),gt.si=Math.abs(Se/He),gt.li=-gt.si)}function J(He,ge,Je,gt,ne,Se,qe,Be,ct,wt,Mt,qt){var Ft=new Object,Tt,Ze,ht,Et,Pt,Ye,nt,O,Z,g,E,T=0,s,x=0;Je.NZ=0,Ye=gt,O=ne;do{if(Ft.li=Ft.lr=Ft.si=Ft.sr=0,re(1,Ye,O,Ft),Je.szr=Ft.sr,Je.szi=Ft.si,Je.lzr=Ft.lr,Je.lzi=Ft.li,Math.abs(Math.abs(Je.szr)-Math.abs(Je.lzr))>.01*Math.abs(Je.lzr))break;for(st(qe,Ye,O,ct,Se,Be),Ze=Math.abs(-(Je.szr*Be.b)+Be.a)+Math.abs(Je.szi*Be.b),g=Math.sqrt(Math.abs(O)),Tt=2*Math.abs(Se[0]),Pt=-(Je.szr*Be.b),E=1;E<ge;E++)Tt=Tt*g+Math.abs(Se[E]);if(Tt=Tt*g+Math.abs(Pt+Be.a),Tt=(9*Tt+2*Math.abs(Pt)-7*(Math.abs(Be.a+Pt)+g*Math.abs(Be.b)))*He,Ze<=20*Tt){Je.NZ=2;break}if(T++,T>20)break;if(T>=2&&Et<=.01&&Ze>=ht&&!x){for(Et=Et<He?Math.sqrt(He):Math.sqrt(Et),Ye-=Ye*Et,O+=O*Et,st(qe,Ye,O,ct,Se,Be),E=0;E<5;E++)s=se(He,ge,Be.a,Be.b,Mt,qt,Ye,O,wt),te(He,ge,s,Be.a,Be.b,Mt,qt,wt,Se);x=1,T=0}ht=Ze,s=se(He,ge,Be.a,Be.b,Mt,qt,Ye,O,wt),te(He,ge,s,Be.a,Be.b,Mt,qt,wt,Se),s=se(He,ge,Be.a,Be.b,Mt,qt,Ye,O,wt),D(s,Be,Be.a,Mt.a1,Mt.a3,Mt.a7,Be.b,Mt.c,Mt.d,Mt.f,Mt.g,Mt.h,Ye,O,qt,ge,ct),nt=Be.a,Z=Be.b,Z!=0&&(Et=Math.abs((-O+Z)/Z),Ye=nt,O=Z)}while(Z!=0)}function Ee(He,ge,Je,gt,ne,Se,qe,Be,ct){var wt,Mt,qt,Ft,Tt,Ze,ht,Et,Pt,Ye,nt,O=gt-1;for(ge.NZ=nt=Pt=0,ht=Je.a;;){for(Ze=ne[0],qe[0]=Ze,Ye=1;Ye<Se;Ye++)qe[Ye]=Ze=Ze*ht+ne[Ye];for(qt=Math.abs(Ze),Ft=Math.abs(ht),wt=.5*Math.abs(qe[0]),Ye=1;Ye<Se;Ye++)wt=wt*Ft+Math.abs(qe[Ye]);if(qt<=20*He*(2*wt-qt)){ge.NZ=1,ge.szr=ht,ge.szi=0;break}if(nt++,nt>10)break;if(nt>=2&&Math.abs(Et)<=.001*Math.abs(-Et+ht)&&qt>Tt){Pt=1,ge.a=ht;break}for(Tt=qt,ct[0]=Mt=Be[0],Ye=1;Ye<gt;Ye++)ct[Ye]=Mt=Mt*ht+Be[Ye];if(Math.abs(Mt)>Math.abs(Be[O])*10*He)for(Et=-(Ze/Mt),Be[0]=qe[0],Ye=1;Ye<gt;Ye++)Be[Ye]=Et*ct[Ye-1]+qe[Ye];else for(Be[0]=0,Ye=1;Ye<gt;Ye++)Be[Ye]=ct[Ye-1];for(Mt=Be[0],Ye=1;Ye<gt;Ye++)Mt=Mt*ht+Be[Ye];Et=Math.abs(Mt)>Math.abs(Be[O])*10*He?-(Ze/Mt):0,ht+=Et}return Pt}function xe(He,ge,Je,gt,ne,Se,qe,Be,ct,wt,Mt,qt){var Ft=new Object,Tt=new Object,Ze=new Array(ge),ht=new Array(ge),Et,Pt,Ye,nt,O,Z,g,E,T,s,x,C,U,G,Y,ce,Me,dt,_t,$t=1,i,S,A,W,ke,Fe;for(qt.NZ=0,nt=Ye=.25,O=gt,E=ne,Ft.b=Ft.a=0,st(ct,Mt,ne,Be,wt,Ft),Et=Ft.a,Pt=Ft.b,Tt.h=Tt.g=Tt.f=Tt.e=Tt.d=Tt.c=Tt.a7=Tt.a3=Tt.a1=0,W=se(He,qe,Et,Pt,Tt,Se,Mt,ne,Ze),i=0;i<Je;i++){if(dt=1,te(He,qe,W,Et,Pt,Tt,Se,Ze,wt),W=se(He,qe,Et,Pt,Tt,Se,Mt,ne,Ze),D(W,Ft,Et,Tt.a1,Tt.a3,Tt.a7,Pt,Tt.c,Tt.d,Tt.f,Tt.g,Tt.h,Mt,ne,Se,qe,Be),Y=Ft.a,Me=ce=Ft.b,s=Se[qe-1]!=0?-(Be[qe]/Se[qe-1]):0,x=U=1,i!=0&&W!=3&&(U=Me!=0?Math.abs((Me-E)/Me):U,x=s!=0?Math.abs((s-O)/s):x,G=U<g?U*g:1,C=x<Z?x*Z:1,ke=G<nt?1:0,S=C<Ye?1:0,S||ke)){for(_t=0;_t<qe;_t++)ht[_t]=Se[_t];for(T=s,A=Fe=0;;){if(!(dt&&(dt=0)==0&&S&&(!ke||C<G))){if(J(He,qe,qt,Y,ce,wt,ct,Ft,Be,Ze,Tt,Se),Et=Ft.a,Pt=Ft.b,qt.NZ>0)return;if($t=Fe=1,nt*=.25,A||!S)$t=0;else for(_t=0;_t<qe;_t++)Se[_t]=ht[_t]}if($t!=0){if(Ft.a=T,$t=Ee(He,qt,Ft,qe,Be,ct,wt,Se,Ze),T=Ft.a,qt.NZ>0)return;if(A=1,Ye*=.25,$t!=0){Y=-(T+T),ce=T*T;continue}}for(_t=0;_t<qe;_t++)Se[_t]=ht[_t];if(!ke||Fe)break}st(ct,Mt,ne,Be,wt,Ft),Et=Ft.a,Pt=Ft.b,W=se(He,qe,Et,Pt,Tt,Se,Mt,ne,Ze)}E=Me,O=s,g=U,Z=x}}function Ce(He,ge,Je,gt){var ne=He.Degree,Se=3.141592653589793/180,qe=Math.LN2,Be=He.Degree+1,ct=new Array(Be),wt=new Array(Be),Mt=new Array(Be),qt=new Array(Be),Ft=new Object,Tt=new Object,Ze,ht,Et,Pt,Ye,nt,O,Z,g,E,T,s,x,C,U,G,Y,ce,Me,dt,_t,$t,i,S;s=1;do ht=s,s/=2,x=1+s;while(x>1);var A=Number.MIN_VALUE/ht,W=Math.cos(94*Se),ke=Math.sin(94*Se),Fe=Math.sqrt(.5),ft=-Fe;for(Tt.NZ=Me=0,Tt.szr=Tt.szi=Tt.lzr=Tt.lzi=0;ge[ne]==0;)Je[Me]=gt[Me]=0,ne--,Me++;for(i=ne+1;ne>=1;){if(ne<=2){ne<2?(Je[He.Degree-1]=-(ge[1]/ge[0]),gt[He.Degree-1]=0):(Ft.li=Ft.lr=Ft.si=Ft.sr=0,re(ge[0],ge[1],ge[2],Ft),Je[He.Degree-2]=Ft.sr,gt[He.Degree-2]=Ft.si,Je[He.Degree-1]=Ft.lr,gt[He.Degree-1]=Ft.li);break}for(O=0,Z=Number.MAX_VALUE,St=0;St<i;St++)E=Math.abs(ge[St]),E>O&&(O=E),E!=0&&E<Z&&(Z=E);if(g=A/Z,(g<=1&&O>=10||g>1&&Number.MAX_VALUE/g>=O)&&(g=g==0?Number.MIN_VALUE:g,_t=Math.floor(Math.log(g)/qe+.5),Ye=Math.pow(2,_t),Ye!=1))for(St=0;St<i;St++)ge[St]*=Ye;for(var St=0;St<i;St++)wt[St]=Math.abs(ge[St]);wt[ne]=-wt[ne],$t=ne-1,E=Math.exp((Math.log(-wt[ne])-Math.log(wt[0]))/ne),wt[$t]!=0&&(T=-wt[ne]/wt[$t],E=T<E?T:E),T=E;do{E=T,T=.1*E,nt=wt[0];for(var St=1;St<i;St++)nt=nt*T+wt[St]}while(nt>0);Pt=E;do{Et=nt=wt[0];for(var St=1;St<ne;St++)nt=E*nt+wt[St],Et=E*Et+nt;nt=E*nt+wt[ne],Pt=nt/Et,E-=Pt}while(Math.abs(Pt/E)>.005);Ze=E;for(var St=1;St<ne;St++)ct[St]=(ne-St)*ge[St]/ne;for(ct[0]=ge[0],s=ge[ne],x=ge[$t],S=ct[$t]==0?1:0,dt=0;dt<5;dt++)if(C=ct[$t],S){for(var St=0;St<$t;St++)Me=$t-St,ct[Me]=ct[Me-1];ct[0]=0,S=ct[$t]==0?1:0}else{G=-s/C;for(var St=0;St<$t;St++)Me=$t-St,ct[Me]=G*ct[Me-1]+ge[Me];ct[0]=ge[0],S=Math.abs(ct[$t])<=Math.abs(x)*ht*10?1:0}for(var St=0;St<ne;St++)qt[St]=ct[St];for(dt=1;dt<=20;dt++)if(ce=-(ke*ft)+W*Fe,ft=ke*Fe+W*ft,Fe=ce,U=Ze*Fe,Y=-(2*U),xe(ht,Be,20*dt,U,Ze,ct,ne,ge,i,Mt,Y,Tt),Tt.NZ!=0){Me=He.Degree-ne,Je[Me]=Tt.szr,gt[Me]=Tt.szi,i=i-Tt.NZ,ne=i-1;for(var St=0;St<i;St++)ge[St]=Mt[St];Tt.NZ!=1&&(Je[Me+1]=Tt.lzr,gt[Me+1]=Tt.lzi);break}else for(var St=0;St<ne;St++)ct[St]=qt[St];if(dt>20){He.Degree-=ne;break}}}Ce(pe,B,ue,fe);var Ke=fe.length;for(me=0;me<Ke;me++){var Ne=De(fe[me],u+8),We=De(ue[me],u+8);We=u-String(We).length>2?We:ue[me];var ae=Ne<0?"-":"";We===0&&(We=""),Ne===0&&(Ne=""),Ne=Math.abs(Ne)===1?ae+"i":Ne?Ne+"*i":"";var Ge=We&&Ne?We+"+"+Ne:We+Ne;ue[me]=Ge.replace(/\+\-/g,"-")}return ue}},roots:function(c){if(c.isConstant(!0,!0))return t.Utils.nroots(c);var u=d.proots(c).map(function(f){return e.parse(f)});return t.Vector.fromArray(u)},froot:function(c,u,f){var v=function(I){for(var q=1e-12,V=f||t.Utils.build(t.Calculus.diff(c.clone())),Q=c instanceof Function?c:t.Utils.build(c),le=1e4,ye=!1,Ae=0;!ye;){var je=I-Q(I)/V(I),it=Math.abs(je)-Math.abs(I),yt=Math.abs(it);I=je,yt<q?ye=!0:Ae>le&&(I=null,ye=!0),Ae++}return I};return v(Number(u))},quad:function(c,u,f){var v=function(I,q,V,Q){return e.parse("-("+q+"+"+Q+"*sqrt(("+q+")^2-4*("+I+")*("+V+")))/(2*"+I+")")};return[v(c,u,f,1),v(c,u,f,-1)]},sumProd:function(c,u){return d.quad(-u,c,-1).map(function(f){return f.invert()})},coeffs:function(c,u,f){u=String(u),c=e.expand(c),f=f||[new ee(0)],c.group===h&&c.contains(u,!0)&&e.error("Unable to get coefficients using expression "+c.toString());var v=de(c);if(v.length===1&&v[0]===u&&!c.isImaginary())for(var I=new ut(c).coeffs.map(function(je){return new ee(je)}),q=0,V=I.length;q<V;q++){var Q=I[q],le=f[q];le&&(Q=e.add(le,Q)),f[q]=Q}else if(u||e.error("Polynomial contains more than one variable. Please specify which variable is to be used!"),v.indexOf(u)===-1)f[0]=e.add(c,f[0]);else if(f=f||[new ee(0)],c.group===R){var ye=c.symbols[u];ye||e.error("Expression is not a polynomial!");var Ae=Number(ye.power);Q=e.divide(c.clone(),ye.clone()),(Q.contains(u,!0)||Ae<0||!Qe(Ae))&&e.error("Expression is not a polynomial!");var le=f[Ae];le&&(Q=e.add(le,Q)),f[Ae]=Q}else c.group===_&&c.each(function(je){d.coeffs(je.clone(),u,f)},!0);for(var q=0,V=f.length;q<V;q++)typeof f[q]=="undefined"&&(f[q]=new ee(0));return f},polyPowers:function(c,u,f){f=f||[];var v=v=c.group;if(v===M&&u===c.value)f=f.concat(ie(c.symbols));else if(v===_)for(var I in c.symbols){var q=c.symbols[I],v=q.group,V=q.value;if(v===l&&u===V)f.push(q.power);else if(v===M||v===_)f=d.polyPowers(q,u,f);else if(v===R&&q.contains(u)){var Q=q.symbols[u];Q&&f.push(Q.power)}else(v===r||u!==V)&&f.push(0)}else v===R&&c.contains(u)&&f.push(t.Utils.decompose_fn(c,u,!0).x.power);return t.Utils.arrayUnique(f).sort()},Factor:{split:function(c){var u=new ee(1),f=new ee(1);return d.Factor.factor(c,new at).each(function(v){var I=e.parse(v);v.isConstant(!0)?u=e.multiply(u,I):f=e.multiply(f,I)}),[u,f]},mix:function(c,u){for(var f=ie(c),v=f.length,I=[],q=0;q<v;q++){for(var V=f[q],Q=c[V],le=I.length,ye=0;ye<le;ye++){var Ae=I[ye]*V;I.push(Ae),u&&I.push(-Ae)}for(var ye=1;ye<=Q;ye++)I.push(Math.pow(V,ye))}return I},common:function(c,u){try{if(c.group===_){for(var f=e.expand(c.clone(),!0).collectSymbols(null,null,function(Ae,je){return(je.length||1)-(Ae.length||1)}),v={},I=[],q=0;q<f.length;q++){var V=f[q];I.push(V.multiplier.clone()),V.each(function(Ae){var je=Number(Ae.power);if(isNaN(je))throw new Error("exiting");Ae.value in v?(je<v[Ae.value][0]&&(v[Ae.value][0]=je),v[Ae.value][1].push(Ae)):v[Ae.value]=[je,[Ae]]})}var Q=new ee(1);for(var le in v)v[le][1].length===f.length&&(Q=e.multiply(Q,e.pow(new ee(le),new ee(v[le][0]))));var ye=t.Math2.QGCD.apply(null,I);if(!ye.equals(1)){u.add(new ee(ye));for(var q=0;q<f.length;q++)f[q].multiplier=f[q].multiplier.divide(ye)}if(!Q.equals(1)){u.add(Q),c=new ee(0);for(var q=0;q<f.length;q++)c=e.add(c,e.divide(f[q],Q.clone()))}}}catch(Ae){}return c},zeroes:function(c,u){var f=function(){throw new t.exceptions.ValueLimitExceededError("Exiting")};try{var v,I,q,V,Q;c=e.expand(c.clone()),Q=c.toString(),v=de(c),q=new ee(0);for(var le=[],ye=[],Ae=0,je=v.length;Ae<v.length;Ae++){for(var it={},yt=0;yt<je;yt++)Ae!==yt&&(it[v[yt]]=0);I=e.parse(Q,it);var me=I.power;Qe(me)||f(),le.push(I),ye.push(I.power)}if(t.Utils.allSame(ye)){var Ue=c.length,Le=le.length;Le===2&&(V=new Ie(ye[0]/(Ue-1))),Le===3&&(V=new Ie(ye[0]/Math.round((Math.sqrt(8*Ue-1)-3)/2)))}else V=t.Math2.QGCD.apply(null,ye);Qe(V)||f();for(var Ae=0;Ae<le.length;Ae++){var Ve=le[Ae],lt=Ve.power.clone().divide(V);Ve.multiplier=new Ie(Math.pow(Ve.multiplier,1/lt)),Ve.power=V.clone(),q=e.add(q,Ve)}if(q.group!==_)return c;for(;;){var Nt=d.div(c.clone(),q.clone());if(Nt[1].equals(0)){if(c=Nt[0],u.add(q.clone()),c.equals(1))break}else break}}catch(Ct){}return c},factor:function(c,u){if(c.isConstant())return t.Math2.factor(c);var f=e.parse(c),v=d.Factor._factor(f,u);if(v.equals(c))return v;if(v.group===R){var I=new ee(1),q=e.parse(v.power),V=e.parse(v.multiplier);v.toUnitMultiplier(),v.multiplier.lessThan(0)&&(I.negate(),v.negate()),v.each(function(Q){var le=e.parse(d.Factor._factor(Q));le.group===R?(V=e.multiply(V,ee.create(le.multiplier)),le.each(function(ye){var Ae=e.parse(d.Factor._factor(ye));I=e.multiply(I,Ae),Ae.group===R&&(V=e.multiply(V,ee.create(Ae.multiplier)))})):I=e.multiply(I,le)}),v=e.pow(e.multiply(V,I),q)}return v},quadFactor:function(c,u){if(c.isPoly()&&d.degree(c.equals(2))){var f=t.Utils.variables(c)[0],v=d.coeffs(c,f),I=d.Factor._factor(v[2].clone());if(I.group===R){var q=I.collectSymbols();if(q.length>2)return c;var V=e.multiply(e.parse(v[0]),e.parse(q[0])),Q=e.parse(v[1]).negate(),le=e.parse(q[1]),ye=d.quad(le,Q,V).filter(function(it){if(t.Utils.isInt(it))return it});if(ye.length===1){var Ae=ye[0],je=e.divide(v[0],e.parse(Ae));t.Utils.isInt(je)&&(u.add(e.parse(ve("({0})*({1})+({2})",q[1],f,je))),u.add(e.parse(ve("({0})*({1})+({2})",q[0],f,Ae))),c=new ee(1))}}}return c},cubeFactor:function(c,u){if(c.isComposite()){var f=c.collectSymbols();if(f.length===2){var v=f[0].sign(),I=f[0].clone().abs(),q=f[1].sign(),V=f[1].clone().abs();if(I.isCube()&&V.isCube()){v<q&&([v,q]=[q,v],[I,V]=[V,I]);var Q=e.parse(I.getNth(3)),le=e.parse(V.getNth(3)),ye=e.multiply(e.expand(e.pow(I.clone().toUnitMultiplier(),e.parse("1/3"))),Q),Ae=e.multiply(e.expand(e.pow(V.clone().toUnitMultiplier(),e.parse("1/3"))),le);v===1&&q===-1?(u.add(e.parse(ve("(({0})-({1}))",ye,Ae))),u.add(e.parse(ve("(({0})^2+({0})*({1})+({1})^2)",ye,Ae))),c=ee(1)):v===1&&q===1&&(u.add(e.parse(ve("(({0})+({1}))",ye,Ae))),u.add(e.parse(ve("(({0})^2-({0})*({1})+({1})^2)",ye,Ae))),c=ee(1))}}}return c},_factor:function(c,u){var f=c.group;if(c.group===L){var v=c.args[0];if(v.group===l&&v.isSimple())return c}else if(c.group===l&&c.isSimple())return c;if(c.group===_){c.distributeMultiplier(!0);var I=new ee(0);c.each(function(st){(st.group===_&&st.power.greaterThan(1)||st.group===R)&&(st=e.expand(st)),I=e.add(I,st)}),I.power=c.power,c=I}c.group===L&&c.fname!=="sqrt"&&(c=t.Utils.evaluate(c));var q=c.clone();try{if(c.group===R){var Le=e.parse(c.power),V,Q,le,ye,Ae,je;if(V=d.Simplify.strip(c.getDenom()),Q=d.Simplify.strip(c.getNum()),le=V.pop(),ye=Q.pop(),ye.equals(c))return c;je=d.Factor.factor(ye),Ae=d.Factor.factor(le);var it=d.Simplify.unstrip(Q,je),yt=d.Simplify.unstrip(V,Ae),me=e.divide(it,yt);return me}if(c.group===l)return c;if(c.isConstant()){if(c.equals(1))return c.clone();var Ue=t.Math2.factor(c);return Ue}var Le=c.power.clone();if(Qe(Le)&&!(Le.lessThan(0)&&c.group===L)){var Ve=Le.sign();c.toLinear(),u=u||new at;var lt={};c=e.parse(t.Utils.subFunctions(c,lt)),ie(lt).length>0&&(u.preAdd=function(se){var te=e.parse(se,t.Utils.getFunctionsSubs(lt));return te}),c.isLinear()||(u.pFactor=c.power.toString(),c.toLinear());var Nt=de(c);c.isImaginary()&&Nt.push(t.Settings.IMAGINARY);var Ct=Nt.length>1;if(Ct){var Xe=!0,he=!0;if(c.each(function(se){se.group!==l&&(Xe=!1),se.multiplier.equals(1)||(he=!1)}),Xe&&he)return e.pow(e.parse(c,t.Utils.getFunctionsSubs(lt)),e.parse(Le))}var et=new at;c=d.Factor.coeffFactor(c,et),et.each(function(se){K(Le)&&se.lessThan(0)&&se.negate(),Ve<0&&se.invert(),u.add(se)});var Lt=new at;if(c=d.Factor.powerFactor(c,Lt),Lt.each(function(se){Ve<0&&se.invert(),u.add(se)}),Ct)c=d.Factor.cubeFactor(c,u),c=d.Factor.mfactor(c,u),u.each(function(se){Ve<0&&se.power.negate()});else{var H=Nt[0];c=d.Factor.squareFree(c,u,H);var P=new at;c=d.Factor.trialAndError(c,P,H);var B=P.toSymbol();if(B.equals(q))return B;for(var fe in P.factors){var pe=P.factors[fe];u.add(e.pow(pe,e.parse(Le)))}c.equals(q)&&(c=d.Factor.quadFactor(c,u))}c=e.parse(c,t.Utils.getFunctionsSubs(lt));var ue=u.length===1;u.add(e.pow(c,e.parse(Le)));var me=u.toSymbol();return ue&&c.equals(1)&&me.isLinear()&&(me=e.pow(me,e.parse(Le))),me}return c}catch(st){return q}},reduce:function(c,u){if(c.group===_&&c.length===2){var f=c.collectSymbols().sort(function(je,it){return it.multiplier-je.multiplier});if(f[0].power.equals(f[1].power)){var v=e.parse(f[0].power),I=f[0].clone().toLinear(),q=f[1].clone().toLinear();u.add(e.add(I.clone(),q.clone())),q.negate();for(var V=Number(v),Q=new ee(0),le=1;le<=V;le++){var ye=e.pow(I.clone(),e.subtract(v.clone(),new ee(le))),Ae=e.pow(q.clone(),e.subtract(new ee(le),new ee(1)));Q=e.add(Q,e.multiply(ye,Ae))}return Q}}return c},squareFree:function(c,u,f){if(c.isConstant()||c.group===l)return c;var v=new ut(c,f),I=v.squareFree(),q=I[2];if(q!==1){var V=I[1].toSymbol();V.power=V.power.multiply(new Ie(q)),u.add(d.Factor.factor(V));var Q=d.Factor.squareFree(I[0].toSymbol(),u);return Q}return c},powerFactor:function(c,u){if(c.group!==M||c.previousGroup===h)return c;var f=ie(c.symbols);if(!t.Utils.allNumeric(f))return c;var v=t.Utils.arrayMin(f),I=new ee(0),q=e.parse(c.value+"^"+v);return c.each(function(V){V=e.divide(V,q.clone()),I=e.add(I,V)}),u.add(q),I},coeffFactor:function(c,u){if(c.isComposite()){var f=t.Math2.QGCD.apply(null,c.coeffs());if(!f.equals(1))c.each(function(V){V.isComposite()?V.each(function(Q){Q.multiplier=Q.multiplier.divide(f)}):V.multiplier=V.multiplier.divide(f)}),c.updateHash();else{var v=function(V){var Q;return V.group===R?(Q=0,V.each(function(le){Q+=le.power})):Q=Number(V.power),Q},I=c.collectSymbols(null,null,null,!0).sort(function(V,Q){return V.isConstant(!0)?1:Q.power-V.power}),q=I[0];(v(q)>v(I[1])||I[1].isConstant(!0))&&q.multiplier.lessThan(0)&&(u.add(new ee(-1)),c.each(function(V){V.negate()},!0))}u&&u.add(new ee(f))}return c},trialAndError:function(c,u,f){var v=c.clone();try{var I=[];if(c.isConstant()||c.group===l)return c;for(var q=new ut(c,f),V=q.coeffs[0],Q=t.Math2.ifactor(V),le=d.proots(c),ye=0;ye<le.length;ye++){var Ae=le[ye],je=1;if(!isNaN(Ae)){for(var it in Q){var yt=t.Utils.round(Math.log(it)/Math.log(Math.abs(Ae)),8);if(Qe(yt)){Ae=it,je=yt;break}}var me=new Ie(Ae),Ue=[new Ie(me.num).negate()];Ue[je]=new Ie(me.den);var Le=ut.fromArray(Ue,q.variable).fill(),Ve=q.divide(Le);Ve[1].equalsNumber(0)&&(q=Ve[0],I.push(Le.toSymbol()))}}return q.equalsNumber(1)||(q=d.Factor.search(q,u)),I.forEach(function(lt){u.add(lt)}),q.toSymbol()}catch(lt){return v}},search:function(c,u,f){f=f||10;var v=c.variable,I=function(Nt,Ct,Xe,he){var et=ut.fit(Nt,Ct,Xe,f,he,v);if(et&&et.coeffs.length>1){var Lt=c.divide(et);if(Lt[1].equalsNumber(0))return u.add(et.toSymbol()),[Lt[0],et]}return null},q=c.coeffs[0],V=t.Math2.ifactor(q),Q=c.lc(),le=t.Math2.ifactor(Q),ye=c.sub(f),Ae=t.Math2.ifactor(ye),je=d.Factor.mix(Ae,ye<0),it=Math.ceil(c.coeffs.length/2),yt=Q.lessThan(0),me=q.lessThan(0);for(le[1]=1,V[1]=1;it--;)for(var Ue in le)for(var Le in V)for(var Ve=0;Ve<je.length;Ve++){var lt=I(Ue,Le,je[Ve],it);if(lt)return c=lt[0],t.Utils.isPrime(c.sub(f))||(c=d.Factor.search(c,u)),c;lt||(yt&&me?lt=I(-Ue,-Le,je[Ve],it):yt?lt=I(-Ue,Le,je[Ve],it):me&&(lt=I(Ue,-Le,je[Ve],it)))}return c},mSqfrFactor:function(c,u){if(c.group!==L)for(var f=de(c).reverse(),v=0;v<f.length;v++)do{if(f[v]===c.value){u.add(c),c=new ee(1);continue}var I=t.Calculus.diff(c,f[v]),q=d.Factor.coeffFactor(I);if(q.equals(0))break;var V=!0;if(q.isConstant()&&c.isComposite()&&c.each(function(ye){ye.multiplier%q!==0&&(V=!1)},!0),V){var Q=d.div(c,q.clone()),le=Q[1].equals(0);if(c.equals(Q[0])&&Q[1].equals(0))break;if(Q[0].isConstant()){u.add(Q[0]);break}}else le=!1;le&&(u.add(Q[0]),c=q)}while(le);return c},sqdiff:function(c,u){if(c.isConstant("all"))return c;try{var f=function(Ae){return t.Utils.block("POSITIVE_MULTIPLIERS",function(){return ee.unwrapPARENS(ze.sqrt(ze.abs(Ae)))},!0)},v=t.Utils.separate(c.clone()),I=[];for(var q in v)q!=="constants"&&I.push(v[q]);if(I.sort(function(Ae,je){return je.power-Ae.power}),I.length===2){var V,Q;if(V=I.pop(),Q=I.pop(),K(V.power)&&K(Q.power)&&V.sign()===Q.sign()&&V.group===l&&Q.group===l)throw new Error("Unable to factor");if(V.isComposite()&&Q.power.equals(2)){Q=f(Q);var le=d.Factor.factor(e.add(V,v.constants));le.power.equals(2)&&(le.toLinear(),u.add(e.subtract(le.clone(),Q.clone())),u.add(e.add(le,Q)),c=new ee(1))}else if(V=V.powSimp(),Q=Q.powSimp(),(V.group===l||V.fname==="")&&V.power.equals(2)&&(Q.group===l||Q.fname==="")&&Q.power.equals(2)&&!v.constants){if(V.multiplier.lessThan(0)){var ye=Q;Q=V,V=ye}V.multiplier.greaterThan(0)&&(V=f(V),Q=f(Q)),u.add(e.subtract(V.clone(),Q.clone())),u.add(e.add(V,Q)),c=new ee(1)}}}catch(Ae){}return c},mfactor:function(c,u){if(c.group===L)if(c.fname==="sqrt"){var f=new at,v=d.Factor.common(c.args[0].clone(),f);v=d.Factor.coeffFactor(v,f),c=e.multiply(e.symfunction("sqrt",[v]),e.parse(c.multiplier)),f.each(function(H){c=e.multiply(c,e.parse(t.Utils.format("sqrt({0})",H)))})}else u.add(c);else{c=d.Factor.mSqfrFactor(c,u);for(var I=de(c),q=c.collectSymbols().map(function(H){return ee.unwrapSQRT(H)}),V={},Q={},le=I.length,ye=q.length,Ae=0;Ae<le;Ae++){var je=I[Ae];V[je]=new ee(0);for(var it=0;it<ye;it++){var yt=q[it];if(yt.contains(je)){var me=yt.value===je?yt.power.toDecimal():yt.symbols[je].power.toDecimal();(!Q[je]||me<Q[je])&&(Q[je]=me),V[je]=e.add(V[je],yt.clone())}}}for(var Ue in V){var Le=e.parse(Ue+"^"+Q[Ue]),Ve=e.divide(V[Ue],Le),lt=e.expand(Ve);if(lt.equals(1))break;var Nt=d.div(c.clone(),lt);if(Nt[0].equals(0))break;if(Nt[1].equals(0)){var Ct=!1;if(Nt[0].each(function(H){Qe(H.multiplier)||(Ct=!0)}),Ct){Nt[1]=e.expand(e.multiply(Nt[1],lt));break}}var Xe=Qe(lt)&&lt.lessThan(0);if(Nt[1].equals(0)&&!Xe){var he=d.div(c.clone(),Nt[0].clone()),Le=he[0];if(Le.equals(0)||(c=he[1],Le.equals(-1)&&!c.equals(0)))return c;var et=Nt[0];if(c.equals(et)){var Lt=d.Factor.reduce(et,u);return c.equals(Lt)?Lt:d.Factor.mfactor(Lt,u)}else if(u.add(et),c.equals(0))return Le;return Le.isConstant("all")?(u.add(Le),Le):d.Factor.mfactor(Le,u)}}}return c=d.Factor.sqdiff(c,u),c=d.Factor.zeroes(c,u),c}},allLinear:function(c){for(var u=c.length,f=0;f<u;f++)if(!d.isLinear(c[f]))return!1;return!0},isLinear:function(c){var u=!1,f=c.group;if(f===M||f===_){u=!0;for(var v in c.symbols){var I=c.symbols[v],q=I.group;if((q===L||q===h)&&(u=!1),q===R)u=de(I).length===1;else if(q===M||q===_)u=d.isLinear(I);else if(I.group!==r&&I.power.toString()!=="1"){u=!1;break}}}else f===l&&c.power===1&&(u=!0);return u},gcd:function(){var c;if(arguments.length===1&&arguments[0]instanceof t.Vector?c=arguments[0].elements:c=t.Utils.arguments2Array(arguments),c.length===0)return new ee(1);if(c.length===1)return c[0];for(var u=[],f=!1,v=0;v<c.length;v++)if(c[v].group===L&&c[v].fname==="gcd")c=c.concat(arguments[v].args),c.splice(v,1);else{var I=de(c[v]);if(t.Utils.haveIntersection(I,u)){f=!0;break}else u=u.concat(I)}if(f||u.length===0)if(c.every(function(V){return V.getDenom().equals(1)})){for(var q=c[0],v=1;v<c.length;v++)q=d.gcd_(c[v],q);return q}else return e.divide(d.gcd.apply(null,c.map(function(V){return V.getNum()})),d.lcm.apply(null,c.map(function(V){return V.getDenom()})));else return e.symfunction("gcd",c)},gcd_:function(c,u){if((c.group===L||c.group===a)&&(c=t.Utils.block("PARSE2NUMBER",function(){return e.parse(c)})),u.group===L&&(u=t.Utils.block("PARSE2NUMBER",function(){return e.parse(u)})),c.isConstant()&&u.isConstant())return new ee(t.Math2.QGCD(new Ie(+c),new Ie(+u)));var f=e.multiply(c.getDenom()||new ee(1),u.getDenom()||new ee(1)).invert();if(c=e.multiply(c.clone(),f.clone()),u=e.multiply(u.clone(),f.clone()),c=e.expand(c),u=e.expand(u),c.group===R||u.group===R){var v=e.divide(c.clone(),u.clone()),I=e.multiply(u.clone(),v.getDenom().invert());if(!I.equals(1))return I}if(c.group===h||u.group===h){var q=new ee(t.Math2.GCD(c.multiplier,u.multiplier)),V=d.gcd_(c.value===Te?new ee(1):e.parse(c.value),u.value===Te?new ee(1):e.parse(u.value)),Q=d.gcd_(e.parse(c.power),e.parse(u.power));return e.multiply(q,e.pow(V,Q))}if(c.length<u.length){var I=c;c=u,u=I}var le=de(c),ye=de(u);if(le.length===ye.length&&le.length===1&&le[0]===ye[0]||le.length===1&&ye.length===0||le.length===0&&ye.length===1)return c=new ut(c),u=new ut(u),e.divide(c.gcd(u).toSymbol(),f);var Ae=[];c.each(function(yt){Ae.push(yt.multiplier)}),u.each(function(yt){Ae.push(yt.multiplier)});for(var je;!u.equals(0);){var I=u.clone();if(c=c.clone(),je=d.div(c,I),u=je[1],je[0].equals(0))return e.divide(new ee(t.Math2.QGCD(c.multiplier,u.multiplier)),f);c=I}var it=t.Math2.QGCD.apply(void 0,Ae);return it.equals(1)||c.each(function(yt){yt.multiplier=yt.multiplier.divide(it)}),c.equals(1)&&!c.isConstant()&&!u.isConstant()?e.divide(e.symfunction("gcd",arguments),f):e.divide(c,f)},lcm:function(){var c;arguments.length===1?arguments[0]instanceof t.Vector?c=arguments[0].elements:e.error("lcm expects either 1 vector or 2 or more arguments"):c=t.Utils.arguments2Array(arguments);var u=c.reduce(function(q,V){return e.multiply(q,V.clone())},new ee(1)),f=function(q,V){V=Number(V);var Q=[],le,ye,Ae,je=Math.pow(2,q.length);for(ye=V;ye<je;ye++){le=[],Ae=q.length-1;do(ye&1<<Ae)!==0&&le.push(q[Ae]);while(Ae--);le.length===V&&Q.push(le)}return Q}(arguments,arguments.length-1).map(function(q){return q.reduce(function(V,Q){return e.multiply(V,Q.clone())},new ee(1))}),v;c.every(function(q){return t.Utils.isVariableSymbol(q)})?v=e.symfunction("gcd",t.Utils.arrayUnique(f)):v=d.gcd.apply(null,f);var I=e.divide(u,v);return I},divide:function(c,u){var f,v,I,q;return I=t.Algebra.Factor.factor(c.clone()),q=I.getDenom(),q.isConstant("all")?q=new ee(1):c=e.expand(ee.unwrapPARENS(e.multiply(I,q.clone()))),f=d.div(c,u),v=e.divide(f[1],u),e.divide(e.add(f[0],v),q)},div:function(c,u){var f=[new ee(0),c.clone()];try{if(u.isConstant("all"))return c.each(function(Ge){Ge.multiplier=Ge.multiplier.divide(u.multiplier)}),[c,new ee(0)];if(c=e.expand(c),u=e.expand(u),c.group===l&&u.group===_){var v=c.value,I=t.Utils.decompose_fn(u.clone(),v,!0);if(c.isLinear()&&I.x&&I.x.isLinear()&&u.isLinear()){var q=ee.create(c.multiplier);return[e.divide(q.clone(),I.a.clone()),e.divide(e.multiply(q,I.b),I.a).negate()]}}if(c.group===l&&u.group===l){var V=e.divide(c.clone(),u.clone());return V.isConstant()?[V,new ee(0)]:[new ee(0),c.clone()]}var Q=c.hasFunc(),le=u.hasFunc(),ye=!1;if(Q||le){ye=!0;var Ae={},c=e.parse(t.Utils.subFunctions(c,Ae)),u=e.parse(t.Utils.subFunctions(u,Ae)),je=t.Utils.getFunctionsSubs(Ae)}var it=t.Utils.arrayUnique(de(c).concat(de(u))),yt,me;if((c.isImaginary()||u.isImaginary())&&it.push(t.Settings.IMAGINARY),it.length===1){var Ue=new ut(c).divide(new ut(u));yt=Ue[0].toSymbol(),me=Ue[1].toSymbol()}else{it.push(Te);var Le=function(Ge){for(var He=new ee(0),ge=0;ge<Ge.length;ge++){var Je=Ge[ge].toSymbol();He=e.add(He,Je)}return He},Ve=function(Ge,He){var ge=Math.max.apply(null,Ge.terms),Je=0,gt;if(!He){for(var ne=0;ne<Ge.terms.length;ne++)if(Ge.terms[ne].equals(ge)&&(gt=ne,Je++),Je>1)return}if(He){for(ne=0;ne<Ge.terms.length;ne++)if(Ge.terms[ne].equals(ge)){gt=ne;break}}return[ge,gt,Ge]},lt=function(Ge,He){He=He||0;var ge=Ge[He],Je=Ge.length;if(!!ge){for(var gt=Ve(ge),ne=He+1;ne<Je;ne++){var Se=Ge[ne],qe=ge.sum.equals(Se.sum);if(!qe&&gt)break;if(qe){for(var Be,ct,wt,Mt,qt=ge.terms.length,Ft=0;Ft<qt;Ft++){var Tt=ge.terms[Ft],Ze=Se.terms[Ft];(typeof Be=="undefined"||Tt.greaterThan(Be))&&(Be=Tt,wt=Ft),(typeof ct=="undefined"||Ze.greaterThan(ct))&&(ct=Ze,Mt=Ft)}var ht=Be.subtract(Se.terms[wt]),Et=ct.subtract(ge.terms[Mt]);if(Et>ht){gt=[ct,Mt,Se];break}if(ht>Et){gt=[Be,wt,ge];break}}else if(gt=Ve(Se),gt)break;gt=Ve(Se)}if(!gt)return Ve(Ge[0],!0);for(var Pt,Ye,ne=0;ne<et.length;ne++){var nt=et[ne].terms;if(Ye=gt[1],Ye===nt.length-1)return;if(Pt=nt[Ye],!Pt.equals(0))break}return Pt.equals(0)?lt(Ge,++He):gt}},Nt=t.Utils.toMapObj(it),Ct=function(Ge,He){return He.sum.subtract(Ge.sum)},Xe=function(Ge,He){if(!Ge||!He)return!1;for(var ge=0;ge<Ge.terms.length;ge++)if(Ge.terms[ge].lessThan(He.terms[ge]))return!1;return!0},he=c.tBase(Nt).sort(Ct),et=u.tBase(Nt).sort(Ct),Lt=Xe(he[0],et[0])&&he[0].count>et[0].count?et:he,H=lt(Lt),P=[];if(H){var B=H[1],fe=function(Ge,He){return Ge[0].sum.equals(He[0].sum)?Ge.length>=He.length:!0},pe=function(Ge,He,ge){for(var Je=[],gt=0;gt<Ge.length;gt++)for(var ne=Ge[gt],Se=0;Se<ne.terms.length;Se++){var qe=Je[Se],Be=ne.terms[Se];gt===0?Je[Se]=Be:qe&&!qe.equals(Be)&&(Je[Se]=void 0)}for(var gt=0;gt<Je.length;gt++){var ne=Je[gt];if(ne&&!ne.equals(0))return gt}return ge},ue=function(Ge,He){var ge=Ge.len(),Je=He.len(),gt=He.terms[B],ne=Ge.terms[B];return Je>ge&&gt.greaterThan(ne)?Je-ge:gt.subtract(ne)};B=pe(he,et,B),he.sort(ue),et.sort(ue);var st=et[0],se=he[0],te=new j(new Ie(1),[],se.map);if(st.sum.greaterThan(se.sum)&&se.len()>1)for(var D=0;D<se.terms.length;D++){var re=st.terms[D].subtract(se.terms[D]);if(re.equals(0))te.terms[D]=new Ie(0);else{var J=re.add(new Ie(1));te.terms[D]=re;for(var Ee=0;Ee<he.length;Ee++)he[Ee].terms[D]=he[Ee].terms[D].add(J)}}for(var xe=Xe(he[0],et[0]),Ce=0,Ke=200;xe&&fe(he,et);){if(Ce++>Ke)throw new t.exceptions.InfiniteLoopError("Unable to compute!");var Ue=he[0].divide(et[0]);P.push(Ue),he.shift();for(var D=1;D<et.length;D++){var Ne=et[D].multiply(Ue).generateImage(),We=he.length;We===0&&(Ne.coeff=Ne.coeff.neg(),he.push(Ne),he.sort(ue));for(var Ee=0;Ee<We;Ee++){var ae=he[Ee];if(ae.getImg()===Ne.getImg()){ae.coeff=ae.coeff.subtract(Ne.coeff),ae.coeff.equals(0)&&(t.Utils.remove(he,Ee),Ee--);break}Ee===We-1&&(Ne.coeff=Ne.coeff.neg(),he.push(Ne),he.sort(ue))}}if(xe=Xe(he[0],et[0]),!xe&&he.length>=et.length){for(var D=1;D<he.length;D++)if(xe=Xe(he[D],et[0]),xe){he.unshift(t.Utils.remove(he,D));break}}}}yt=Le(P),me=Le(he),typeof te!="undefined"&&(te=te.toSymbol(),yt=e.divide(yt,te.clone()),me=e.divide(me,te))}return ye&&(yt=e.parse(yt.text(),je),me=e.parse(me.text(),je)),[yt,me]}catch(Ge){return f}},line:function(c,u,f){t.Utils.isArray(c)&&(c=t.Utils.convertToVector(c)),t.Utils.isArray(u)&&(u=t.Utils.convertToVector(u)),f=e.parse(f||"x"),(!t.Utils.isVector(c)||!t.Utils.isVector(u))&&e.error('Line expects a vector! Received "'+c+'" & "'+u+'"');var v=e.subtract(u.e(1).clone(),c.e(1).clone()),I=e.subtract(u.e(2).clone(),c.e(2).clone()),q=e.divide(I,v),V=e.multiply(f,q.clone()),Q=e.multiply(c.e(1).clone(),q);return e.add(e.subtract(V,Q),c.e(2).clone())},PartFrac:{createTemplate:function(c,u,f,v){c=d.Factor.factor(c),c.each(function(Le,Ve){if(Le.group===L&&Le.fname===""&&Le.args[0].group===l){var lt=Le.args[0];this.symbols?(delete this.symbols[Ve],this.symbols[lt.value]=lt):c=Le.args[0]}});var I,q,V,Q,le,ye,Ae;I=u.collectFactors(),q=[],ye=[],Ae=new ee(1);for(var je=0;je<I.length;je++){var it=ee.unwrapPARENS(I[je]);if(it.power.greaterThan(1)){Q=Number(it.power),V=it.clone().toLinear(),le=Number(d.degree(V,v));for(var yt=0;yt<Q;yt++){var me=e.pow(V.clone(),new ee(yt+1));f.push(me.clone());var Ue=e.divide(c.clone(),me.clone());ye.push(le),q.push(Ue)}}else{le=Number(d.degree(it,v)),f.push(it);var Ue=e.divide(c.clone(),it.clone());Ue=e.expand(ee.unwrapPARENS(Ue)),ye.push(le),q.push(Ue)}}return f=f.map(function(Le){return e.multiply(Le,Ae.clone())}),[f,q,ye]},partfrac:function(c,u,f){var v=de(c);u=u||e.parse(v[0]);try{var I,q,V,Ct,Q,le,ye,Ae,je,it,yt,me,Ue,Le,Ve,lt,Nt,Ct;if(I=e.expand(c.getNum()),q=e.expand(c.getDenom().toUnitMultiplier()),I.multiplier=c.multiplier,le=I.groupTerms(u),Number(d.degree(I,u))>=Number(d.degree(q,u))?(Ue=d.div(I.clone(),e.expand(q.clone())),Le=Ue[0],I=Ue[1],le=I.groupTerms(u)):Le=new ee(0),Number(d.degree(q,u))===1){var Xe=e.divide(I,q);return f?[Le,Xe]:e.add(Le,Xe)}Q=d.Factor.factor(q),Nt=d.PartFrac.createTemplate(q.clone(),Q,[],u),Ct=Nt[0],Ve=Nt[1],ye=Nt[2],me=[le.length],Ae=[],V=[],lt=[];var he,et;Ve.map(function(ue,st){he=Ct[st],et=ye[st];for(var se=0;se<et;se++){V.push(he.clone());var te=ee.create(u,se),D=e.expand(e.multiply(ue,te.clone())).groupTerms(u),re=D.length;me.push(re),Ae.push(D),lt.push(te.clone())}}),je=t.Utils.arrayMax(me),yt=new t.Matrix(t.Utils.fillHoles(le,je)).transpose(),it=new t.Matrix;for(var Lt=0;Lt<Ae.length;Lt++)it.elements.push(t.Utils.fillHoles(Ae[Lt],je));var H=e.multiply(it.transpose().invert(),yt),P=f?[Le]:Le;return H.each(function(ue,st){var se=e.multiply(lt[st],e.divide(ue,V[st]));f?P.push(se):P=e.add(P,se)}),P}catch(ue){try{if(c.isComposite()){var B={};c.each(function(st){var se=st.getDenom(),te=st.getNum(),D=B[se];B[se]=D?e.add(D,te):te});var fe=new ee(0);for(var pe in B)fe=e.add(fe,e.divide(B[pe],e.parse(pe)));c=fe}}catch(st){}}return c}},degree:function(c,u,f){if(f=f||{nd:[],sd:[],depth:0},!u){var v=de(c);if(v.length>1)throw new Error("You must specify the variable for multivariate polynomials!");if(v.length===0)return new ee(0);u=e.parse(v[0])}var I=c.group;c.isComposite()?(c=c.clone(),c.distributeExponent(),c.each(function(V){f.depth++,d.degree(V,u,f),f.depth--})):c.group===R?c.each(function(V){f.depth++,d.degree(V,u,f),f.depth++}):I===h&&c.value===u.value?f.sd.push(c.power.clone()):I===l&&c.value===u.value?f.nd.push(e.parse(c.power)):f.nd.push(new ee(0));var q=f.nd.length>0?t.Utils.arrayMax(f.nd):void 0;return f.depth===0&&f.sd.length>0?(q!==void 0&&f.sd.unshift(q),e.symfunction("max",f.sd)):(t.Utils.isSymbol(q)||(q=e.parse(q)),q)},sqComplete:function(c,u,f){t.Utils.isSymbol(u)||(u=e.parse(u));var v=function(Ue){throw Ue=Ue||"Stopping",new t.exceptions.ValueLimitExceededError(Ue)};c.isPoly(!0)||v("Must be a polynomial!");var I,q,V,Q,le,ye,Ae,je,it,yt,me;return it=t.Utils.inBrackets,c=c.clone(),I=t.Algebra.degree(c,u),I.equals(2)||v("Cannot complete square for degree "+I),Ae=t.Algebra.coeffs(c,u),q=Ae[2],je=Ae[1].sign(),V=e.divide(Ae[1],new ee(2)),Q=e.pow(V.clone(),new ee(2)),f?[q,V,le]:(me=ze.sqrt(q),ye=e.divide(ze.sqrt(Q),me.clone()),le=e.subtract(Ae[0],e.pow(ye.clone(),new ee(2))),yt=e.parse(it(me.clone()+"*"+u+(je<0?"-":"+")+ye)),{a:yt,c:le,f:e.add(e.pow(yt.clone(),new ee(2)),le.clone())})},Simplify:{strip:function(c){var u=e.parse(c.multiplier);c.toUnitMultiplier();var f=e.parse(c.power);return c.toLinear(),[u,f,c]},unstrip:function(c,u){var f=c[0],v=c[1];return e.multiply(f,e.pow(u,v))},complexSimp:function(c,u){var f,v,I,q,V,Q,le,ye,Ae;return Q=c.realpart(),ye=c.imagpart(),le=u.realpart(),Ae=u.imagpart(),f=e.multiply(Q.clone(),le.clone()),v=e.multiply(ye.clone(),Ae.clone()),I=e.multiply(le.clone(),ye),q=e.multiply(Q,Ae.clone()),V=e.add(e.pow(le,new ee(2)),e.pow(Ae,new ee(2))),e.divide(e.add(e.add(f,v),e.multiply(e.subtract(I,q),ee.imaginary())),V)},trigSimp:function(c){if(c.containsFunction(["cos","sin","tan"])){c=c.clone();var u=d.Simplify.strip(c);c=u.pop();var f=c.clone();if(c.group===_){var v=new ee(0);c.each(function(Q){var le=d.Simplify.trigSimp(Q.fnTransform());v=e.add(v,le)},!0),f=e.pow(e.multiply(new ee(c.multiplier),v),new ee(c.power))}else if(c.group===R){var I=c.getNum(),q=c.getDenom();if(I.fname==="sin"&&q.fname==="cos"&&I.args[0].equals(q.args[0])&&I.power.equals(q.power)&&(f=e.parse(t.Utils.format("({0})*({1})*tan({2})^({3})",q.multiplier,I.multiplier,I.args[0],I.power))),f.group===R){var V=new ee(1);f.each(function(Q){Q.fname==="tan"&&(Q=e.parse(t.Utils.format("({0})*sin({1})^({2})/cos({1})^({2})",Q.multiplier,d.Simplify.simplify(Q.args[0]),Q.power))),V=e.multiply(V,Q)}),f=V}}f=d.Simplify.unstrip(u,f).distributeMultiplier(),c=f}return c},fracSimp:function(c){var u=c.getDenom(),f=c.getNum();if(f.isImaginary()&&u.isImaginary()&&(c=d.Simplify.complexSimp(f,u)),c.isComposite()){c.power>1&&(c=e.expand(c));var v=c.collectSymbols(),I,q,V,Q,le,ye,Ae,je,it,yt,me,u,f;for(q=v.pop();v.length;)V=v.pop(),Q=e.parse(q.getDenom()),le=e.parse(V.getDenom()),ye=q.getNum(),Ae=V.getNum(),me=e.multiply(Q.clone(),le.clone()),it=e.multiply(ye,le),yt=e.multiply(Ae,Q),je=e.add(it,yt),q=e.divide(je,me);return u=e.expand(q.getDenom()),f=e.expand(q.getNum()),f.isImaginary()&&u.isImaginary()?I=d.Simplify.complexSimp(f,u):I=e.divide(f,u),I.equals(c)?c:d.Simplify.simplify(I)}return c},ratSimp:function(c){if(c.group===R){var u=c.getDenom(),f=c.getNum().distributeMultiplier(),v=d.Simplify.fracSimp(u),I=d.Simplify.fracSimp(f);c=e.divide(I,v)}return c},sqrtSimp:function(c,u){var f;if(c.isSQRT()){var v=d.Factor.factor(c.args[0].clone()),I=e.parse(v.multiplier),q=I.sign(),f=e.sqrt(I.abs()),V;if(Qe(f)){if(v.group===R){var Q=new ee(1);v.each(function(Ae){if(Ae.group===r){var je=e.sqrt(Ae.clone());Qe(je)?f=e.multiply(f,je):Q=e.multiply(Q,Ae)}else Q=e.multiply(Q,Ae)});var le=e.multiply(Q,e.parse(q));V=e.sqrt(le.clone()),V.isImaginary&&(V=e.sqrt(e.expand(le.clone())))}else V=e.sqrt(v.clone().toUnitMultiplier());return e.multiply(f,V)}}else c.isComposite()&&c.isLinear()?(f=new ee(0),c.each(function(ye){f=e.add(f,d.Simplify.sqrtSimp(ye))},!0),f=e.multiply(f,e.parse(c.multiplier))):c.group===R&&(f=e.parse(c.multiplier),c.each(function(ye){var Ae=d.Simplify.sqrtSimp(ye);f=e.multiply(f,Ae)},!0),f=e.pow(f,e.parse(c.power)));return f||e.parse(c)},patternSub:function(c){var u={},f=function(I){var q=!1;return I.each(function(V){V.group===_?q=!0:V.symbols&&(q=f(V))}),q},v=function(I){I.each(function(q){if(!(!q.symbols&&q.group!==L)){if(f(q))v(q);else if(!u[q.value]){var V=t.Utils.getU(c);u[q.value]=V,c=c.sub(q.value,V)}}},!0)};return v(c),[c,u]},simplify:function(c){var u=d.Simplify.strip(c);if(c=u.pop(),c=d.Simplify.fracSimp(c),c.isConstant()||c.group===t.groups.S){u.push(c);var f=d.Simplify.unstrip(u,c);return f}var v=c.clone();if(v=d.Simplify.trigSimp(v),v=d.Simplify.ratSimp(v),v=d.Factor.factor(v),v.group===t.groups.CP&&v.isLinear()){var I=v.multiplier.clone();v.toUnitMultiplier();var q=new ee(0);v.each(function(Q){var le=d.Simplify.simplify(Q);q=e.add(q,le)}),v=q,q.multiplier=q.multiplier.multiply(I)}var V=d.Simplify.unstrip(u,v);return V}},Classes:{Polynomial:ut,Factors:at,MVTerm:j}};t.Expression.prototype.simplify=function(){return d.Simplify.simplify(this.symbol)},Z1.useAlgebraDiv=function(){var c=d.divideFn=e.divide,u=0;e.divide=function(f,v){u++;var I;return u===1?I=t.Algebra.divide(f,v):I=c(f,v),u=0,I}},Z1.useParserDiv=function(){d.divideFn&&(e.divide=d.divideFn),delete d.divideFn},Z1.register([{name:"factor",visible:!0,numargs:1,build:function(){return d.Factor.factor}},{name:"simplify",visible:!0,numargs:1,build:function(){return d.Simplify.simplify}},{name:"gcd",visible:!0,numargs:[1],build:function(){return d.gcd}},{name:"lcm",visible:!0,numargs:[1],build:function(){return d.lcm}},{name:"roots",visible:!0,numargs:-1,build:function(){return d.roots}},{name:"divide",visible:!0,numargs:2,build:function(){return d.divide}},{name:"div",visible:!0,numargs:2,build:function(){return d.div}},{name:"partfrac",visible:!0,numargs:[1,2],build:function(){return d.PartFrac.partfrac}},{name:"deg",visible:!0,numargs:[1,2],build:function(){return d.degree}},{name:"coeffs",visible:!0,numargs:[1,2],build:function(){var c=function(){var u=d.coeffs.apply(d,arguments);return new t.Vector(u)};return c}},{name:"line",visible:!0,numargs:[2,3],build:function(){return d.line}},{name:"sqcomp",visible:!0,numargs:[1,2],build:function(){var c=function(u,f){try{f=f||de(u)[0];var v=d.sqComplete(u.clone(),f);return v.f}catch(I){return u}};return c}}]),Z1.updateAPI()})()});var V0=an((RS,O7)=>{typeof O7!="undefined"&&typeof Z2=="undefined"&&(Z2=N0(),z0());var Z2;(function(){"use strict";var t=Z2.getCore(),e=t.PARSER,r=t.Frac,a=t.Settings,l=t.Utils.isSymbol,De=t.groups.FN,h=t.Symbol,L=t.Utils.text,M=t.Utils.inBrackets,_=t.Utils.isInt,R=t.Utils.format,ie=t.Utils.even,K=t.Utils.evaluate,de=t.groups.N,ve=t.groups.S,De=t.groups.FN,Ie=t.groups.PL,Qe=t.groups.CP,ee=t.groups.CB,Te=t.groups.EX,ze=t.groups.P,Oe=a.LOG,ut="exp",at="abs",j="sqrt",d="sin",c="cos",u="tan",f="sec",v="csc",I="cot",q="asin",V="acos",Q="atan",le="asec",ye="acsc",Ae="acot",je="sinh",it="cosh",yt="tanh",me="csch",Ue="sech",Le="coth",Ve="asech",lt="acsch",Nt="acoth";function Ct(B){this.message=B||""}Ct.prototype=new Error,h.prototype.hasIntegral=function(){return this.containsFunction("integrate")},h.prototype.fnTransform=function(){if(this.group!==De)return this;var B,fe=this.args[0],pe=new h(this.multiplier),ue=this.clone().toUnitMultiplier();if(this.isLinear())switch(this.fname){case je:B=e.parse(R("(e^({0})-e^(-({0})))/2",fe));break;case it:B=e.parse(R("(e^({0})+e^(-({0})))/2",fe));break;case yt:B=e.parse(R("(e^({0})-e^(-({0})))/(e^({0})+e^(-({0})))",fe));break;case u:B=e.parse(R("sin({0})/cos({0})",fe));break;case v:B=e.parse(R("1/sin({0})",fe));break;case f:B=e.parse(R("1/cos({0})",fe));break;default:B=ue}else if(this.power.equals(2))switch(this.fname){case d:B=e.parse(R("1/2-cos(2*({0}))/2",fe));break;case c:B=e.parse(R("1/2+cos(2*({0}))/2",fe));break;case u:B=e.parse(R("sin({0})^2/cos({0})^2",fe));break;case it:B=e.parse(R("1/2+cosh(2*({0}))/2",fe));break;case je:B=e.parse(R("-1/2+cosh(2*({0}))/2",fe));break;case yt:B=e.parse(R("(1+cosh(2*({0})))/(-1+cosh(2*({0})))",fe));break;case f:B=e.parse(R("(1-cos(2*({0})))/(1+cos(2*({0})))+1",fe));break;default:B=ue}else if(this.fname===f)B=e.parse(R("1/cos({0})^({1})",this.args[0],this.power));else if(this.fname===v)B=e.parse(R("1/sin({0})^({1})",this.args[0],this.power));else if(this.fname===u)this.power.lessThan(0)?B=e.parse(R("cos({0})^(-({1}))/sin({0})^({1})",this.args[0],this.power.negate())):B=e.parse(R("sin({0})^({1})/cos({0})^({1})",this.args[0],this.power));else if(this.fname===d&&this.power.lessThan(0))B=e.parse(R("csc({0})^(-({1}))",this.args[0],this.power.negate()));else if(this.fname===c&&this.power.lessThan(0))B=e.parse(R("sec({0})^(-({1}))",this.args[0],this.power.negate()));else if(this.fname===d&&this.power.equals(3))B=e.parse(R("(3*sin({0})-sin(3*({0})))/4",this.args[0]));else if(this.fname===c&&this.power.equals(3))B=e.parse(R("(cos(3*({0}))+3*cos({0}))/4",this.args[0]));else if((this.fname===c||this.fname===d)&&ie(this.power)){var st=this.power/2,se=e.pow(this.clone().toLinear(),e.parse(2)).fnTransform(),te=e.expand(e.pow(se,e.parse(st)));B=new h(0),te.each(function(D){var re=D.fnTransform();B=e.add(B,re)},!0)}else B=ue;return e.multiply(B,pe)},h.prototype.hasTrig=function(){if(this.isConstant(!0)||this.group===ve)return!1;if(this.fname&&(t.Utils.in_trig(this.fname)||t.Utils.in_inverse_trig(this.fname)))return!0;if(this.symbols){for(var B in this.symbols)if(this.symbols[B].hasTrig())return!0}return!1},t.Expression.prototype.hasIntegral=function(){return this.symbol.hasIntegral()},t.Utils.toCommonDenominator=function(B){if(B.isComposite()&&B.isLinear()){var fe=new h(B.multiplier),pe=new h(1),ue=new h(0);B.each(function(se){pe=e.multiply(pe,se.getDenom())},!0),B.each(function(se){var te=se.getNum(),D=se.getDenom(),re=e.multiply(te,e.divide(pe.clone(),D));ue=e.add(ue,re)});var st=e.multiply(fe,t.Algebra.divide(e.expand(ue),e.expand(pe)));return st}return B},t.Utils.in_inverse_trig=function(B){var fe=[q,V,Q,ye,le,Ae];return fe.indexOf(B)!==-1},t.Utils.in_trig=function(B){var fe=[c,d,u,f,v,I];return fe.indexOf(B)!==-1},t.Utils.in_htrig=function(B){var fe=[je,it,yt,lt,Ve,Nt];return fe.indexOf(B)!==-1},t.Matrix.jacobian=function(B,fe){var pe=new t.Matrix;return fe||(fe=t.Utils.arrayGetVariables(B)),fe.forEach(function(ue,st){B.forEach(function(se,te){var D=t.Calculus.diff(se.clone(),ue);pe.set(te,st,D)})}),pe},t.Matrix.prototype.max=function(){var B=new h(0);return this.each(function(fe){var pe=fe.abs();pe.gt(B)&&(B=pe)}),B},t.Matrix.cMatrix=function(B,fe){var pe=new t.Matrix;return fe.forEach(function(ue,st){pe.set(st,0,e.parse(B))}),pe};var Xe=t.Utils.all_functions=function(B){for(var fe=0,pe=B.length;fe<pe;fe++)if(B[fe].group!==De)return!1;return!0},he=t.Utils.cosAsinBtranform=function(B,fe){var pe,ue;return pe=B.args[0],ue=fe.args[0],e.parse(R("(sin(({0})+({1}))-sin(({0})-({1})))/2",pe,ue))},et=t.Utils.cosAsinAtranform=function(B,fe){if(Number(fe.power)!==1)return e.multiply(B,fe);var pe;return pe=B.args[0],e.parse(R("(sin(2*({0})))/2",pe))},Lt=t.Utils.cosAsinBtranform=function(B,fe){var pe,ue;return pe=B.args[0],ue=fe.args[0],e.parse(R("(cos(({0})+({1}))-cos(({0})-({1})))/2",pe,ue))},H=t.Utils.trigTransform=function(B){for(var fe={},pe,ue,st=new h(1),se=0,te=B.length;se<te;se++)if(pe=B[se],pe.group===De){var D=pe.fname;D===c&&fe[d]?(fe[d].args[0].toString()!==pe.args[0].toString()?ue=he(pe,fe[d]):ue=et(pe,fe[d]),delete fe[d],st=e.multiply(st,ue)):D===d&&fe[c]?(fe[c].args[0].toString()!==pe.args[0].toString()?ue=he(pe,fe[c]):ue=et(pe,fe[c]),delete fe[c],st=e.multiply(st,ue)):D===d&&fe[d]?(fe[d].args[0].toString()!==pe.args[0].toString()?(ue=Lt(pe,fe[d]),delete fe[d]):(ue=e.multiply(pe,fe[d]),delete fe[d]),st=ue):fe[D]=pe}else st=e.multiply(st,pe);for(var re in fe)st=e.multiply(st,fe[re]);return st};t.Settings.integration_depth=10,t.Settings.max_lim_depth=10;var P=t.Calculus={version:"1.4.6",sum:function(B,fe,pe,ue){if(fe.group!==t.groups.S)throw new t.exceptions.NerdamerTypeError("Index must be symbol. "+L(fe)+" provided");fe=fe.value;var st;if(t.Utils.isNumericSymbol(pe)&&t.Utils.isNumericSymbol(ue)){var se=ue-pe<200?"":"PARSE2NUMBER";pe=Number(pe),ue=Number(ue),st=t.Utils.block(se,function(){for(var te=B.text(),D={"~":!0},re=new t.Symbol(0),J=pe;J<=ue;J++){D[fe]=new h(J);var Ee=e.parse(te,D);re=e.add(re,Ee)}return re})}else st=e.symfunction("sum",arguments);return st},product:function(B,fe,pe,ue){if(fe.group!==t.groups.S)throw new t.exceptions.NerdamerTypeError("Index must be symbol. "+L(fe)+" provided");fe=fe.value;var st;if(t.Utils.isNumericSymbol(pe)&&t.Utils.isNumericSymbol(ue)){var se=ue-pe<200?"":"PARSE2NUMBER";st=t.Utils.block(se,function(){pe=Number(pe),ue=Number(ue.multiplier);for(var te=B.text(),D={},re=new t.Symbol(1),J=pe;J<=ue;J++)D[fe]=new h(J),re=e.multiply(re,e.parse(te,D));return re})}else st=e.symfunction("product",arguments);return st},diff:function(B,fe,pe){if(t.Utils.isVector(B)){var ue=new t.Vector([]);return B.each(function(Ne){ue.elements.push(P.diff(Ne,fe,pe))}),ue}else if(t.Utils.isMatrix(B)){var st=new t.Matrix;return B.each(function(Ne,We,ae){st.set(We,ae,P.diff(Ne,fe,pe))}),st}var se=l(fe)?fe.text():fe;if(pe=l(pe)?pe.multiplier:pe||1,se===void 0&&(se=t.Utils.variables(B)[0]),B.group===De&&B.fname===j){var te=B.args[0],D=B.power.clone();(te.group!==de||te.group!==ze)&&(te.power=l(te.power)?e.multiply(te.power,e.multiply(new h(1/2)),D):te.power.multiply(new r(.5)).multiply(D),te.multiplier=te.multiplier.multiply(B.multiplier)),B=te}if(B.group===De&&!l(B.power)){var re=xe(e.parse(B)),J=P.diff(B.args[0].clone(),se);B=e.multiply(re,J)}else B=xe(B);return pe>1&&(pe--,B=P.diff(B,fe,pe)),B;function Ee(Ne){return(Ne.value===se||Ne.contains(se,!0))&&(Ne.multiplier=Ne.multiplier.multiply(Ne.power),Ne.power=Ne.power.subtract(new r(1)),Ne.power.equals(0)&&(Ne=h(Ne.multiplier))),Ne}function xe(Ne){var We=Ne.group,ae,Ge,He;if(We===de||We===ve&&Ne.value!==se||We===ze)Ne=h(0);else if(We===ve)Ne=Ee(Ne);else if(We===ee){var ge=Ne.multiplier.clone();Ne.toUnitMultiplier();var Je=e.multiply(Ke(Ne),Ee(Ne));return Je.multiplier=Je.multiplier.multiply(ge),Je}else if(We===De&&Ne.power.equals(1))switch(Ne.fname){case Oe:He=Ne.clone(),Ne=Ne.args[0].clone(),Ne.power=Ne.power.negate(),Ne.multiplier=He.multiplier.divide(Ne.multiplier);break;case c:Ne.fname=d,Ne.multiplier.negate();break;case d:Ne.fname=c;break;case u:Ne.fname=f,Ne.power=new r(2);break;case f:Ne=Ce(Ne,u);break;case v:Ne=Ce(Ne,"-cot");break;case I:Ne.fname=v,Ne.multiplier.negate(),Ne.power=new r(2);break;case q:Ne=e.parse("(sqrt(1-("+L(Ne.args[0])+")^2))^(-1)");break;case V:Ne=e.parse("-(sqrt(1-("+L(Ne.args[0])+")^2))^(-1)");break;case Q:Ne=e.parse("(1+("+L(Ne.args[0])+")^2)^(-1)");break;case at:ge=Ne.multiplier.clone(),Ne.toUnitMultiplier(),Ge=Ne.args[0].clone(),Ge.toUnitMultiplier(),Ne=e.parse(M(L(Ne.args[0]))+"/abs"+M(L(Ge))),Ne.multiplier=ge;break;case"parens":Ne=h(1);break;case"cosh":Ne.fname="sinh";break;case"sinh":Ne.fname="cosh";break;case yt:Ne.fname=Ue,Ne.power=new r(2);break;case Ue:Ne=Ce(Ne,"-tanh");break;case me:var gt=String(Ne.args[0]);return e.parse("-coth("+gt+")*csch("+gt+")");case Le:var gt=String(Ne.args[0]);return e.parse("-csch("+gt+")^2");case"asinh":Ne=e.parse("(sqrt(1+("+L(Ne.args[0])+")^2))^(-1)");break;case"acosh":Ne=e.parse("(sqrt(-1+("+L(Ne.args[0])+")^2))^(-1)");break;case"atanh":Ne=e.parse("(1-("+L(Ne.args[0])+")^2)^(-1)");break;case Ve:var gt=String(Ne.args[0]);Ne=e.parse("-1/(sqrt(1/("+gt+")^2-1)*("+gt+")^2)");break;case Nt:Ne=e.parse("-1/(("+Ne.args[0]+")^2-1)");break;case lt:var gt=String(Ne.args[0]);Ne=e.parse("-1/(sqrt(1/("+gt+")^2+1)*("+gt+")^2)");break;case le:var gt=String(Ne.args[0]);Ne=e.parse("1/(sqrt(1-1/("+gt+")^2)*("+gt+")^2)");break;case ye:var gt=String(Ne.args[0]);Ne=e.parse("-1/(sqrt(1-1/("+gt+")^2)*("+gt+")^2)");break;case Ae:Ne=e.parse("-1/(("+Ne.args[0]+")^2+1)");break;case"S":var gt=String(Ne.args[0]);Ne=e.parse("sin((pi*("+gt+")^2)/2)");break;case"C":var gt=String(Ne.args[0]);Ne=e.parse("cos((pi*("+gt+")^2)/2)");break;case"Si":var gt=Ne.args[0];Ne=e.parse("sin("+gt+")/("+gt+")");break;case"Shi":var gt=Ne.args[0];Ne=e.parse("sinh("+gt+")/("+gt+")");break;case"Ci":var gt=Ne.args[0];Ne=e.parse("cos("+gt+")/("+gt+")");break;case"Chi":var gt=Ne.args[0];Ne=e.parse("cosh("+gt+")/("+gt+")");break;case"Ei":var gt=Ne.args[0];Ne=e.parse("e^("+gt+")/("+gt+")");break;case"Li":var gt=Ne.args[0];Ne=e.parse("1/"+a.LOG+"("+gt+")");break;case"erf":Ne=e.parse("(2*e^(-("+Ne.args[0]+")^2))/sqrt(pi)");break;case"atan2":var ne=String(Ne.args[0]),Se=String(Ne.args[1]);Ne=e.parse("("+Se+")/(("+Se+")^2+("+ne+")^2)");break;case"sign":Ne=new h(0);break;case"sinc":Ne=e.parse(R("(({0})*cos({0})-sin({0}))*({0})^(-2)",Ne.args[0]));break;case a.LOG10:Ne=e.parse("1/(("+Ne.args[0]+")*"+a.LOG+"(10))");break;default:Ne=e.symfunction("diff",[Ne,fe])}else if(We===Te||We===De&&l(Ne.power)){var qe;We===Te?qe=Ne.value:We===De&&Ne.contains(se)?qe=Ne.fname+M(L(Ne.args[0])):qe=Ne.value+M(L(Ne.args[0])),ae=e.multiply(e.parse(Oe+M(qe)),Ne.power.clone()),Ge=P.diff(e.multiply(e.parse(Oe+M(qe)),Ne.power.clone()),se),Ne=e.multiply(Ne,Ge)}else if(We===De&&!Ne.power.equals(1))Ge=Ne.clone(),Ge.toLinear(),Ge.toUnitMultiplier(),Ne=e.multiply(Ee(Ne.clone()),xe(Ge));else if(We===Qe||We===Ie){var Be=Ne.clone(),ct=new h(0);for(var wt in Ne.symbols)ct=e.add(ct,P.diff(Ne.symbols[wt].clone(),se));Ne=e.multiply(Ee(Be),ct)}return Ne.updateHash(),Ne}function Ce(Ne,We,ae){return e.multiply(Ne,e.parse(We+M(ae||L(Ne.args[0]))))}function Ke(Ne){for(var We=Ne.collectSymbols(),ae=new h(0),Ge=We.length,He=0;He<Ge;He++){for(var ge=P.diff(We[He].clone(),se),Je=0;Je<Ge;Je++)He!==Je&&(ge=e.multiply(ge,We[Je].clone()));ae=e.add(ae,ge)}return ae}},integration:{u_substitution:function(B,fe){function pe(ne,Se,qe){var Be=P.diff(Se,fe),ct=qe?qe(ne,Se):e.divide(ne.clone(),Be);return ct.contains(fe,!0)?null:ct}function ue(ne,Se){var qe=P.integrate(e.symfunction(ne,[new h(re)]),re,0);return qe=qe.sub(new h(re),Se),qe.updateHash(),qe}var st=B[0].clone(),se=B[1].clone(),te=st.group,D=se.group,re="__u__",J;if(te===De&&D!==De){var Ee=st.args[0];if(J=pe(se,Ee.clone()),J)return e.multiply(J,ue(st.fname,Ee));if(J=pe(se,st),J)return P.integration.poly_integrate(st)}else if(D===De&&te!==De){var Ee=se.args[0];if(J=pe(st,Ee.clone()),J)return e.multiply(J,ue(se.fname,Ee))}else if(te===De&&D===De){if(J=pe(st.clone(),se.clone()),J||(J=pe(se.clone(),st.clone()),J))return e.multiply(P.integration.poly_integrate(se),J)}else if(te===Te&&D!==Te){var xe=st.power;if(J=pe(se,xe.clone()),!J){var Ce=P.integration.decompose_arg(xe.clone(),fe),Ke=P.diff(Ce[2].clone(),fe),Ne=P.integration.decompose_arg(Ke.clone(),fe);if(e.multiply(Ce[1],Ne[1]).power.equals(se.power)){var We=e.divide(Ce[0].clone(),Ne[0].clone()),ae=e.multiply(We.clone(),e.pow(new h(st.value),e.multiply(Ce[0],new h(re))));return ae=e.multiply(ae,new h(re)),P.integration.by_parts(ae,re,0,{}).sub(re,Ce[1].clone())}}var Ge=P.integrate(st.sub(xe.clone(),new h(re)),re,0),He=e.multiply(Ge.sub(new h(re),xe),J);return He}else if(D===Te&&te!==Te){var xe=se.power;J=pe(st,xe.clone());var Ge=P.integrate(se.sub(xe,new h(re)),re,0);return e.multiply(Ge.sub(new h(re),xe),J)}else if(st.isComposite()||se.isComposite()){var ge=function(ne,Se){var qe=P.diff(Se,fe),Be=t.Algebra.Factor.factor(ne),ct=t.Algebra.Factor.factor(qe),wt=e.divide(Be,ct);return wt},Je=st.isComposite()?st.clone().toLinear():st.clone(),gt=se.isComposite()?se.clone().toLinear():se.clone();if(J=pe(Je.clone(),gt.clone(),ge),J)return e.multiply(P.integration.poly_integrate(se),J);if(J=pe(gt.clone(),Je.clone(),ge),J)return e.multiply(P.integration.poly_integrate(st),J)}},poly_integrate:function(B){var fe=B.power.toString(),pe=B.multiplier.toDecimal(),ue=B.toUnitMultiplier().toLinear();return Number(fe)===-1?e.multiply(new h(pe),e.symfunction(Oe,[ue])):e.parse(R("({0})*({1})^(({2})+1)/(({2})+1)",pe,ue,fe))},stop:function(B){throw B=B||"Unable to compute integral!",t.Utils.warn(B),new Ct(B)},partial_fraction:function(B,fe,pe,ue){l(fe)||(fe=e.parse(fe));var st,se;return st=new h(0),se=t.Algebra.PartFrac.partfrac(B,fe),se.group===ee&&se.isLinear()?(se.each(function(te){te.isLinear()||P.integration.stop()}),se.each(function(te){st=e.add(st,P.integrate(te,fe,pe,ue))})):st=e.add(st,P.integrate(se,fe,pe,ue)),st},get_udv:function(B){var fe=[[],[],[],[],[]],pe=function(Ee){var xe=Ee.group;if(xe===De){var Ce=Ee.fname;t.Utils.in_trig(Ce)||t.Utils.in_htrig(Ce)?fe[3].push(Ee):t.Utils.in_inverse_trig(Ce)?fe[1].push(Ee):Ce===Oe?fe[0].push(Ee):P.integration.stop()}else xe===ve||Ee.isComposite()&&Ee.isLinear()||xe===ee&&Ee.isLinear()?fe[2].push(Ee):xe===Te||Ee.isComposite()&&!Ee.isLinear()?fe[4].push(Ee):P.integration.stop()};B.group===ee?B.each(function(Ee){pe(h.unwrapSQRT(Ee,!0))}):pe(B);for(var ue,st=new h(1),se=0;se<5;se++){var te=fe[se],D,re=te.length;if(re>0){if(re>1){D=new h(1);for(var J=0;J<re;J++)D=e.multiply(D,te[J].clone())}else D=te[0].clone();ue?st=e.multiply(st,D):(ue=D,ue.multiplier=ue.multiplier.multiply(B.multiplier))}}return[ue,st]},trig_sub:function(B,fe,pe,ue,st,se){st=st||P.integration.decompose_arg(B.clone().toLinear(),fe);var te=st[3],D=st[2],re=st[0],J=st[1];if(J.power.equals(2)&&re.greaterThan(0)){var Ee=t.Utils.getU(B),xe=e.parse(u+M(Ee)),Ce=e.parse(f+M(Ee)+"^2"),Ke=e.multiply(B.sub(J,xe),Ce),Ne=P.integrate(Ke,Ee,pe,ue).sub(xe,J);return t.Utils.clearU(xe),Ne}},by_parts:function(B,fe,pe,ue){ue.previous=ue.previous||[];var st,se,te,D,re,J,Ee,xe,Ce,Ke,Ne,We;if(st=P.integration.get_udv(B),se=st[0],te=st[1],D=h.unwrapSQRT(e.expand(P.diff(se.clone(),fe)),!0),Ne=D.clone().stripVar(fe),D=e.divide(D,Ne.clone()),re=P.integrate(te.clone(),fe,pe||0),J=e.multiply(re.clone(),D),We=J.toString(),ue.previous.indexOf(We)!==-1&&t.Utils.in_trig(se.fname)&&te.isE())return ue.is_cyclic=!0,new h(1);if(ue.previous.push(We),Ee=e.multiply(se,re),Ke=J.multiplier.clone(),J.toUnitMultiplier(),Ce=e.multiply(P.integrate(J.clone(),fe,pe,ue),Ne),Ce.multiplier=Ce.multiplier.multiply(Ke),xe=e.subtract(Ee,Ce),ue.is_cyclic&&(ue.previous.pop(),ue.previous.length===0)){xe=e.expand(xe);var ae=new h(0);xe.each(function(Ge){Ge.contains(fe)||(ae=e.add(ae,Ge.clone()))}),xe=e.divide(e.subtract(xe,ae.clone()),e.subtract(new h(1),ae))}return xe},decompose_arg:t.Utils.decompose_fn},integrate:function(B,fe,pe,ue){if(!fe){var st=t.Utils.variables(B);st.length===1&&(fe=st[0]),fe=fe||"x"}if(t.Utils.isVector(B)){var se=new t.Vector([]);return B.each(function(te){se.elements.push(P.integrate(te,fe))}),se}return isNaN(fe)||e.error("variable expected but received "+fe),B.isConstant(!0)?e.multiply(B.clone(),e.parse(fe)):(ue=ue||{},t.Utils.block("PARSE2NUMBER",function(){pe=pe||0;var te=l(fe)?fe.toString():fe,D=h.unwrapSQRT(B.clone(),!0),re=D.group,J;try{if(++pe>t.Settings.integration_depth&&P.integration.stop("Maximum depth reached. Exiting!"),!D.contains(te,!0))J=e.multiply(D.clone(),e.parse(te));else if(re===ve)J=P.integration.poly_integrate(D,te,pe);else if(re===Te)if(D.previousGroup===De&&!(D.fname==="sqrt"||D.fname===a.PARENTHESIS)&&P.integration.stop(),D.contains(te)&&D.previousGroup!==De)if(D.power.contains(te))P.integration.stop();else{var Ee=P.diff(D.clone().toLinear(),te);Ee.contains(te)&&P.integration.stop(),J=P.integration.poly_integrate(D,te,pe)}else{var xe=P.diff(D.power.clone(),te);if(xe.contains(te)){var Ce=xe.stripVar(te),Ke=e.divide(xe.clone(),Ce.clone());if(Ke.group===ve&&Ke.isLinear())return Ce.multiplier=Ce.multiplier.divide(new r(2)),e.parse(R("({2})*(sqrt(pi)*erf(sqrt(-{0})*{1}))/(2*sqrt(-{0}))",Ce,te,D.multiplier));P.integration.stop()}if(D.isE())xe.isLinear()?J=D:xe.isE()&&xe.power.group===ve&&xe.power.power.equals(1)?J=e.multiply(e.symfunction("Ei",[D.power.clone()]),D.power):P.integration.stop();else{var Ne=e.symfunction(Oe,[e.parse(D.value)]);J=e.divide(D,Ne)}J=e.divide(J,xe)}else if(D.isComposite()&&D.isLinear()){var We=e.parse(D.multiplier);D.toUnitMultiplier(),J=new h(0),D.each(function(Rn){J=e.add(J,P.integrate(Rn,te,pe))}),J=e.multiply(We,J)}else if(re===Qe)if(D.power.greaterThan(1)&&(D=e.expand(D)),D.power.equals(1))J=new h(0),D.each(function(Rn){J=e.add(J,P.integrate(Rn,te,pe))},!0);else{var ae=Number(D.power),We=D.multiplier.clone();D.toUnitMultiplier();var Ge=D.clone().toLinear(),He=P.integration.decompose_arg(Ge,te),ge=He[3],Je=He[2],xe=He[0],Ke=He[1];if(ae===-1&&Ke.group!==Ie&&Ke.power.equals(2)){var gt=_(ge)?ge>0:!0;if(Ke.group===ve&&Ke.power.equals(2)&&gt){var ne=function(Xi){var jr=new h(1);return Xi.each(function(Kn){jr=e.multiply(jr,Kn.fname==="abs"?Kn.args[0]:Kn)}),jr},Se=xe.clone(),qe=ge.clone();Se=e.pow(Se,new h(1/2)),qe=e.pow(qe,new h(1/2));var Ne=e.multiply(ne(qe),ne(Se)),Be=e.symfunction(Q,[e.divide(e.multiply(xe,Ke.toLinear()),Ne.clone())]);J=e.divide(Be,Ne)}else if(Ke.group===ve&&Ke.isLinear())J=e.divide(P.integration.poly_integrate(D),xe);else if(Ke.power.equals(4)){var Se,qe,ct,wt,Mt,qt,Ft,Tt,Ze,ht,Et,Pt,Ye=M;Se=e.parse(j+Ye(xe)+"*"+te+"^2"),qe=e.parse(j+Ye(2)+"*"+Ye(xe)+"^"+Ye("1/4")+"*"+Ye(ge)+"^"+Ye("1/4")+"*"+te),ct=e.parse(j+Ye(ge)),Ft=e.add(e.add(Se.clone(),qe.clone()),ct.clone()),Tt=e.add(e.subtract(Se,qe),ct),wt=e.parse(j+Ye(2)+"*"+Ye(ge)+"^"+Ye("3/4")),Mt=e.parse(j+Ye(ge)+"*"+Ye(ge)+"^"+Ye("1/4")+"*"+te),qt=e.parse(2+"*"+Ye(ge)+"*"+j+Ye(2)+"*"+Ye(ge)+"^"+Ye("1/4")),Et=e.divide(e.subtract(wt.clone(),Mt.clone()),e.multiply(qt.clone(),Tt)),Pt=e.divide(e.add(wt,Mt),e.multiply(qt,Ft.clone())),J=e.add(P.integrate(Et,te,pe,ue),P.integrate(Pt,te,pe,ue))}else J=P.integration.partial_fraction(D,te,pe)}else if(ae===-1/2)if(Ke.group===ve&&Ke.power.equals(2))if(Je.multiplier.lessThan(0)&&!ge.multiplier.lessThan(0))if(xe.negate(),ge.isConstant()&&xe.isConstant()){var Ne=e.symfunction(j,[xe.clone()]),nt=e.symfunction(j,[e.multiply(xe.clone(),ge)]);J=e.divide(e.symfunction(q,[e.divide(Je.toLinear(),nt)]),Ne)}else{var O=e.symfunction(j,[xe]),Z=e.multiply(O.clone(),Ke.clone().toLinear());J=e.divide(e.symfunction(Q,[e.divide(Z,e.symfunction(j,[Ge.clone()]))]),O)}else P.integration.stop();else P.integration.stop();else if(ae===1/2&&Ke.power.equals(2)&&xe.greaterThan(0))P.integration.stop();else if(Ke.isLinear()&&Ke.group!==Ie)J=e.divide(P.integration.poly_integrate(D),xe);else if(Ke.power.equals(2)&&xe.greaterThan(0)){var g,E,T,s,G,Y,x,C,U;g=e.parse(j+M(xe)),E=e.parse(j+M(ge)),T=e.multiply(g.clone(),E.clone()).invert(),s=e.pow(ge,new h(D.power)),U=t.Utils.getU(D),x=e.multiply(T,Ke.clone().toLinear()),C=e.parse(Q+M(x));var G=(Math.abs(D.power)-1)*2,Y=P.integrate(e.parse(c+M(U)+"^"+G));return t.Utils.clearU(U),e.multiply(Y.sub(U,C),s)}else if(D.group!==ee&&!D.power.lessThan(0))J=P.integration.by_parts(D,te,pe,ue);else{var Be=D.clone().toLinear(),ce=t.Algebra.Factor.factor(Be),Me=ce.toString()!==Be.toString();if(t.Algebra.degree(Be,e.parse(te)).equals(2)&&!Me)try{var Ft,dt,x,_t;_t=t.Algebra.sqComplete(Be,te),x=t.Utils.getU(Be),Ft=_t.f.sub(_t.a,x),dt=e.pow(Ft,e.parse(D.power)),J=P.integrate(dt,x).sub(x,_t.a)}catch(Xi){P.integration.stop()}else J=P.integration.partial_fraction(D,te,pe,ue)}J.multiplier=J.multiplier.multiply(We)}else if(re===De){var $t=D.args[0],We=D.multiplier.clone();D.toUnitMultiplier();var He=P.integration.decompose_arg($t,te),xe=He[0],Ke=He[1],i=D.fname;if(i===Oe||i===q||i===V||i===Q&&Ke.isLinear()){var ae=D.power.toString();if(_(ae)&&(pe=pe-ae),!$t.isComposite())J=e.multiply(e.parse(We),P.integration.by_parts(D,te,pe,ue));else{var x=t.Utils.getU(D),Be=e.pow(e.parse(Oe+M(x)),new h(ae)),S=P.diff($t,te),A=e.multiply(Be,S),Y=P.integrate(A,x,pe,ue);J=e.multiply(e.parse(We),Y.sub(x,$t))}}else if(i===u&&D.power.lessThan(0)){var W=D.clone();return W.power.negate(),W.fname=I,e.multiply(e.parse(We),P.integrate(W,te,pe))}else{if(!xe.contains(te,!0)&&D.isLinear())if(i===at){var Ke=e.divide($t.clone(),xe.clone());if(Ke.group===ve&&!Ke.power.lessThan(0))if(t.Utils.even(Ke.power))J=P.integrate($t,te,pe);else{var ke=P.integrate(Ke,te,pe);ke.power=ke.power.subtract(new r(1)),J=e.multiply(e.multiply(e.symfunction(at,[Ke.toLinear()]),ke),xe)}else P.integration.stop()}else{var Fe=D.args[0].group,ft=P.integration.decompose_arg($t,te);switch((!(Fe===Qe||Fe===ve||Fe===ee)||!ft[1].power.equals(1)||$t.hasFunc())&&P.integration.stop(),i){case c:J=e.symfunction(d,[$t]);break;case d:J=e.symfunction(c,[$t]),J.negate();break;case u:J=e.parse(R(a.LOG+"(sec({0}))",$t));break;case f:J=e.parse(R(a.LOG+"(tan({0})+sec({0}))",$t));break;case v:J=e.parse(R("-"+a.LOG+"(csc({0})+cot({0}))",$t));break;case I:J=e.parse(R(a.LOG+"(sin({0}))",$t));break;case je:J=e.symfunction(it,[$t]);break;case it:J=e.symfunction(je,[$t]);break;case yt:J=e.parse(R(a.LOG+"(cosh({0}))",$t));break;case le:J=P.integration.by_parts(D,te,pe,ue);break;case ye:J=P.integration.by_parts(D,te,pe,ue);break;case Ae:J=P.integration.by_parts(D,te,pe,ue);break;case Ve:J=P.integration.by_parts(D,te,pe,ue);break;case lt:J=P.integration.by_parts(D,te,pe,ue);break;case Nt:J=P.integration.by_parts(D,te,pe,ue);break;case Ue:J=e.parse(R("atan(sinh({0}))",$t));break;case me:J=e.parse(R(a.LOG+"(tanh(({0})/2))",$t));break;case Le:J=e.parse(R(a.LOG+"(sinh({0}))",$t));break;case ut:J=P.integrate(e.parse(R("e^({0})",$t)),te,pe);break;case"S":var $t=D.args[0].clone(),Vt=P.integration.decompose_arg($t,te),zt=Vt[1],oe=Vt[0],St=Vt[3];J=e.parse(R("(cos((1/2)*pi*(({1})+({0})*({2}))^2)+pi*(({1})+({0})*({2}))*S(({1})+({0})*({2})))/(({0})*pi)",oe,St,Ke));break;case"C":var $t=D.args[0].clone(),Vt=P.integration.decompose_arg($t,te),zt=Vt[1],oe=Vt[0],St=Vt[3];J=e.parse(R("(pi*(({1})+({0})*({2}))*C(({1})+({0})*({2}))-sin((1/2)*pi*(({1})+({0})*({2}))^2))/(({0})*pi)",oe,St,zt));break;case"erf":var $t=D.args[0].clone(),Vt=P.integration.decompose_arg($t,te),zt=Vt[1],oe=Vt[0];J=e.parse(R("e^(-(({2}))^2)/(({0})*sqrt(pi))+(1/({0})+({1}))*erf(({2}))",oe,zt,$t));break;case"sign":J=e.multiply(D.clone(),$t.clone());break;default:P.integration.stop()}J=e.divide(J,xe)}else if(Ke.isLinear())if(i===c||i===d){var ae=Number(D.power);if(ae<0)D.fname=i===d?v:f,D.invert().updateHash(),J=P.integrate(D,te,pe);else{var $t=D.args[0],$=D.clone(),Ot=D.clone(),kt=new h((ae-1)/ae),xt=e.multiply(xe.clone(),new h(ae)).invert();$.power=$.power.subtract(new r(1)),Ot.power=Ot.power.subtract(new r(2));var Ee=e.symfunction(i===c?d:c,[$t.clone()]);i===d&&Ee.negate(),J=e.add(e.multiply(e.multiply(xt,$),Ee),e.multiply(kt,P.integrate(e.parse(Ot),te,pe)))}}else if(i===u||i===I){if(D.args[0].isLinear(te)){var G=D.power.subtract(new r(1)).toString(),At=D.clone().toUnitMultiplier(),Gt=e.parse(R((i===I?"-":"")+"1/({2}*{0})*{3}({1})^({0})",G,$t,xe,i));At.power=At.power.subtract(new r(2)),At.power.equals(0)&&(At=e.parse(At)),J=e.subtract(Gt,P.integrate(At,te,pe))}}else if(i===f||i===v){var Kt=D.power.subtract(new r(1)).toString(),Jt=D.power.subtract(new r(2)).toString(),Tt=i===f?u:I,At=D.clone().toUnitMultiplier(),cn=R((i===v?"-":"")+"1/({0}*{1})*{4}({3})^({2})*{5}({3})",xe,Kt,Jt,$t,i,Tt),Gt=e.parse(cn);At.power=At.power.subtract(new r(2)),At.power.equals(0)&&(At=e.parse(At)),J=e.add(Gt,e.multiply(new h(Jt/Kt),P.integrate(At,te,pe)))}else(i===it||i===je)&&D.power.equals(2)?J=P.integrate(D.fnTransform(),te,pe):P.integration.stop();else P.integration.stop();J.multiplier=J.multiplier.multiply(We)}}else if(re===Ie)J=P.integration.partial_fraction(D,te,pe);else if(re===ee){var nn=D.getDenom();nn.group===ve&&(D=e.expand(D));var un=D.stripVar(te),o=e.divide(D.clone(),un.clone());if(un.contains(te)&&(o=e.multiply(o,un),un=new h(1)),o.group!==ee){if(o.equals(1))return P.integrate(e.expand(D),te,pe);o.clone().toLinear().isPoly(!0)&&t.Utils.variables(o).length>1&&(o=t.Algebra.Factor.factor(o)),J=P.integrate(o,te,pe)}else{var y=o.collectSymbols().sort(function(Rn,Yn){return Rn.group===Yn.group?Number(Rn.power)===Number(Yn.power)?Rn<Yn?1:-1:Yn.power-Rn.power:Yn.group-Rn.group}).map(function(Rn){var Yn=h.unwrapSQRT(Rn,!0);return Yn.fname===ut?e.parse(R("({1})*e^({0})",Yn.args[0],Yn.multiplier)):Yn}),F=y.length;if(D.power<0){if(F===2)return P.integrate(e.expand(D),te,pe,ue)}else if(F===2){try{J=P.integration.u_substitution(y,te)}catch(Rn){}if(!J){var X=y[0].group,w=y[1].group,b=y[0],z=y[1],_e=b.fname,tt=z.fname;if(D=e.multiply(b.clone(),z.clone()),X===De&&w===De)if(_e===Oe||tt===Oe)J=P.integration.by_parts(D.clone(),te,pe,ue);else{y.sort(function(Yn,Hr){return Hr.fname>Yn.fname});var be=b.args[0];(!be.isLinear()||!(be.group===Qe||be.group===ee||be.group===ve))&&P.integration.stop();var He=P.integration.decompose_arg(be,te);Ke=He[1],xe=He[0],Ke.isLinear()||P.integration.stop();var $e=z.args[0];if(be.equals($e))if(_e===d&&tt===c||_e===c&&tt===d)if(b.power.lessThan(0)&&P.integration.stop(),_e===d&&b.power.add(z.power).equals(0))b.fname=u,b.updateHash(),J=P.integrate(b,te,pe);else if(ie(b.power)&&tt===c&&z.power.lessThan(0)){var G=Number(b.power)/2,pt=e.parse(R("(1-cos({0})^2)^({1})",b.args[0],G));J=P.integrate(e.expand(e.multiply(pt,z.clone())),te,pe,ue)}else if(ie(b.power)&&tt===d&&z.power.lessThan(0)){var G=Number(b.power)/2,pt=e.parse(R("(1-sin({0})^2)^({1})",b.args[0],G));J=P.integrate(e.expand(e.multiply(pt,z.clone())),te,pe,ue)}else{var vt=t.Utils.even(b.power),p=t.Utils.even(z.power);if(J=new h(0),!vt||!p){var x,At,Re;vt?(x=b,At=z):(x=z,At=b);var N=x.fname===c?-1:1,G=At.power,we=(G-1)/2,Re=e.parse("(1-"+x.fname+t.Utils.inBrackets(be)+"^2)^"+we),W=e.expand(e.multiply(new h(N),e.multiply(x.clone(),Re)));W.each(function(jr){J=e.add(J,P.integration.poly_integrate(jr.clone()))})}else{var rt=function(jr){var Kn=jr.power,S1=Kn/2,G2;return jr.fname===c?G2="((1/2)+(cos(2*("+jr.args[0]+"))/2))^"+S1:G2="((1/2)-(cos(2*("+jr.args[0]+"))/2))^"+S1,e.parse(G2)},xe=rt(b),ge=rt(z),Ee=e.multiply(xe,ge),W=e.expand(Ee);return W.each(function(jr){J=e.add(J,P.integrate(jr,te,pe))}),e.multiply(J,un)}}else if(_e===f&&tt===u&&Ke.isLinear()&&z.isLinear())J=e.parse(R("sec({0})^({1})/({1})",b.args[0],b.power));else if(_e===u&&tt===f&&Ke.isLinear())if(b.isLinear()&&z.isLinear())J=e.divide(e.symfunction(f,[be.clone()]),xe);else if(ie(b.power)){var ae=Number(b.power)/2,Ee=e.parse(R("(sec({0})^2-1)^({1})",b.args[0],ae));J=P.integrate(e.expand(e.multiply(Ee,z)),te,pe)}else P.integration.stop();else if(_e===f&&tt===c)b.fname=c,b.invert().updateHash(),J=P.integrate(e.multiply(b,z),te,pe);else if(_e===d&&tt===v)z.fname=d,z.invert().updateHash(),J=P.integrate(e.multiply(b,z),te,pe);else if(_e===u&&(tt===c||tt===d)&&z.power.lessThan(0)){var Ee=e.multiply(b.fnTransform(),z);J=P.integrate(e.expand(Ee),te,pe)}else{var Ee=e.multiply(b.fnTransform(),z.fnTransform());J=P.integrate(e.expand(Ee),te,pe)}else if((_e===d||_e===c)&&(tt===d||tt===c))if(b.isLinear()&&z.isLinear())if(b.args[0].isLinear()&&z.args[0].isLinear()){var Je,mt;tt===d?(Je=b.args[0],mt=z.args[0]):(mt=b.args[0],Je=z.args[0]),Be=e.parse(R("(sin(({1})+({0}))+sin(({1})-({0})))/2",Je.toString(),mt.toString())),J=P.integrate(Be,te,pe)}else{var It=H(y);J=P.integrate(e.expand(It),te,pe)}else{var It=new h(1);y.map(function(F0){var Xi=F0.fnTransform();It=e.multiply(It,Xi)});var Ee=e.expand(It);J=P.integrate(Ee,te,pe),J.hasIntegral()&&(J=P.integrate(H(It.collectSymbols()),te,pe))}else P.integration.stop()}else if(X===De&&w===ve){var Bt=b.isLinear();if(b.fname===c&&Bt&&z.power.equals(-1))J=e.symfunction("Ci",[b.args[0]]);else if(b.fname===c&&z.power.equals(-1))J=P.integrate(e.multiply(b.fnTransform(),z.clone()),te,pe);else if(b.fname===it&&Bt&&z.power.equals(-1))J=e.symfunction("Chi",[b.args[0]]);else if(b.fname===it&&z.power.equals(-1))J=P.integrate(e.multiply(b.fnTransform(),z.clone()),te,pe);else if(b.fname===d&&Bt&&z.power.equals(-1))J=e.symfunction("Si",[b.args[0]]);else if(b.fname===d&&z.power.equals(-1))J=P.integrate(e.multiply(b.fnTransform(),z.clone()),te,pe);else if(b.fname===je&&Bt&&z.power.equals(-1))J=e.symfunction("Shi",[b.args[0]]);else if(b.fname===je&&z.power.equals(-1))J=P.integrate(e.multiply(b.fnTransform(),z.clone()),te,pe);else if(b.fname===Oe&&z.power.equals(-1))J=P.integration.poly_integrate(b,te,pe);else if(b.fname==="erf"){if(z.power.equals(1)){var Vt=P.integration.decompose_arg(b.args[0],te),oe=Vt[0],zt=Vt[1],$t=b.args[0].toString();J=e.parse(R("(e^(-(({2}))^2)*(sqrt(pi)*e^((({2}))^2)*(2*({0})^2*({1})^2-3)*erf(({2}))+2*({0})*({1})-2))/(4*sqrt(pi)*({0})^2)",oe,zt,$t))}}else J=P.integration.by_parts(D,te,pe,ue)}else if(X===Te&&w===ve){var Ke=_e===Oe?P.integration.decompose_arg(b.args[0],te)[1]:null;b.isE()&&(b.power.group===ve||b.power.group===ee)&&z.power.equals(-1)?J=e.symfunction("Ei",[b.power.clone()]):_e===Oe&&Ke.value===z.value?J=P.integration.poly_integrate(b,te,pe):J=P.integration.by_parts(D,te,pe,ue)}else if(X===Ie&&w===ve){if(z.value===b.value&&b.power.equals(-1)){var Rt=Math.min.apply(null,t.Utils.keys(b.symbols)),jt=Math.min(Rt,z.power),Ut=z.clone();Ut.power=new r(jt),z=e.divide(z,Ut.clone());var Ee=new h(0);b.each(function(Yn){Ee=e.add(Ee,e.divide(Yn.clone(),Ut.clone()))}),Ee.multiplier=b.multiplier,D=e.divide(z,Ee)}else D=e.expand(D);J=P.integration.partial_fraction(D,te,pe)}else if(X===Qe&&w===ve){var Be=b.clone().toLinear(),en=t.Algebra.degree(Be,e.parse(te)).equals(1);if(b.power.equals(-1/2)){var He=P.integration.decompose_arg(b.clone().toLinear(),te),xe=He[0].negate(),Ke=He[1],ge=He[3],Wt=Number(b.power),Qt=Number(z.power);if(_(Qt)&&t.Utils.even(Qt)&&Ke.power.equals(2)){var sn=e.divide(e.multiply(e.pow(ge.clone(),new h(2)),e.symfunction(j,[e.divide(ge.clone(),xe.clone())])),e.pow(xe.clone(),new h(2)));sn=e.multiply(sn,e.symfunction(j,[ge]).invert());var ln=e.parse("sin(u)");ln.power=ln.power.multiply(z.power);var Y=P.integrate(ln,"u",pe),dn=e.parse(q+"("+j+"("+xe+"/"+ge+")*"+te+")");J=e.multiply(sn,Y.sub(new h("u"),dn))}else if(Wt===-1/2){var En=function(jr,Kn){var S1=e.parse(P.integrate(jr,te,pe,ue).sub(te,R(Kn,te)));if(!S1.hasIntegral())return S1};Qt===-1?J=En(e.expand(e.expand(e.pow(e.multiply(b.invert(),z.invert()),new h(2)))).invert(),"sqrt(1-1/({0})^2)"):Qt===-2&&(J=En(e.sqrt(e.expand(e.divide(e.pow(D,new h(2)).invert(),e.pow(new h(te),new h(2))).negate())).invert(),"sqrt(1-1/({0})^2)"))}}else if(b.power.equals(-1)&&z.isLinear()&&en)J=P.integration.partial_fraction(D,te,pe);else if(!b.power.lessThan(0)&&_(b.power)){var vn=e.expand(b);J=new h(0),vn.each(function(Yn){Yn.group===Ie?Yn.each(function(Hr){J=e.add(J,P.integrate(e.multiply(z.clone(),Hr),te,pe))}):J=e.add(J,P.integrate(e.multiply(z.clone(),Yn),te,pe))})}else if(b.power.lessThan(-2))J=P.integration.by_parts(D,te,pe,ue);else if(b.power.lessThan(0)&&z.power.greaterThan(1)){var He=P.integration.decompose_arg(b.clone().toLinear(),te),xe=He[0].negate(),Ke=He[1],ge=He[3],Ge=b.clone().toLinear();if(Ke.group!==Ie&&Ke.isLinear()){var ae=Number(z.power),S="_u_",x=new h(S),Dt=e.expand(e.divide(e.pow(e.subtract(x.clone(),ge.clone()),new h(ae)),x.clone())),tn={};tn[S]=Ge;var hn=e.parse(Dt,tn);J=P.integrate(hn,te,0)}else if(z.power.greaterThan(Ke.power)||z.power.equals(Ke.power)){var pn=new t.Algebra.Classes.Factors;b=t.Algebra.Factor.coeffFactor(b.invert(),pn);var Nn=t.Algebra.divide(z,b);Nn.group!==ee?(J=new h(0),Nn.each(function(Kn){J=e.add(J,P.integrate(Kn,te,pe))}),pn.each(function(Kn){J=e.divide(J,Kn)}),J=e.expand(J)):J=P.integration.by_parts(D,te,pe,ue)}else J=P.integration.partial_fraction(D,te,pe)}else if(b.power.den.equals(2)){var Vt=P.integration.decompose_arg(b.clone().toLinear(),te),xe=Vt[3],Ke=Vt[1],ge=Vt[0],mt=Vt[2];if(Ke.power.equals(2)&&ge.lessThan(0)){xe.equals(1)||(un=e.multiply(un,e.pow(xe,new h(2))));var x=te,sn=e.divide(e.pow(ge.clone().negate(),new h(1/2)),e.pow(xe,new h(1/2))),S=e.symfunction(c,[new h(x)]),wn=e.pow(e.symfunction(c,[new h(x)]),new h(b.power.num)),Mn=e.pow(e.symfunction(d,[new h(x)]),new h(z.power)),xn=e.multiply(e.multiply(wn,S),Mn),Y=P.integrate(xn,x,pe);J=Y.sub(x,e.symfunction(q,[e.multiply(new h(te),sn)]))}else J=P.integration.partial_fraction(D,te,pe,ue)}else en&&(J=P.integration.partial_fraction(D,te,pe))}else if(b.isComposite()&&z.isComposite())if(J=new 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p.substring(wn,Mn-1)}(rt)),rt=(It=It+tn.length-2)-1;jt.push.apply(jt,function(wn){for(var Mn=rt-wn.length,xn=[],$n=wn.charAt(0),An=1,Jn=wn.length;An<Jn;An++)var ei=wn.charAt(An),Xr=$n+ei,$n=Xr in zt?Xr:(xn.push(new Fe($n,Fe.OPERATOR,Mn+An)),ei);return xn.push(new Fe($n,Fe.OPERATOR,Mn+An)),xn}(tn))}else if(Dt in oe){var hn,tn=oe[Dt];if(tn.is_open)en.push([tn,It]),(hn=p.substring(It,rt))in $?dn(hn):hn!==""&&jt.push(new Fe(hn,Fe.VARIABLE_OR_LITERAL,It)),Qt(tn.maps_to,rt);else if(tn.is_close){var pn=en.pop();if(!pn)throw new wt("Missing open bracket for bracket at: "+(rt+1));if(pn[0].id!==tn.id-1)throw new wt("Parity error");ln(rt),sn()}En(rt)}else Dt===" "&&(pn=p.substring(It,rt),Dt=p.charAt(rt+1),Wt?(pn in zt?jt.push(new Fe(pn,Fe.OPERATOR,rt)):(ln(void 0,pn),sn(),((vn=Dt in zt)&&zt[Dt].value==="-"||!vn)&&jt.push(new Fe("*",Fe.OPERATOR,rt))),Wt=!1):(hn=p.substring(It,rt))in $?(Wt=!0,dn(hn),Qt()):hn in zt?jt.push(new Fe(hn,Fe.OPERATOR,rt)):(ln(void 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It=p[rt];if(It=Array.isArray(It)?this.parseRPN(It,N):It)if(It.type===Fe.OPERATOR)if(It.is_prefix||It.postfix)Re.push(It.operation(Re.pop()));else{var Bt=Re.pop(),Rt=Re.pop();if(Rt===void 0)throw new Mt(It+" is not a valid postfix operator at "+It.column);var jt=It.action==="comma",Ut=(Rt instanceof ce&&!jt&&(Rt=G.fromSet(Rt)),Bt instanceof ce&&!jt&&(Bt=G.fromSet(Bt)),this.callPeekers("pre_operator",Rt,Bt,It),i[It.action](Rt,Bt));this.callPeekers("post_operator",Ut,Rt,Bt,It),Re.push(Ut)}else if(It.type===Fe.FUNCTION){var en=Re.pop(),Wt=en.parent,Qt=(en instanceof ke||(en=ke.create(en)),It.value),sn=en.getItems(),ln=(this.callPeekers("pre_function",Qt,sn),i.callfunction(Qt,sn)),dn=(this.callPeekers("post_function",ln,Qt,sn),Re[Re.length-1]),En=p[rt+1];if(!(En&&En.type===Fe.OPERATOR&&En.value===",")&&ln instanceof G&&dn&&dn.elements&&!(dn instanceof ke)){var vn=Re.pop(),Dt=ln.elements[0];if(Dt.isConstant())if(Dt instanceof W)Re.push(G.fromArray(vn.elements.slice(Dt.start,Dt.end)));else{var tn=Number(Dt),hn=vn.elements.length;if((tn=tn<0?hn+tn:tn)<0||hn<=tn)throw new qt("Index out of range "+(It.column+1));var pn=vn.elements[tn];vn.getter=tn,pn.parent=vn,Re.push(pn)}else vn.getter=Dt,Re.push(vn),Re.push(ln)}else Wt&&(ln.parent=Wt),Re.push(ln)}else{var Nn,wn=It.value;wn in M.ALIASES?It=i.parse(M.ALIASES[It]):It.type===Fe.VARIABLE_OR_LITERAL?It=new s(wn):It.type===Fe.UNIT&&((It=new s(wn)).isUnit=!0),wn in i.CONSTANTS?(Nn=It,It=new s(i.CONSTANTS[wn])):wn in N&&wn!==N[wn].toString()?(Nn=It,It=N[wn].clone()):wn in yt&&(Nn=It,It=yt[wn].clone()),Nn&&(It.subbed=Nn),Re.push(It)}}var Mn=Re[0];if(["undefined","string","number"].indexOf(typeof Mn)!==-1)throw new Pt("Unexpected token!");return Mn}catch(xn){throw[Be].forEach(function(An){if(xn instanceof An)throw new An(xn.message+": "+It.column)}),new Se(xn.message+": "+It.column)}},Ot.prototype.toString=function(){var p=this.left?this.left.toString()+"---":"",N=this.right?"---"+this.right.toString():"";return p+"("+this.value+")"+N},Ot.prototype.toHTML=function(p,N){p=p||0,N=N===void 0?4:N;function we(It){return" ".repeat(N*It)}var mt="",Re=this.left?we(p+1)+`<li>
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`:"",rt=this.right?we(p+1)+`<li>
`+this.right.toHTML(p+2,N)+we(p+1)+`</li>
`:"",mt=we(p)+'<div class="'+this.type.toLowerCase()+'"><span>'+this.value+"</span></div>"+we(p)+`
`;return(Re||rt)&&(mt+=we(p)+`<ul>
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mt+(jt=(Rt=rt.charAt(Bt).match(/[\+\-\/\*]/)?Rt:rt.charAt(Bt-1)).match(/[a-z]/i)?"":jt)+It}).replace(/([a-z0-9_]+)/gi,function(rt,mt){return!(M.USE_MULTICHARACTER_VARS!==!1||mt in $)&&isNaN(mt)?mt.split("").join("*"):mt}).replace(/\)\(/g,")*(")||"0";we!==(we=we.replace(/([a-z0-9_]+)(\()|(\))([a-z0-9]+)/gi,function(rt,mt,It,Bt,Rt){return mt=mt||Bt,Bt=It||Rt,mt in $?mt+Bt:mt+"*"+Bt})););return we}(p),N=N||{},p=this.tokenize(p),p=this.toRPN(p),this.parseRPN(p,N)},this.toObject=function(p){var N=function(we){for(var Re=[],rt=0,mt=we.length;rt<mt;rt++){var It,Bt=we[rt],Rt=Bt.value;Bt.type===Fe.VARIABLE_OR_LITERAL?Re.push(new s(Rt)):Bt.type===Fe.FUNCTION?(rt++,(It=i.symfunction(Rt,N(we[rt]))).isConversion=!0,Re.push(It)):Bt.type===Fe.OPERATOR?Re.push(Rt):Re.push(N(Bt))}return Re};return N(i.tokenize(p))};function kt(p){for(var N=0,we=[[]],Re=0,rt=p.length;Re<rt;Re++)p[Re]===","?we[++N]=[]:we[N].push(p[Re]);return we}function xt(p){return p.replace(/^\\left\((.+)\\right\)$/g,function(N,we){return we||N})}function At(p){if(p.isInfinity)return s.infinity();if(p.multiplier.lessThan(0)&&p.multiplier.negate(),p.isImaginary()){var Re=p.realpart(),N=p.imagpart();if(Re.isConstant()&&N.isConstant())return cn(i.add(i.pow(Re,new s(2)),i.pow(N,new s(2))))}else if(fe(p)||Ce(p.power))return p;p.isComposite()&&(we=[],p.each(function(rt){we.push(rt.multiplier)}),nt.QGCD.apply(null,we).lessThan(0)&&(p.multiplier=p.multiplier.multiply(new T(-1)),p.distributeMultiplier()));var we,Re=i.parse(p.multiplier);return p.toUnitMultiplier(),i.multiply(Re,i.symfunction(ye,[p]))}function Gt(p){var N,we,Re,rt,mt;return H(p)?(N=new G,p.each(function(It,Bt){N.set(Bt-1,Gt(It))}),N):P(p)?(we=new Y,p.each(function(It,Bt,Rt){we.set(Bt,Rt,Gt(It))}),we):M.PARSE2NUMBER&&p.isConstant()?be(ue(p)?nt.bigfactorial(p):nt.gamma(p.multiplier.add(new T(1)).toDecimal())):p.isConstant()&&p.getDenom().equals(2)?(rt=p.getNum(),rt=p.multiplier.isNegative()?(mt=i.subtract(rt.negate(),new s(1)).multiplier.divide(new T(2)),Re=i.pow(new s(-4),new s(mt)).multiplier.multiply(nt.bigfactorial(mt)),nt.bigfactorial(new T(2).multiply(mt))):(mt=i.add(rt,new s(1)).multiplier.divide(new T(2)),Re=nt.bigfactorial(new T(2).multiply(mt)),i.pow(new s(4),new s(mt)).multiplier.multiply(nt.bigfactorial(mt))),mt=Re.divide(rt),i.multiply(i.parse("sqrt(pi)"),new s(mt))):i.symfunction(Ae,[p])}function Kt(p,N){var we;return p.isConstant()&&N.isConstant()?((we=new s(1)).multiplier=we.multiplier.multiply(p.multiplier.mod(N.multiplier)),we):(we=i.divide(p.clone(),N.clone()),ue(we)?new s(0):i.symfunction("mod",[p,N]))}function Jt(p){var N,we,Re,rt,mt;return p.isComposite()?(N=new s(0),p.each(function(It){mt=It.getNum(),we=It.getDenom(),rt=N.getNum(),Re=N.getDenom(),rt=i.multiply(we,rt),mt=i.multiply(mt,Re),rt=i.expand(i.add(rt,mt)),mt=i.multiply(Re,we),N=i.divide(rt,mt)},!0),N):p}function cn(p){if((p=et(p)?p:i.parse(p)).group===u)return i.symfunction(le,[p]);var N=(p=p.fname===""&&p.power.equals(1)?p.args[0]:p).multiplier.sign()<0;if(M.PARSE2NUMBER){if(p.isConstant()&&!N)return new s(a.sqrt(p.multiplier.toDecimal()));if(p.isImaginary())return ft.sqrt(p);if(p.group===c)return i.symfunction("sqrt",[p])}var we,Re=p.isConstant();if(p.group===I&&p.isLinear()){var rt=cn(s(p.multiplier));for(It in p.symbols){var mt=p.symbols[It];rt=i.multiply(rt,cn(mt))}jt=rt}else if(p.fname===le){var It=p.args[0],Bt=p.multiplier;It.setPower(p.power.multiply(new T(.25))),jt=It,Bt.equals(1)||(jt=i.multiply(cn(i.parse(Bt)),jt))}else if(p.power.isInteger())if(p.multiplier<0&&p.group===c)var Bt=i.parse(p.multiplier).negate(),Rt=i.parse(p).toUnitMultiplier().negate(),jt=i.multiply(i.symfunction(M.SQRT,[Rt]),cn(Bt));else{var Rt=p.power.sign(),Ut=(p.power=p.power.abs(),Re&&p.multiplier.lessThan(0)&&(we=s.imaginary(),p.multiplier=p.multiplier.abs()),p.multiplier.toDecimal()),Bt=Math.abs(Ut),Re=Math.sqrt(Bt);if(ue(Re))rt=new s(Re);else if(ue(Ut)){var en=nt.ifactor(Ut),Wt=1;for(mt in en){var Qt,sn=(ln=en[mt])-ln%2;sn&&(Qt=Math.pow(mt,sn),Wt*=Math.pow(mt,sn/2),Ut/=Qt)}rt=i.multiply(i.symfunction(le,[new s(Ut)]),new s(Wt))}else{for(var ln,dn=[new s(p.multiplier.num),new s(p.multiplier.den)],En=[new s(1),new s(1)],vn=[new s(1),new s(1)],Dt=0;Dt<2;Dt++)o(ln=dn[Dt]).each(function(Mn){var wn=(Mn=s.unwrapPARENS(Mn)).clone().toLinear(),Mn=Number(Mn.power),xn=Mn%2;En[Dt]=i.multiply(En[Dt],i.pow(wn,new s((Mn-xn)/2))),vn[Dt]=i.multiply(vn[Dt],cn(i.pow(wn,new s(xn))))});rt=i.divide(i.multiply(En[0],vn[0]),i.multiply(En[1],vn[1]))}jt=(p=p.toUnitMultiplier(!0)).isOne()?p:Ce(p.power.toString())?i.pow(p.clone(),new s(.5)):i.symfunction(le,[p]),Rt<0&&jt.power.negate(),rt&&(jt=i.multiply(rt,jt)),we&&(jt=i.multiply(we,jt))}else p.setPower(p.power.multiply(new T(.5))),jt=p;return N&&M.PARSE2NUMBER?i.parse(jt):jt}function nn(p){var N,we,Re;return p.isConstant(!0)?un(p,new s(3)):(we=p.power/3,Re=i.pow(i.parse(p.multiplier),new s(.3333333333333333)),p=p.toUnitMultiplier(),ue(we)?N=i.pow(p.toLinear(),i.parse(we)):p.group===I?(N=new s(1),p.each(function(rt){N=i.multiply(N,nn(rt))})):N=i.symfunction("cbrt",[p]),i.multiply(Re,N))}function un(p,N,we,Re){if((N=He(i.parse(N))).equals(0))throw new qe("Unable to calculate nthroots of zero");if(p<0&&Ce(N))throw new Error("Cannot calculate nthroot of negative number for even powers");if(!p.isConstant(!0))return i.symfunction("nthroot",arguments);Re===void 0&&(Re=!0),we=we||25;var rt,mt=(p=p.group!==j?He(p):p).sign();return mt<0&&(p=At(p)),ue(p)&&N.isConstant()?(p=p<18446744073709552e3?T.create(Math.pow(p,1/N)):nt.nthroot(p,N),Re&&(rt=new s(p)),rt=new s(p.toDecimal(we)),i.multiply(new s(mt),rt)):void 0}function o(p){if(p.greaterThan(9999999999998891e26)||p.equals(-1))return p;if(p.equals(Math.PI))return new s(Math.PI);if((p=He(p.clone())).isConstant()){var N=new s(1),we=p.toString();if(ue(we)){var Re,rt=nt.ifactor(we);for(Re in rt)var mt=rt[Re],N=i.multiply(N,i.symfunction("parens",[new s(Re).setPower(new T(mt))]))}else we=o(new s(p.multiplier.num)),p=o(new s(p.multiplier.den)),N=i.multiply(i.symfunction("parens",[we]),i.symfunction("parens",[p]).invert())}else N=i.symfunction("pfactor",arguments);return N}function y(p){return p.realpart()}function F(p){return p.imagpart()}function X(we){var N=we.realpart(),we=we.imagpart();return i.add(N,i.multiply(we.negate(),s.imaginary()))}function w(we){var N=we.realpart(),we=we.imagpart();return N.isConstant()&&we.isConstant()?we.equals(0)&&N.equals(-1)?i.parse("pi"):we.equals(1)&&N.equals(0)?i.parse("pi/2"):we.equals(1)&&N.equals(1)?i.parse("pi/4"):new s(Math.atan2(we,N)):i.symfunction("atan2",[we,N])}function b(p,N){var we,Re;for(N.map(function(rt){rt.numVal=He(rt).multiplier});;){if((Re=N.length)<2)return N[0];we=N.pop(),Re=N[Re-2],(p==="min"?we.numVal<Re.numVal:we.numVal>Re.numVal)&&(N.pop(),N.push(we))}}function z(p,N){if(p.equals(1))return new s(0);var we,Re,rt;if(p.fname===le&&p.multiplier.equals(1))we=i.divide(z(p.args[0]),new s(2)),p.power.sign()<0&&we.negate();else{if(p.equals(0))throw new qe(M.LOG+"(0) is undefined!");if(p.isImaginary())return ft.evaluate(p,M.LOG);p.isConstant()&&N!==void 0&&N.isConstant()?we=new s(Math.log(p)/Math.log(N)):p.group===u&&p.power.multiplier.lessThan(0)||p.power.toString()==="-1"?(p.power.negate(),we=z(p).negate()):p.value==="e"&&p.multiplier.equals(1)?(N=p.power,we=et(N)?N:new 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v<0&&!d||(c[0]=(-f+Math.sqrt(v))/(2*u),c[1]=(-f-Math.sqrt(v))/(2*u)),c},squareFree:function(){for(var d=this.clone(),c=1,u=d.clone().diff(),f=d.clone().gcd(u),v=d.divide(f)[0],I=Oe.fromArray([new Ie(1)],d.variable);!f.equalsNumber(1);){var q=v.gcd(f),V=v.divide(q)[0];if(!V.equalsNumber(1)&&1<c){for(var Q=V.clone(),le=1;le<c;le++)Q.multiply(V.clone());V=Q}I=I.multiply(V),c++,f=f.divide(v=q)[0]}return[I,v,c]},toSymbol:function(){var d=this.coeffs.length,c=this.variable;if(d===0)return new t.Symbol(0);for(var u=d-1,f="",v=0;v<d;v++){var I=v===u?"":"+",q=this.coeffs[v];q.equals(0)||(f+=q+"*"+c+"^"+v+I)}return e.parse(f)},equalsNumber:function(d){return this.trim(),this.coeffs.length===1&&this.coeffs[0].toDecimal()===String(d)},toString:function(){return this.toSymbol().toString()}},ee.prototype.coeffs=function(d,c){c&&!this.isPoly(!0)&&e.error("Polynomial expected when requesting coefficients with order"),d=d||[];var u,f=this.clone().distributeMultiplier();if(f.isComposite())for(var v in f.symbols)v=f.symbols[v],v.isComposite()?v.clone().distributeMultiplier().coeffs(d,c):c?d[v.isConstant()?0:v.power.toDecimal()]=v.multiplier:d.push(v.multiplier);else c?d[f.isConstant(!0)?0:f.power.toDecimal()]=f.multiplier:f.group===R&&f.isImaginary()?(u=new ee(f.multiplier),f.each(function(q){(q.isConstant(!0)||q.imaginary)&&(u=e.multiply(u,q))}),d.push(u)):d.push(f.multiplier);if(c)for(var I=0;I<d.length;I++)d[I]===void 0&&(d[I]=new ee(0));return d},ee.prototype.tBase=function(d){if(d===void 0)throw new Error("Symbol.tBase requires a map object!");for(var c=[],u=this.collectSymbols(null,null,null,!0),f=u.length,v=0;v<f;v++){var I=u[v],q=I.group,V=new at(I.multiplier,[],d);if(q===R)for(var Q in I.symbols){var le=I.symbols[Q];V.terms[d[Q]]=le.power}else V.terms[d[I.value]]=I.power;c.push(V.fill()),V.updateCount()}return c},ee.prototype.altVar=function(d){var c=this.multiplier.toString(),u=this.power.toString();return(c==="1"?"":c+"*")+d+(u==="1"?"":"^"+u)},ee.prototype.sameVars=function(d){if(!this.symbols&&this.group!==d.group)return!1;for(var c in this.symbols){var u=this.symbols[c],c=d.symbols[c];if(!c||u.value!==c.value)return!1}return!0},ee.prototype.groupTerms=function(d){d=String(d);var c,u,f,v=[];return this.each(function(I){if(I.group===M){f=I.groupTerms(d);for(var q=0;q<f.length;q++){var V=f[q];V&&(v[q]=V)}}else c=t.Utils.decompose_fn(I,d,!0),u=c.x.value===d?Number(c.x.power):0,v[u]=e.add(v[u]||new ee(0),c.a)}),v},ee.prototype.collectFactors=function(){var d=[];return this.group===R?this.each(function(c){d.push(c.clone())}):d.push(this.clone()),d},ut.prototype.getNumberSymbolics=function(){var d=0;return this.each(function(c){c.isConstant(!0)||d++}),d},ut.prototype.add=function(d){if(!d.equals(0))if(d.equals(-1)&&0<this.length)u=t.Utils.firstObject(this.factors,null,!0),this.add(e.symfunction(t.Settings.PARENTHESIS,[u.obj]).negate()),delete this.factors[u.key],this.length--;else if(d.group===R){var c=this;d.multiplier.equals(1)||c.add(new ee(d.multiplier)),d.each(function(f){c.add(f)})}else{this.preAdd&&(d=this.preAdd(d));var u=(d=this.pFactor?e.pow(d,new ee(this.pFactor)):d).isConstant();if(u&&d.equals(1))return this;u=u?d.value:d.text(),u in this.factors?(this.factors[u]=e.multiply(this.factors[u],d),this.factors[u].equals(1)&&(delete this.factors[u],this.length--)):(this.factors[u]=d,this.length++)}return this},ut.prototype.toSymbol=function(){for(var v=new ee(1),d=Object.values(this.factors).sort(function(I,q){return I.group>q.group}),c=0,u=d.length;c<u;c++)var f=d[c],f=f.power.equals(1)&&f.fname!==""?e.symfunction(t.PARENTHESIS,[f]):f,v=e.multiply(v,f);return v=v.fname===""?ee.unwrapPARENS(v):v},ut.prototype.merge=function(d){for(var c in d)c in this.factors?this.factors[c]=e.multiply(this.factors[c],d[c]):this.factors[c]=d[c];return this},ut.prototype.each=function(d){for(var c in this.factors){var u=this.factors[c];u.fname===t.PARENTHESIS&&u.isLinear()&&(u=u.args[0]),d.call(this,u,c)}return this},ut.prototype.count=function(){return ie(this.factors).length},ut.prototype.clean=function(){try{var d=t.Settings.CONST_HASH;this.factors[d].lessThan(0)&&(this.factors[d].equals(-1)?delete this.factors[d]:this.factors[d].negate(),this.each(function(c){c.negate()}))}catch(c){}},ut.prototype.toString=function(){return this.toSymbol().toString()},at.prototype.updateCount=function(){this.count=this.count||0;for(var d=0;d<this.terms.length;d++)this.terms[d].equals(0)||this.count++;return this},at.prototype.getVars=function(){for(var d=[],c=0;c<this.terms.length;c++){var u=this.terms[c];this.getRevMap(),u.equals(0)||d.push(this.rev_map[c])}return d.join(" ")},at.prototype.len=function(){return this.count===void 0&&this.updateCount(),this.count},at.prototype.toSymbol=function(d){d=d||this.getRevMap();for(var c=new ee(this.coeff),u=0;u<this.terms.length;u++){var f=d[u],v=this.terms[u];v.equals(0)||f===Te||((f=new ee(f)).power=v,c=e.multiply(c,f))}return c},at.prototype.getRevMap=function(){if(this.rev_map)return this.rev_map;var d,c={};for(d in this.map)c[this.map[d]]=d;return this.rev_map=c},at.prototype.generateImage=function(){return this.image=this.terms.join(" "),this},at.prototype.getImg=function(){return this.image||this.generateImage(),this.image},at.prototype.fill=function(){for(var d=this.map.length,c=0;c<d;c++)this.terms[c]===void 0?this.terms[c]=new t.Frac(0):this.sum=this.sum.add(this.terms[c]);return this},at.prototype.divide=function(d){for(var c=this.coeff.divide(d.coeff),u=this.terms.length,f=new at(c,[],this.map),v=0;v<u;v++)f.terms[v]=this.terms[v].subtract(d.terms[v]),f.sum=f.sum.add(f.terms[v]);return f},at.prototype.multiply=function(d){for(var c=this.coeff.multiply(d.coeff),u=this.terms.length,f=new at(c,[],this.map),v=0;v<u;v++)f.terms[v]=this.terms[v].add(d.terms[v]),f.sum=f.sum.add(f.terms[v]);return f},at.prototype.isZero=function(){return this.coeff.equals(0)},at.prototype.toString=function(){return"{ coeff: "+this.coeff.toString()+", terms: ["+this.terms.join(",")+"]: sum: "+this.sum.toString()+", count: "+this.count+"}"},t.Utils.toMapObj=function(d){for(var c=0,u={},f=0;f<d.length;f++){var v=d[f];u[v]===void 0&&(u[v]=c,c++)}return u.length=c,u},t.Utils.filledArray=function(d,c,u){for(var f=[];c--;)f[c]=u?new u(d):d;return f},t.Utils.arrSum=function(d){for(var c=0,u=d.length,f=0;f<u;f++)c+=d[f];return c},t.Utils.haveIntersection=function(d,c){var u;return c.length>d.length&&(u=c,c=d,d=u),d.some(function(f){return-1<c.indexOf(f)})},t.Utils.subFunctions=function(d,c){c=c||{};var u=[];return d.each(function(f){var v,I;f.group===L||f.previousGroup===L?(v=t.Utils.text(f,"hash"),(I=c[v])||(I=f.fname+ie(c).length,c[v]=I),u.push(f.altVar(I))):f.group===R||f.group===M||f.group===_?u.push(t.Utils.subFunctions(f,c)):u.push(f.text())}),d.group===_||d.group===M?d.altVar(t.Utils.inBrackets(u.join("+"))):d.group===R?d.altVar(t.Utils.inBrackets(u.join("*"))):d.text()},t.Utils.getFunctionsSubs=function(d){var c,u={};for(c in d)u[d[c]]=e.parse(c);return u};var j=t.Algebra={version:"1.4.6",proots:function(d,c){c=c||7;function u(Ve,lt,Nt){for(var Ct=function(P,et){var Lt=P.slice(0);if(P.unshift(et),100<et)throw new t.exceptions.ValueLimitExceededError("This utility accepts polynomials of degree up to 100. ");var H=[],P={};for(P.Degree=et,ye=0;ye<et;ye++)H.push(0);var B=H.slice(0);function fe(xe,Ce,Ke,Ne,We,ae){We[0]=ae.b=Ne[0],We[1]=ae.a=-(Ce*ae.b)+Ne[1];for(var Ge=2;Ge<xe;Ge++)We[Ge]=-(Ce*ae.a+Ke*ae.b)+Ne[Ge],ae.b=ae.a,ae.a=We[Ge]}function pe(xe,Ce,Ke,Ne,We,ae,Ge,He,ge){var Je=new Object,gt=3;return Je.b=Je.a=0,fe(Ce,Ge,He,ae,ge,Je),We.c=Je.a,We.d=Je.b,Math.abs(We.c)<=100*xe*Math.abs(ae[Ce-1])&&Math.abs(We.d)<=100*xe*Math.abs(ae[Ce-2])||(We.h=He*Ne,Math.abs(We.d)>=Math.abs(We.c)?(gt=2,We.e=Ke/We.d,We.f=We.c/We.d,We.g=Ge*Ne,We.a3=We.e*(We.g+Ke)+We.h*(Ne/We.d),We.a1=-Ke+We.f*Ne,We.a7=We.h+(We.f+Ge)*Ke):(gt=1,We.e=Ke/We.c,We.f=We.d/We.c,We.g=We.e*Ge,We.a3=We.e*Ke+(We.g+We.h/We.c)*Ne,We.a1=-(Ke*(We.d/We.c))+Ne,We.a7=We.g*We.d+We.h*We.f+Ke)),gt}function ue(xe,Ce,Ke,Ne,We,ae,Ge,He,ge){if(Ke==3){Ge[1]=Ge[0]=0;for(var Je=2;Je<Ce;Je++)Ge[Je]=He[Je-2]}else if(Ke=Ke==1?We:Ne,Math.abs(ae.a1)>10*xe*Math.abs(Ke))for(ae.a7/=ae.a1,ae.a3/=ae.a1,Ge[0]=ge[0],Ge[1]=-(ge[0]*ae.a7)+ge[1],Je=2;Je<Ce;Je++)Ge[Je]=-(ge[Je-1]*ae.a7)+He[Je-2]*ae.a3+ge[Je];else for(Ge[0]=0,Ge[1]=-(ge[0]*ae.a7),Je=2;Je<Ce;Je++)Ge[Je]=-(ge[Je-1]*ae.a7)+He[Je-2]*ae.a3}function st(xe,Ce,Ke,Ne,We,ae,Ge,He,ge,Je,gt,ne,Se,qe,Be,ct,wt){var Mt;Ce.b=Ce.a=0,xe!=3&&(xe=xe!=2?(Mt=Ke+Se*Ge+ne*Je,He+(Se+qe*Je)*ge):(Mt=(Ke+gt)*Je+ne,(Je+Se)*He+qe*ge),Ge=-(Be[ct-1]/wt[ct]),(He=-(Je=qe*(Ke=-(Be[ct-2]+Ge*wt[ct-1])/wt[ct])*Ne-((gt=Ge*ae)+(ne=Ge*Ge*We)))+xe+Ge*Mt)!=0&&(Ce.a=-(Se*(ne+gt)+qe*(Ge*Ne+Ke*ae))/He+Se,Ce.b=qe*(1+Je/He)))}function se(xe,Ce,Ke,Ne){var We,ae;(Ne.sr=Ne.si=Ne.lr=Ne.li=0)==xe?Ne.sr=Ce!=0?-Ke/Ce:Ne.sr:Ke==0?Ne.lr=-Ce/xe:(Ce=Ce/2,We=Math.abs(Ce)<Math.abs(Ke)?(ae=-(ae=0<=Ke?xe:-xe)+Ce*(Ce/Math.abs(Ke)),Math.sqrt(Math.abs(ae))*Math.sqrt(Math.abs(Ke))):(ae=-xe/Ce*(Ke/Ce)+1,Math.sqrt(Math.abs(ae))*Math.abs(Ce)),0<=ae?(Ne.lr=(-Ce+(We=0<=Ce?-We:We))/xe,Ne.sr=Ne.lr!=0?Ke/Ne.lr/xe:Ne.sr):(Ne.lr=Ne.sr=-Ce/xe,Ne.si=Math.abs(We/xe),Ne.li=-Ne.si))}function te(xe,Ce,Ke,Ne,We,ae,Ge,He,ge,Je,gt,ne){var Se,qe,Be,ct,wt,Mt,qt,Ft,Tt,Ze,ht,Et,Pt,Ye,nt,O,Z,g,E,T,s,x,C,U,G,Y=new Object,ce=new Object,Me=new Array(Ce),dt=new Array(Ce),_t=1;for(ne.NZ=0,ct=Be=.25,wt=Ne,Ft=We,Y.b=Y.a=0,fe(ge,gt,We,He,Je,Y),Se=Y.a,qe=Y.b,ce.h=ce.g=ce.f=ce.e=ce.d=ce.c=ce.a7=ce.a3=ce.a1=0,C=pe(xe,Ge,Se,qe,ce,ae,gt,We,Me),T=0;T<Ke;T++){if(g=1,ue(xe,Ge,C,Se,qe,ce,ae,Me,Je),st(C=pe(xe,Ge,Se,qe,ce,ae,gt,We,Me),Y,Se,ce.a1,ce.a3,ce.a7,qe,ce.c,ce.d,ce.f,ce.g,ce.h,gt,We,ae,Ge,He),nt=Y.a,Z=O=Y.b,Ze=ae[Ge-1]!=0?-(He[Ge]/ae[Ge-1]):0,ht=Pt=1,T!=0&&C!=3&&(U=(Ye=(Pt=Z!=0?Math.abs((Z-Ft)/Z):Pt)<qt?Pt*qt:1)<ct?1:0,(s=(Et=(ht=Ze!=0?Math.abs((Ze-wt)/Ze):ht)<Mt?ht*Mt:1)<Be?1:0)||U)){for(E=0;E<Ge;E++)dt[E]=ae[E];for(Tt=Ze,x=G=0;;){if(!g||(g=0)!=0||!s||U&&!(Et<Ye)){o=un=St=ft=Fe=ke=W=A=W=S=i=Fe=$t=nn=cn=Jt=Kt=Gt=At=xt=kt=Ot=$=oe=zt=Vt=void 0;var $t,i,S,A,W,ke,Fe,ft,St,Vt=xe,zt=Ge,oe=ne,$=nt,Ot=O,kt=Je,xt=ge,At=Y,Gt=He,Kt=Me,Jt=ce,cn=ae,nn=new Object,un=0,o=0;oe.NZ=0,A=$,ke=Ot;do{if(nn.li=nn.lr=nn.si=nn.sr=0,se(1,A,ke,nn),oe.szr=nn.sr,oe.szi=nn.si,oe.lzr=nn.lr,oe.lzi=nn.li,Math.abs(Math.abs(oe.szr)-Math.abs(oe.lzr))>.01*Math.abs(oe.lzr))break;for(fe(xt,A,ke,Gt,kt,At),Fe=Math.abs(-(oe.szr*At.b)+At.a)+Math.abs(oe.szi*At.b),ft=Math.sqrt(Math.abs(ke)),$t=2*Math.abs(kt[0]),W=-(oe.szr*At.b),St=1;St<zt;St++)$t=$t*ft+Math.abs(kt[St]);if(Fe<=20*($t=(9*($t=$t*ft+Math.abs(W+At.a))+2*Math.abs(W)-7*(Math.abs(At.a+W)+ft*Math.abs(At.b)))*Vt)){oe.NZ=2;break}if(20<++un)break;if(2<=un&&S<=.01&&i<=Fe&&!o){for(fe(xt,A-=A*(S=S<Vt?Math.sqrt(Vt):Math.sqrt(S)),ke+=ke*S,Gt,kt,At),St=0;St<5;St++)ue(Vt,zt,pe(Vt,zt,At.a,At.b,Jt,cn,A,ke,Kt),At.a,At.b,Jt,cn,Kt,kt);o=1,un=0}}while(i=Fe,ue(Vt,zt,pe(Vt,zt,At.a,At.b,Jt,cn,A,ke,Kt),At.a,At.b,Jt,cn,Kt,kt),st(pe(Vt,zt,At.a,At.b,Jt,cn,A,ke,Kt),At,At.a,Jt.a1,Jt.a3,Jt.a7,At.b,Jt.c,Jt.d,Jt.f,Jt.g,Jt.h,A,ke,cn,zt,Gt),W=At.a,(Fe=At.b)!=0&&(S=Math.abs((-ke+Fe)/Fe),A=W,ke=Fe),Fe!=0);if(Se=Y.a,qe=Y.b,0<ne.NZ)return;if(_t=G=1,ct*=.25,x||!s)_t=0;else for(E=0;E<Ge;E++)ae[E]=dt[E]}if(_t!=0){if(Y.a=Tt,_t=function(y,F,X,w,b,z,_e,tt,be){var $e,pt,vt,p,N,we,Re,rt,mt,It,Bt,Rt=w-1;for(F.NZ=Bt=mt=0,Re=X.a;;){for(we=b[0],_e[0]=we,It=1;It<z;It++)_e[It]=we=we*Re+b[It];for(vt=Math.abs(we),p=Math.abs(Re),$e=.5*Math.abs(_e[0]),It=1;It<z;It++)$e=$e*p+Math.abs(_e[It]);if(vt<=20*y*(2*$e-vt)){F.NZ=1,F.szr=Re,F.szi=0;break}if(10<++Bt)break;if(2<=Bt&&Math.abs(rt)<=.001*Math.abs(-rt+Re)&&N<vt){mt=1,F.a=Re;break}for(N=vt,be[0]=pt=tt[0],It=1;It<w;It++)be[It]=pt=pt*Re+tt[It];if(Math.abs(pt)>10*Math.abs(tt[Rt])*y)for(rt=-we/pt,tt[0]=_e[0],It=1;It<w;It++)tt[It]=rt*be[It-1]+_e[It];else for(tt[0]=0,It=1;It<w;It++)tt[It]=be[It-1];for(pt=tt[0],It=1;It<w;It++)pt=pt*Re+tt[It];Re+=rt=Math.abs(pt)>10*Math.abs(tt[Rt])*y?-we/pt:0}return mt}(xe,ne,Y,Ge,He,ge,Je,ae,Me),Tt=Y.a,0<ne.NZ)return;if(x=1,Be*=.25,_t!=0){nt=-(Tt+Tt),O=Tt*Tt;continue}}for(E=0;E<Ge;E++)ae[E]=dt[E];if(!U||G)break}fe(ge,gt,We,He,Je,Y),C=pe(xe,Ge,Se=Y.a,qe=Y.b,ce,ae,gt,We,Me)}Ft=Z,wt=Ze,qt=Pt,Mt=ht}}(function(xe,Ce,Ke,Ne){for(var We,ae,Ge,He,ge,Je,gt,ne,Se,qe,Be,ct,wt,Mt,qt=xe.Degree,Ft=.017453292519943295,Tt=Math.LN2,Ze=xe.Degree+1,ht=new Array(Ze),Et=new Array(Ze),Pt=new Array(Ze),Ye=new Array(Ze),nt=new Object,O=new Object,Z=1;We=Z,1<(Je=1+(Z/=2)););var g=Number.MIN_VALUE/We,E=Math.cos(94*Ft),T=Math.sin(94*Ft),s=Math.sqrt(.5),x=-s;for(O.NZ=Se=0,O.szr=O.szi=O.lzr=O.lzi=0;Ce[qt]==0;)Ke[Se]=Ne[Se]=0,qt--,Se++;for(wt=qt+1;1<=qt;){if(qt<=2){qt<2?(Ke[xe.Degree-1]=-(Ce[1]/Ce[0]),Ne[xe.Degree-1]=0):(se(Ce[nt.li=nt.lr=nt.si=nt.sr=0],Ce[1],Ce[2],nt),Ke[xe.Degree-2]=nt.sr,Ne[xe.Degree-2]=nt.si,Ke[xe.Degree-1]=nt.lr,Ne[xe.Degree-1]=nt.li);break}for(He=0,ge=Number.MAX_VALUE,C=0;C<wt;C++)He<(U=Math.abs(Ce[C]))&&(He=U),U!=0&&U<ge&&(ge=U);if(((Be=g/ge)<=1&&10<=He||1<Be&&Number.MAX_VALUE/Be>=He)&&(Be=Be==0?Number.MIN_VALUE:Be,Be=Math.floor(Math.log(Be)/Tt+.5),(Ge=Math.pow(2,Be))!=1))for(C=0;C<wt;C++)Ce[C]*=Ge;for(var C=0;C<wt;C++)Et[C]=Math.abs(Ce[C]);Et[qt]=-Et[qt],ct=qt-1,U=Math.exp((Math.log(-Et[qt])-Math.log(Et[0]))/qt),G=U=Et[ct]!=0&&(G=-Et[qt]/Et[ct])<U?G:U;do for(var U,G=.1*(U=G),Y=Et[0],C=1;C<wt;C++)Y=Y*G+Et[C];while(0<Y);do for(var ce=Y=Et[0],C=1;C<qt;C++)ce=U*ce+(Y=U*Y+Et[C]);while(U-=ae=(Y=U*Y+Et[qt])/ce,.005<Math.abs(ae/U));for(var Me=U,C=1;C<qt;C++)ht[C]=(qt-C)*Ce[C]/qt;for(ht[0]=Ce[0],Z=Ce[qt],Je=Ce[ct],Mt=ht[ct]==0?1:0,qe=0;qe<5;qe++)if(gt=ht[ct],Mt){for(C=0;C<ct;C++)ht[Se=ct-C]=ht[Se-1];Mt=(ht[0]=0)==ht[ct]?1:0}else{for(var dt=-Z/gt,C=0;C<ct;C++)ht[Se=ct-C]=dt*ht[Se-1]+Ce[Se];ht[0]=Ce[0],Mt=Math.abs(ht[ct])<=Math.abs(Je)*We*10?1:0}for(C=0;C<qt;C++)Ye[C]=ht[C];for(qe=1;qe<=20;qe++){if(ne=-T*x+E*s,x=T*s+E*x,te(We,Ze,20*qe,ne=Me*(s=ne),Me,ht,qt,Ce,wt,Pt,-2*ne,O),O.NZ!=0){for(Ke[Se=xe.Degree-qt]=O.szr,Ne[Se]=O.szi,qt=(wt-=O.NZ)-1,C=0;C<wt;C++)Ce[C]=Pt[C];O.NZ!=1&&(Ke[Se+1]=O.lzr,Ne[Se+1]=O.lzi);break}for(C=0;C<qt;C++)ht[C]=Ye[C]}if(20<qe){xe.Degree-=qt;break}}})(P,Lt,B,H);var D=H.length;for(ye=0;ye<D;ye++){var re=De(H[ye],c+8),J=De(B[ye],c+8),Ee=(J=2<c-String(J).length?J:B[ye],re<0?"-":""),Ee=(J===0&&(J=""),re===0&&(re=""),re=Math.abs(re)===1?Ee+"i":re?re+"*i":"",J&&re?J+"+"+re:J+re);B[ye]=Ee.replace(/\+\-/g,"-")}return B}(Ve,Nt).concat(f),Xe=0;Xe<0;Xe++)Ct.unshift(0);return Ct}var f=[];if(d instanceof ee&&d.isPoly()){if(d.distributeMultiplier(),d.group===M&&(v=t.Utils.arrayMin(ie(d.symbols)),v=d.symbols[v].clone().toUnitMultiplier(),d=e.expand(e.divide(d,v)),f.push(0)),d.group===t.groups.S)return[0];d.group===t.groups.PL&&(V=ie(d.symbols),v=t.Utils.arrayMin(V),d=t.PARSER.divide(d,t.PARSER.parse(d.value+"^"+v)));for(var v=ie(d.symbols).sort().pop(),I=d.group===t.groups.PL?d.symbols:d.symbols[v],q=I.group,V=q===l?[I.power.toDecimal()]:ie(I.symbols),Q=[],le=t.Utils.arrayMax(V),ye=1;ye<=le;ye++){var Ae=0;V.indexOf(ye+"")!==-1&&(Ae=(q===l?I:I.symbols[ye]).multiplier),Q.unshift(Ae)}return Q.push(d.symbols[Te].multiplier),I.group===l&&(Q[0]=I.multiplier),u(Q,0,le)}if(t.Utils.isArray(d)){for(var je=d,Q=[],V=[],it=0,ye=0;ye<je.length;ye++){for(var yt=je[ye][0],me=je[ye][1],Ue=me-it-1,Le=0;Le<Ue;Le++)Q.unshift(0);Q.unshift(yt),me!==0&&V.push(me),it=me}return u(Q,0,le=Math.max.apply(void 0,V))}throw new t.exceptions.NerdamerTypeError("Cannot calculate roots. Symbol must be a polynomial!")},roots:function(d){return d.isConstant(!0,!0)?t.Utils.nroots(d):(d=j.proots(d).map(function(c){return e.parse(c)}),t.Vector.fromArray(d))},froot:function(d,c,u){for(var f=Number(c),v=u||t.Utils.build(t.Calculus.diff(d.clone())),I=d instanceof Function?d:t.Utils.build(d),q=!1,V=0;!q;){var Q=f-I(f)/v(f),le=Math.abs(Q)-Math.abs(f);f=Q,Math.abs(le)<1e-12?q=!0:1e4<V&&(q=!(f=null)),V++}return f},quad:function(d,c,u){function f(v,I,q,V){return e.parse("-("+I+"+"+V+"*sqrt(("+I+")^2-4*("+v+")*("+q+")))/(2*"+v+")")}return[f(d,c,u,1),f(d,c,u,-1)]},sumProd:function(d,c){return j.quad(-c,d,-1).map(function(u){return u.invert()})},coeffs:function(d,c,u){c=String(c),d=e.expand(d),u=u||[new ee(0)],d.group===h&&d.contains(c,!0)&&e.error("Unable to get coefficients using expression "+d.toString());var f,v=de(d);if(v.length!==1||v[0]!==c||d.isImaginary())c||e.error("Polynomial contains more than one variable. Please specify which variable is to be used!"),v.indexOf(c)===-1?u[0]=e.add(d,u[0]):(u=u||[new ee(0)],d.group===R?((v=d.symbols[c])||e.error("Expression is not a polynomial!"),f=Number(v.power),((le=e.divide(d.clone(),v.clone())).contains(c,!0)||f<0||!Qe(f))&&e.error("Expression is not a polynomial!"),(Q=u[f])&&(le=e.add(Q,le)),u[f]=le):d.group===_&&d.each(function(ye){j.coeffs(ye.clone(),c,u)},!0));else for(var I=new Oe(d).coeffs.map(function(ye){return new ee(ye)}),q=0,V=I.length;q<V;q++){var Q,le=I[q];(Q=u[q])&&(le=e.add(Q,le)),u[q]=le}for(q=0,V=u.length;q<V;q++)u[q]===void 0&&(u[q]=new ee(0));return u},polyPowers:function(d,c,u){if(u=u||[],(v=d.group)===M&&c===d.value)u=u.concat(ie(d.symbols));else if(v===_)for(var f in d.symbols){var f=d.symbols[f],v=f.group,I=f.value;v===l&&c===I?u.push(f.power):v===M||v===_?u=j.polyPowers(f,c,u):v===R&&f.contains(c)?(f=f.symbols[c])&&u.push(f.power):v!==r&&c===I||u.push(0)}else v===R&&d.contains(c)&&u.push(t.Utils.decompose_fn(d,c,!0).x.power);return t.Utils.arrayUnique(u).sort()},Factor:{split:function(d){var c=new ee(1),u=new ee(1);return j.Factor.factor(d,new ut).each(function(f){var v=e.parse(f);f.isConstant(!0)?c=e.multiply(c,v):u=e.multiply(u,v)}),[c,u]},mix:function(d,c){for(var u=ie(d),f=u.length,v=[],I=0;I<f;I++){for(var q=u[I],V=d[q],Q=v.length,le=0;le<Q;le++){var ye=v[le]*q;v.push(ye),c&&v.push(-ye)}for(le=1;le<=V;le++)v.push(Math.pow(q,le))}return v},common:function(d,c){try{if(d.group===_){for(var u=e.expand(d.clone(),!0).collectSymbols(null,null,function(ye,Ae){return(Ae.length||1)-(ye.length||1)}),f={},v=[],I=0;I<u.length;I++){var q=u[I];v.push(q.multiplier.clone()),q.each(function(ye){var Ae=Number(ye.power);if(isNaN(Ae))throw new Error("exiting");ye.value in f?(Ae<f[ye.value][0]&&(f[ye.value][0]=Ae),f[ye.value][1].push(ye)):f[ye.value]=[Ae,[ye]]})}var V,Q=new ee(1);for(V in f)f[V][1].length===u.length&&(Q=e.multiply(Q,e.pow(new ee(V),new ee(f[V][0]))));var le=t.Math2.QGCD.apply(null,v);if(!le.equals(1))for(c.add(new ee(le)),I=0;I<u.length;I++)u[I].multiplier=u[I].multiplier.divide(le);if(!Q.equals(1))for(c.add(Q),d=new ee(0),I=0;I<u.length;I++)d=e.add(d,e.divide(u[I],Q.clone()))}}catch(ye){}return d},zeroes:function(d,c){function u(){throw new t.exceptions.ValueLimitExceededError("Exiting")}try{q=(d=e.expand(d.clone())).toString(),f=de(d),v=new ee(0);for(var f,v,I,q,V,Q,le=[],ye=[],Ae=0,je=f.length;Ae<f.length;Ae++){for(var it={},yt=0;yt<je;yt++)Ae!==yt&&(it[f[yt]]=0);var me,Ue=(me=e.parse(q,it)).power;Qe(Ue)||u(),le.push(me),ye.push(me.power)}for(t.Utils.allSame(ye)?(V=d.length,(Q=le.length)===2&&(I=new Ie(ye[0]/(V-1))),Q===3&&(I=new Ie(ye[0]/Math.round((Math.sqrt(8*V-1)-3)/2)))):I=t.Math2.QGCD.apply(null,ye),Qe(I)||u(),Ae=0;Ae<le.length;Ae++){var Le=le[Ae],Ve=Le.power.clone().divide(I);Le.multiplier=new Ie(Math.pow(Le.multiplier,1/Ve)),Le.power=I.clone(),v=e.add(v,Le)}if(v.group!==_)return d;for(;;){var lt=j.div(d.clone(),v.clone());if(!lt[1].equals(0)||(d=lt[0],c.add(v.clone()),d.equals(1)))break}}catch(Nt){}return d},factor:function(d,c){var u,f,v;return d.isConstant()?t.Math2.factor(d):(u=e.parse(d),(u=j.Factor._factor(u,c)).equals(d)||u.group===R&&(f=new ee(1),c=e.parse(u.power),v=e.parse(u.multiplier),u.toUnitMultiplier(),u.multiplier.lessThan(0)&&(f.negate(),u.negate()),u.each(function(I){I=e.parse(j.Factor._factor(I)),I.group===R?(v=e.multiply(v,ee.create(I.multiplier)),I.each(function(q){q=e.parse(j.Factor._factor(q)),f=e.multiply(f,q),q.group===R&&(v=e.multiply(v,ee.create(q.multiplier)))})):f=e.multiply(f,I)}),u=e.pow(e.multiply(v,f),c)),u)},quadFactor:function(d,c){if(d.isPoly()&&j.degree(d.equals(2))){var u=t.Utils.variables(d)[0],f=j.coeffs(d,u),v=j.Factor._factor(f[2].clone());if(v.group===R){if(v=v.collectSymbols(),2<v.length)return d;var I=e.multiply(e.parse(f[0]),e.parse(v[0])),q=e.parse(f[1]).negate(),V=e.parse(v[1]),V=j.quad(V,q,I).filter(function(Q){if(t.Utils.isInt(Q))return Q});V.length===1&&(q=V[0],I=e.divide(f[0],e.parse(q)),t.Utils.isInt(I)&&(c.add(e.parse(ve("({0})*({1})+({2})",v[1],u,I))),c.add(e.parse(ve("({0})*({1})+({2})",v[0],u,q))),d=new ee(1)))}}return d},cubeFactor:function(d,c){var u,f,v,I,q,V;return d.isComposite()&&(v=d.collectSymbols()).length===2&&(u=v[0].sign(),q=v[0].clone().abs(),f=v[1].sign(),v=v[1].clone().abs(),q.isCube()&&v.isCube()&&(u<f&&([u,f]=[f,u],[q,v]=[v,q]),V=e.parse(q.getNth(3)),I=e.parse(v.getNth(3)),q=e.multiply(e.expand(e.pow(q.clone().toUnitMultiplier(),e.parse("1/3"))),V),V=e.multiply(e.expand(e.pow(v.clone().toUnitMultiplier(),e.parse("1/3"))),I),u===1&&f===-1?(c.add(e.parse(ve("(({0})-({1}))",q,V))),c.add(e.parse(ve("(({0})^2+({0})*({1})+({1})^2)",q,V))),d=ee(1)):u===1&&f===1&&(c.add(e.parse(ve("(({0})+({1}))",q,V))),c.add(e.parse(ve("(({0})^2-({0})*({1})+({1})^2)",q,V))),d=ee(1)))),d},_factor:function(d,c){var u;if(d.group,d.group===L){var Ae=d.args[0];if(Ae.group===l&&Ae.isSimple())return d}else if(d.group===l&&d.isSimple())return d;d.group===_&&(d.distributeMultiplier(!0),u=new ee(0),d.each(function(B){(B.group===_&&B.power.greaterThan(1)||B.group===R)&&(B=e.expand(B)),u=e.add(u,B)}),u.power=d.power,d=u);var f,v,I,q,V,Q,le,ye,Ae=(d=d.group===L&&d.fname!=="sqrt"?t.Utils.evaluate(d):d).clone();try{if(d.group===R)return je=e.parse(d.power),f=j.Simplify.strip(d.getDenom()),v=j.Simplify.strip(d.getNum()),I=f.pop(),(q=v.pop()).equals(d)?d:(V=j.Factor.factor(q),Q=j.Factor.factor(I),le=j.Simplify.unstrip(v,V),ye=j.Simplify.unstrip(f,Q),P=e.divide(le,ye));if(d.group===l)return d;if(d.isConstant())return d.equals(1)?d.clone():t.Math2.factor(d);var je=d.power.clone();if(!Qe(je)||je.lessThan(0)&&d.group===L)return d;var it=je.sign(),yt=(d.toLinear(),c=c||new ut,{}),me=(d=e.parse(t.Utils.subFunctions(d,yt)),0<ie(yt).length&&(c.preAdd=function(B){return e.parse(B,t.Utils.getFunctionsSubs(yt))}),d.isLinear()||(c.pFactor=d.power.toString(),d.toLinear()),de(d)),Ue=(d.isImaginary()&&me.push(t.Settings.IMAGINARY),1<me.length);if(Ue){var Le=!0,Ve=!0;if(d.each(function(B){B.group!==l&&(Le=!1),B.multiplier.equals(1)||(Ve=!1)}),Le&&Ve)return e.pow(e.parse(d,t.Utils.getFunctionsSubs(yt)),e.parse(je))}var lt=new ut,Nt=(d=j.Factor.coeffFactor(d,lt),lt.each(function(B){K(je)&&B.lessThan(0)&&B.negate(),it<0&&B.invert(),c.add(B)}),new ut);if(d=j.Factor.powerFactor(d,Nt),Nt.each(function(B){it<0&&B.invert(),c.add(B)}),Ue)d=j.Factor.cubeFactor(d,c),d=j.Factor.mfactor(d,c),c.each(function(B){it<0&&B.power.negate()});else{var Ct,Xe=me[0],he=(d=j.Factor.squareFree(d,c,Xe),new ut),et=(d=j.Factor.trialAndError(d,he,Xe),he.toSymbol());if(et.equals(Ae))return et;for(Ct in he.factors){var Lt=he.factors[Ct];c.add(e.pow(Lt,e.parse(je)))}d.equals(Ae)&&(d=j.Factor.quadFactor(d,c))}d=e.parse(d,t.Utils.getFunctionsSubs(yt));var H=c.length===1,P=(c.add(e.pow(d,e.parse(je))),c.toSymbol());return P=H&&d.equals(1)&&P.isLinear()?e.pow(P,e.parse(je)):P}catch(B){return Ae}},reduce:function(d,c){if(d.group===_&&d.length===2){var u=d.collectSymbols().sort(function(Ae,je){return je.multiplier-Ae.multiplier});if(u[0].power.equals(u[1].power)){for(var f=e.parse(u[0].power),v=u[0].clone().toLinear(),I=u[1].clone().toLinear(),q=(c.add(e.add(v.clone(),I.clone())),I.negate(),Number(f)),ye=new ee(0),V=1;V<=q;V++)var Q=e.pow(v.clone(),e.subtract(f.clone(),new ee(V))),le=e.pow(I.clone(),e.subtract(new ee(V),new ee(1))),ye=e.add(ye,e.multiply(Q,le));return ye}}return d},squareFree:function(d,c,u){var f,v;return!d.isConstant()&&d.group!==l&&(f=(u=new Oe(d,u).squareFree())[2])!==1?((v=u[1].toSymbol()).power=v.power.multiply(new Ie(f)),c.add(j.Factor.factor(v)),j.Factor.squareFree(u[0].toSymbol(),c)):d},powerFactor:function(d,c){var u,f,v;return d.group===M&&d.previousGroup!==h&&(u=ie(d.symbols),t.Utils.allNumeric(u))?(u=t.Utils.arrayMin(u),f=new ee(0),v=e.parse(d.value+"^"+u),d.each(function(I){I=e.divide(I,v.clone()),f=e.add(f,I)}),c.add(v),f):d},coeffFactor:function(d,c){var u,f,v,I;return d.isComposite()&&((u=t.Math2.QGCD.apply(null,d.coeffs())).equals(1)?((f=function(q){var V;return q.group===R?(V=0,q.each(function(Q){V+=Q.power})):V=Number(q.power),V})(I=(v=d.collectSymbols(null,null,null,!0).sort(function(q,V){return q.isConstant(!0)?1:V.power-q.power}))[0])>f(v[1])||v[1].isConstant(!0))&&I.multiplier.lessThan(0)&&(c.add(new ee(-1)),d.each(function(q){q.negate()},!0)):(d.each(function(q){q.isComposite()?q.each(function(V){V.multiplier=V.multiplier.divide(u)}):q.multiplier=q.multiplier.divide(u)}),d.updateHash()),c&&c.add(new ee(u))),d},trialAndError:function(d,c,u){var f=d.clone();try{var v=[];if(d.isConstant()||d.group===l)return d;for(var I=new Oe(d,u),q=I.coeffs[0],V=t.Math2.ifactor(q),Q=j.proots(d),le=0;le<Q.length;le++){var ye=Q[le],Ae=1;if(!isNaN(ye)){for(var je in V){var it=t.Utils.round(Math.log(je)/Math.log(Math.abs(ye)),8);if(Qe(it)){ye=je,Ae=it;break}}var yt=new Ie(ye),me=[new Ie(yt.num).negate()],Ue=(me[Ae]=new Ie(yt.den),Oe.fromArray(me,I.variable).fill()),Le=I.divide(Ue);Le[1].equalsNumber(0)&&(I=Le[0],v.push(Ue.toSymbol()))}}return I.equalsNumber(1)||(I=j.Factor.search(I,c)),v.forEach(function(Ve){c.add(Ve)}),I.toSymbol()}catch(Ve){return f}},search:function(d,c,u){u=u||10;function f(lt,Nt,Ct,Xe){return(lt=Oe.fit(lt,Nt,Ct,u,Xe,v))&&1<lt.coeffs.length&&(Nt=d.divide(lt),Nt[1].equalsNumber(0))?(c.add(lt.toSymbol()),[Nt[0],lt]):null}var v=d.variable,I=d.coeffs[0],q=t.Math2.ifactor(I),V=d.lc(),Q=t.Math2.ifactor(V),le=d.sub(u),ye=t.Math2.ifactor(le),Ae=j.Factor.mix(ye,le<0),je=Math.ceil(d.coeffs.length/2),it=V.lessThan(0),yt=I.lessThan(0);for(q[Q[1]=1]=1;je--;)for(var me in Q)for(var Ue in q)for(var Le=0;Le<Ae.length;Le++){var Ve=f(me,Ue,Ae[Le],je);if(Ve)return d=Ve[0],d=t.Utils.isPrime(d.sub(u))?d:j.Factor.search(d,c);it&&yt?Ve=f(-me,-Ue,Ae[Le],je):it?Ve=f(-me,Ue,Ae[Le],je):yt&&(Ve=f(me,-Ue,Ae[Le],je))}return d},mSqfrFactor:function(d,c){if(d.group!==L)for(var u=de(d).reverse(),f=0;f<u.length;f++)do if(u[f]===d.value)c.add(d),d=new ee(1);else{var v=t.Calculus.diff(d,u[f]),I=j.Factor.coeffFactor(v);if(I.equals(0))break;var q=!0;if(I.isConstant()&&d.isComposite()&&d.each(function(le){le.multiplier%I!=0&&(q=!1)},!0),q){var V=j.div(d,I.clone()),Q=V[1].equals(0);if(d.equals(V[0])&&V[1].equals(0))break;if(V[0].isConstant()){c.add(V[0]);break}}else Q=!1;Q&&(c.add(V[0]),d=I)}while(Q);return d},sqdiff:function(d,c){if(!d.isConstant("all"))try{var u,f,v,I,q,V=function(ye){return t.Utils.block("POSITIVE_MULTIPLIERS",function(){return ee.unwrapPARENS(ze.sqrt(ze.abs(ye)))},!0)},Q=t.Utils.separate(d.clone()),le=[];for(u in Q)u!=="constants"&&le.push(Q[u]);if(le.sort(function(ye,Ae){return Ae.power-ye.power}),le.length===2){if(q=le.pop(),f=le.pop(),K(q.power)&&K(f.power)&&q.sign()===f.sign()&&q.group===l&&f.group===l)throw new Error("Unable to factor");q.isComposite()&&f.power.equals(2)?(f=V(f),(v=j.Factor.factor(e.add(q,Q.constants))).power.equals(2)&&(v.toLinear(),c.add(e.subtract(v.clone(),f.clone())),c.add(e.add(v,f)),d=new ee(1))):(q=q.powSimp(),f=f.powSimp(),q.group!==l&&q.fname!==""||!q.power.equals(2)||f.group!==l&&f.fname!==""||!f.power.equals(2)||Q.constants||(q.multiplier.lessThan(0)&&(I=f,f=q,q=I),q.multiplier.greaterThan(0)&&(q=V(q),f=V(f)),c.add(e.subtract(q.clone(),f.clone())),c.add(e.add(q,f)),d=new ee(1)))}}catch(ye){}return d},mfactor:function(d,c){if(d.group===L){var u,f;d.fname==="sqrt"?(u=new ut,f=j.Factor.common(d.args[0].clone(),u),f=j.Factor.coeffFactor(f,u),d=e.multiply(e.symfunction("sqrt",[f]),e.parse(d.multiplier)),u.each(function(Nt){d=e.multiply(d,e.parse(t.Utils.format("sqrt({0})",Nt)))})):c.add(d)}else{d=j.Factor.mSqfrFactor(d,c);for(var v,I=de(d),q=d.collectSymbols().map(function(Nt){return ee.unwrapSQRT(Nt)}),V={},Q={},le=I.length,ye=q.length,Ae=0;Ae<le;Ae++){var je=I[Ae];V[je]=new ee(0);for(var it=0;it<ye;it++){var yt,me=q[it];me.contains(je)&&(yt=(me.value===je?me:me.symbols[je]).power.toDecimal(),(!Q[je]||yt<Q[je])&&(Q[je]=yt),V[je]=e.add(V[je],me.clone()))}}for(v in V){var Ue=e.parse(v+"^"+Q[v]),lt=e.divide(V[v],Ue),lt=e.expand(lt);if(lt.equals(1))break;var Le=j.div(d.clone(),lt);if(Le[0].equals(0))break;if(Le[1].equals(0)){var Ve=!1;if(Le[0].each(function(Nt){Qe(Nt.multiplier)||(Ve=!0)}),Ve){Le[1]=e.expand(e.multiply(Le[1],lt));break}}var lt=Qe(lt)&&lt.lessThan(0);if(Le[1].equals(0)&&!lt)return(Ue=(lt=j.div(d.clone(),Le[0].clone()))[0]).equals(0)||(d=lt[1],Ue.equals(-1)&&!d.equals(0))?d:(lt=Le[0],d.equals(lt)?(Le=j.Factor.reduce(lt,c),d.equals(Le)?Le:j.Factor.mfactor(Le,c)):(c.add(lt),d.equals(0)?Ue:Ue.isConstant("all")?(c.add(Ue),Ue):j.Factor.mfactor(Ue,c)))}}return d=j.Factor.sqdiff(d,c),d=j.Factor.zeroes(d,c)}},allLinear:function(d){for(var c=d.length,u=0;u<c;u++)if(!j.isLinear(d[u]))return!1;return!0},isLinear:function(d){var c=!1,u=d.group;if(u===M||u===_)for(var f in c=!0,d.symbols){var f=d.symbols[f],v=f.group;if(v!==L&&v!==h||(c=!1),v===R)c=de(f).length===1;else if(v===M||v===_)c=j.isLinear(f);else if(f.group!==r&&f.power.toString()!=="1"){c=!1;break}}else u===l&&d.power===1&&(c=!0);return c},gcd:function(){var d=arguments.length===1&&arguments[0]instanceof t.Vector?arguments[0].elements:t.Utils.arguments2Array(arguments);if(d.length===0)return new ee(1);if(d.length===1)return d[0];for(var c=[],u=!1,f=0;f<d.length;f++)if(d[f].group===L&&d[f].fname==="gcd")(d=d.concat(arguments[f].args)).splice(f,1);else{var v=de(d[f]);if(t.Utils.haveIntersection(v,c)){u=!0;break}c=c.concat(v)}if(u||c.length===0){if(d.every(function(q){return q.getDenom().equals(1)})){for(var I=d[0],f=1;f<d.length;f++)I=j.gcd_(d[f],I);return I}return e.divide(j.gcd.apply(null,d.map(function(q){return q.getNum()})),j.lcm.apply(null,d.map(function(q){return q.getDenom()})))}return e.symfunction("gcd",d)},gcd_:function(d,c){if(d.group!==L&&d.group!==a||(d=t.Utils.block("PARSE2NUMBER",function(){return e.parse(d)})),c.group===L&&(c=t.Utils.block("PARSE2NUMBER",function(){return e.parse(c)})),d.isConstant()&&c.isConstant())return new ee(t.Math2.QGCD(new Ie(+d),new Ie(+c)));var u,f=e.multiply(d.getDenom()||new ee(1),c.getDenom()||new ee(1)).invert();if(d=e.multiply(d.clone(),f.clone()),c=e.multiply(c.clone(),f.clone()),d=e.expand(d),c=e.expand(c),d.group===R||c.group===R){var v=e.divide(d.clone(),c.clone());if(!(Q=e.multiply(c.clone(),v.getDenom().invert())).equals(1))return Q}if(d.group===h||c.group===h)return v=new ee(t.Math2.GCD(d.multiplier,c.multiplier)),I=j.gcd_(d.value===Te?new ee(1):e.parse(d.value),c.value===Te?new ee(1):e.parse(c.value)),u=j.gcd_(e.parse(d.power),e.parse(c.power)),e.multiply(v,e.pow(I,u));d.length<c.length&&(Q=d,d=c,c=Q);var v=de(d),I=de(c);if(v.length===I.length&&v.length===1&&v[0]===I[0]||v.length===1&&I.length===0||v.length===0&&I.length===1)return d=new Oe(d),c=new Oe(c),e.divide(d.gcd(c).toSymbol(),f);var q,V=[];for(d.each(function(ye){V.push(ye.multiplier)}),c.each(function(ye){V.push(ye.multiplier)});!c.equals(0);){var Q=c.clone();if(d=d.clone(),q=j.div(d,Q),c=q[1],q[0].equals(0))return e.divide(new ee(t.Math2.QGCD(d.multiplier,c.multiplier)),f);d=Q}var le=t.Math2.QGCD.apply(void 0,V);return le.equals(1)||d.each(function(ye){ye.multiplier=ye.multiplier.divide(le)}),!d.equals(1)||d.isConstant()||c.isConstant()?e.divide(d,f):e.divide(e.symfunction("gcd",arguments),f)},lcm:function(){arguments.length===1?arguments[0]instanceof t.Vector?u=arguments[0].elements:e.error("lcm expects either 1 vector or 2 or more arguments"):u=t.Utils.arguments2Array(arguments);var d=u.reduce(function(f,v){return e.multiply(f,v.clone())},new ee(1)),c=function(f,v){v=Number(v);for(var I,q,V=[],Q=Math.pow(2,f.length),le=v;le<Q;le++){for(I=[],q=f.length-1;(le&1<<q)!=0&&I.push(f[q]),q--;);I.length===v&&V.push(I)}return V}(arguments,arguments.length-1).map(function(f){return f.reduce(function(v,I){return e.multiply(v,I.clone())},new ee(1))}),u=u.every(function(f){return t.Utils.isVariableSymbol(f)})?e.symfunction("gcd",t.Utils.arrayUnique(c)):j.gcd.apply(null,c);return e.divide(d,u)},divide:function(d,c){var u=t.Algebra.Factor.factor(d.clone()),f=u.getDenom();return f.isConstant("all")?f=new ee(1):d=e.expand(ee.unwrapPARENS(e.multiply(u,f.clone()))),u=j.div(d,c),d=e.divide(u[1],c),e.divide(e.add(u[0],d),f)},div:function(d,c){var u,f,v,I=[new ee(0),d.clone()];try{if(c.isConstant("all"))return d.each(function(We){We.multiplier=We.multiplier.divide(c.multiplier)}),[d,new ee(0)];if(d=e.expand(d),c=e.expand(c),d.group===l&&c.group===_){var q,V=d.value,Q=t.Utils.decompose_fn(c.clone(),V,!0);if(d.isLinear()&&Q.x&&Q.x.isLinear()&&c.isLinear())return q=ee.create(d.multiplier),[e.divide(q.clone(),Q.a.clone()),e.divide(e.multiply(q,Q.b),Q.a).negate()]}if(d.group===l&&c.group===l)return(u=e.divide(d.clone(),c.clone())).isConstant()?[u,new ee(0)]:[new ee(0),d.clone()];var le,ye,Ae=d.hasFunc(),je=c.hasFunc(),it=!1,yt=((Ae||je)&&(it=!0,le={},d=e.parse(t.Utils.subFunctions(d,le)),c=e.parse(t.Utils.subFunctions(c,le)),ye=t.Utils.getFunctionsSubs(le)),t.Utils.arrayUnique(de(d).concat(de(c))));if((d.isImaginary()||c.isImaginary())&&yt.push(t.Settings.IMAGINARY),yt.length===1)var me=(xe=new Oe(d).divide(new Oe(c)))[0].toSymbol(),Ue=xe[1].toSymbol();else{yt.push(Te);var Le=function(We){for(var He=new ee(0),ae=0;ae<We.length;ae++)var Ge=We[ae].toSymbol(),He=e.add(He,Ge);return He},Ve=function(We,ae){var Ge,He=Math.max.apply(null,We.terms),ge=0;if(!ae){for(var Je=0;Je<We.terms.length;Je++)if(We.terms[Je].equals(He)&&(Ge=Je,ge++),1<ge)return}if(ae){for(Je=0;Je<We.terms.length;Je++)if(We.terms[Je].equals(He)){Ge=Je;break}}return[He,Ge,We]},lt=function(We,ae){var Ge=We[ae=ae||0],He=We.length;if(Ge){for(var ge,Je=Ve(Ge),gt=ae+1;gt<He;gt++){var ne=We[gt],Se=Ge.sum.equals(ne.sum);if(!Se&&Je)break;if(Se){for(var qe,Be,ct,wt,Mt=Ge.terms.length,qt=0;qt<Mt;qt++){var Ft=Ge.terms[qt],Tt=ne.terms[qt];qe!==void 0&&!Ft.greaterThan(qe)||(qe=Ft,ct=qt),Be!==void 0&&!Tt.greaterThan(Be)||(Be=Tt,wt=qt)}var Se=qe.subtract(ne.terms[ct]),Ze=Be.subtract(Ge.terms[wt]);if(Se<Ze){Je=[Be,wt,ne];break}if(Ze<Se){Je=[qe,ct,Ge];break}}else if(Je=Ve(ne))break;Je=Ve(ne)}if(!Je)return Ve(We[0],!0);for(gt=0;gt<et.length;gt++){var ht,Et=et[gt].terms;if((ht=Je[1])===Et.length-1)return;if(!(ge=Et[ht]).equals(0))break}return ge.equals(0)?lt(We,++ae):Je}},Nt=t.Utils.toMapObj(yt),Ct=function(We,ae){return ae.sum.subtract(We.sum)},Xe=function(We,ae){if(!We||!ae)return!1;for(var Ge=0;Ge<We.terms.length;Ge++)if(We.terms[Ge].lessThan(ae.terms[Ge]))return!1;return!0},he=d.tBase(Nt).sort(Ct),et=c.tBase(Nt).sort(Ct),Lt=Xe(he[0],et[0])&&he[0].count>et[0].count?et:he,H=lt(Lt),P=[];if(H){var fe=H[1],B=function(Je,ge){var Ge=Je.len(),He=ge.len(),ge=ge.terms[fe],Je=Je.terms[fe];return Ge<He&&ge.greaterThan(Je)?He-Ge:ge.subtract(Je)},fe=function(We,ae){for(var Ge=[],He=0;He<We.length;He++)for(var ge=We[He],Je=0;Je<ge.terms.length;Je++){var gt=Ge[Je],ne=ge.terms[Je];He===0?Ge[Je]=ne:gt&&!gt.equals(ne)&&(Ge[Je]=void 0)}for(He=0;He<Ge.length;He++)if((ge=Ge[He])&&!ge.equals(0))return He;return ae}(he,fe),pe=(he.sort(B),et.sort(B),et[0]),ue=he[0],st=new at(new Ie(1),[],ue.map);if(pe.sum.greaterThan(ue.sum)&&1<ue.len())for(var se=0;se<ue.terms.length;se++){var te=pe.terms[se].subtract(ue.terms[se]);if(te.equals(0))st.terms[se]=new Ie(0);else{var D=te.add(new Ie(1));st.terms[se]=te;for(var re=0;re<he.length;re++)he[re].terms[se]=he[re].terms[se].add(D)}}for(var J=Xe(he[0],et[0]),Ee=0;J&&(v=et,!(f=he)[0].sum.equals(v[0].sum)||f.length>=v.length);){if(200<Ee++)throw new t.exceptions.InfiniteLoopError("Unable to compute!");var xe=he[0].divide(et[0]);for(P.push(xe),he.shift(),se=1;se<et.length;se++){var Ce=et[se].multiply(xe).generateImage(),Ke=he.length;for(Ke===0&&(Ce.coeff=Ce.coeff.neg(),he.push(Ce),he.sort(B)),re=0;re<Ke;re++){var Ne=he[re];if(Ne.getImg()===Ce.getImg()){Ne.coeff=Ne.coeff.subtract(Ce.coeff),Ne.coeff.equals(0)&&(t.Utils.remove(he,re),re--);break}re===Ke-1&&(Ce.coeff=Ce.coeff.neg(),he.push(Ce),he.sort(B))}}if(!(J=Xe(he[0],et[0]))&&he.length>=et.length){for(se=1;se<he.length;se++)if(J=Xe(he[se],et[0])){he.unshift(t.Utils.remove(he,se));break}}}}me=Le(P),Ue=Le(he),st!==void 0&&(st=st.toSymbol(),me=e.divide(me,st.clone()),Ue=e.divide(Ue,st))}return it&&(me=e.parse(me.text(),ye),Ue=e.parse(Ue.text(),ye)),[me,Ue]}catch(We){return I}},line:function(d,f,I){t.Utils.isArray(d)&&(d=t.Utils.convertToVector(d)),t.Utils.isArray(f)&&(f=t.Utils.convertToVector(f)),I=e.parse(I||"x"),t.Utils.isVector(d)&&t.Utils.isVector(f)||e.error('Line expects a vector! Received "'+d+'" & "'+f+'"');var v=e.subtract(f.e(1).clone(),d.e(1).clone()),f=e.subtract(f.e(2).clone(),d.e(2).clone()),f=e.divide(f,v),v=e.multiply(I,f.clone()),I=e.multiply(d.e(1).clone(),f);return e.add(e.subtract(v,I),d.e(2).clone())},PartFrac:{createTemplate:function(d,c,u,f){(d=j.Factor.factor(d)).each(function(Ue,Le){var Ve;Ue.group===L&&Ue.fname===""&&Ue.args[0].group===l&&(Ve=Ue.args[0],this.symbols?(delete this.symbols[Le],this.symbols[Ve.value]=Ve):d=Ue.args[0])});for(var v=c.collectFactors(),I=[],q=[],V=new ee(1),Q=0;Q<v.length;Q++){var le=ee.unwrapPARENS(v[Q]);if(le.power.greaterThan(1))for(var ye=Number(le.power),Ae=le.clone().toLinear(),je=Number(j.degree(Ae,f)),it=0;it<ye;it++){var yt=e.pow(Ae.clone(),new ee(it+1)),me=(u.push(yt.clone()),e.divide(d.clone(),yt.clone()));q.push(je),I.push(me)}else je=Number(j.degree(le,f)),u.push(le),me=e.divide(d.clone(),le.clone()),me=e.expand(ee.unwrapPARENS(me)),q.push(je),I.push(me)}return[u=u.map(function(Ue){return e.multiply(Ue,V.clone())}),I,q]},partfrac:function(d,c,u){var f=de(d);c=c||e.parse(f[0]);try{var v,I,q,V,Q,le,ye,Ae,je,it,yt,me,Ue,Le,Ve,lt=e.expand(d.getNum()),Nt=e.expand(d.getDenom().toUnitMultiplier());if(lt.multiplier=d.multiplier,q=lt.groupTerms(c),Number(j.degree(lt,c))>=Number(j.degree(Nt,c))?(Ae=(ye=j.div(lt.clone(),e.expand(Nt.clone())))[0],q=(lt=ye[1]).groupTerms(c)):Ae=new ee(0),Number(j.degree(Nt,c))===1)return Ue=e.divide(lt,Nt),u?[Ae,Ue]:e.add(Ae,Ue);I=j.Factor.factor(Nt),yt=j.PartFrac.createTemplate(Nt.clone(),I,[],c),me=yt[0],je=yt[1],V=yt[2],le=[q.length],Q=[],v=[],it=[],je.map(function(pe,ue){Le=me[ue],Ve=V[ue];for(var st=0;st<Ve;st++){v.push(Le.clone());var se=ee.create(c,st),te=e.expand(e.multiply(pe,se.clone())).groupTerms(c),D=te.length;le.push(D),Q.push(te),it.push(se.clone())}});for(var Ct=t.Utils.arrayMax(le),Xe=new t.Matrix(t.Utils.fillHoles(q,Ct)).transpose(),he=new t.Matrix,et=0;et<Q.length;et++)he.elements.push(t.Utils.fillHoles(Q[et],Ct));var Lt=e.multiply(he.transpose().invert(),Xe),H=u?[Ae]:Ae;return Lt.each(function(pe,ue){pe=e.multiply(it[ue],e.divide(pe,v[ue])),u?H.push(pe):H=e.add(H,pe)}),H}catch(pe){try{if(d.isComposite()){var P,B={},fe=(d.each(function(se){var st=se.getDenom(),se=se.getNum(),te=B[st];B[st]=te?e.add(te,se):se}),new ee(0));for(P in B)fe=e.add(fe,e.divide(B[P],e.parse(P)));d=fe}}catch(ue){}}return d}},degree:function(d,c,u){if(u=u||{nd:[],sd:[],depth:0},!c){var f=de(d);if(1<f.length)throw new Error("You must specify the variable for multivariate polynomials!");if(f.length===0)return new ee(0);c=e.parse(f[0])}return f=d.group,d.isComposite()?((d=d.clone()).distributeExponent(),d.each(function(v){u.depth++,j.degree(v,c,u),u.depth--})):d.group===R?d.each(function(v){u.depth++,j.degree(v,c,u),u.depth++}):f===h&&d.value===c.value?u.sd.push(d.power.clone()):f===l&&d.value===c.value?u.nd.push(e.parse(d.power)):u.nd.push(new ee(0)),f=0<u.nd.length?t.Utils.arrayMax(u.nd):void 0,u.depth===0&&0<u.sd.length?(f!==void 0&&u.sd.unshift(f),e.symfunction("max",u.sd)):t.Utils.isSymbol(f)?f:e.parse(f)},sqComplete:function(d,c,u){t.Utils.isSymbol(c)||(c=e.parse(c));function f(ye){throw new t.exceptions.ValueLimitExceededError(ye=ye||"Stopping")}var v,I,q,V,Q,le;return d.isPoly(!0)||f("Must be a polynomial!"),le=t.Utils.inBrackets,d=d.clone(),(V=t.Algebra.degree(d,c)).equals(2)||f("Cannot complete square for degree "+V),d=(V=t.Algebra.coeffs(d,c))[2],Q=V[1].sign(),q=e.divide(V[1],new ee(2)),v=e.pow(q.clone(),new ee(2)),u?[d,q,I]:(u=ze.sqrt(d),q=e.divide(ze.sqrt(v),u.clone()),I=e.subtract(V[0],e.pow(q.clone(),new ee(2))),{a:d=e.parse(le(u.clone()+"*"+c+(Q<0?"-":"+")+q)),c:I,f:e.add(e.pow(d.clone(),new ee(2)),I.clone())})},Simplify:{strip:function(d){var c=e.parse(d.multiplier),u=(d.toUnitMultiplier(),e.parse(d.power));return d.toLinear(),[c,u,d]},unstrip:function(f,c){var u=f[0],f=f[1];return e.multiply(u,e.pow(c,f))},complexSimp:function(I,u){var q=I.realpart(),I=I.imagpart(),V=u.realpart(),u=u.imagpart(),f=e.multiply(q.clone(),V.clone()),v=e.multiply(I.clone(),u.clone()),I=e.multiply(V.clone(),I),q=e.multiply(q,u.clone()),V=e.add(e.pow(V,new ee(2)),e.pow(u,new ee(2)));return e.divide(e.add(e.add(f,v),e.multiply(e.subtract(I,q),ee.imaginary())),V)},trigSimp:function(d){var c,u,f,v,I,q;return d.containsFunction(["cos","sin","tan"])&&(d=d.clone(),u=(d=(c=j.Simplify.strip(d)).pop()).clone(),d.group===_?(f=new ee(0),d.each(function(V){V=j.Simplify.trigSimp(V.fnTransform()),f=e.add(f,V)},!0),u=e.pow(e.multiply(new ee(d.multiplier),f),new ee(d.power))):d.group===R&&(v=d.getNum(),I=d.getDenom(),(u=v.fname==="sin"&&I.fname==="cos"&&v.args[0].equals(I.args[0])&&v.power.equals(I.power)?e.parse(t.Utils.format("({0})*({1})*tan({2})^({3})",I.multiplier,v.multiplier,v.args[0],v.power)):u).group===R&&(q=new ee(1),u.each(function(V){V.fname==="tan"&&(V=e.parse(t.Utils.format("({0})*sin({1})^({2})/cos({1})^({2})",V.multiplier,j.Simplify.simplify(V.args[0]),V.power))),q=e.multiply(q,V)}),u=q)),d=u=j.Simplify.unstrip(c,u).distributeMultiplier()),d},fracSimp:function(d){var c=d.getDenom();if((d=(V=d.getNum()).isImaginary()&&c.isImaginary()?j.Simplify.complexSimp(V,c):d).isComposite()){for(var u,f,v,I,q,V,Q=(d=1<d.power?e.expand(d):d).collectSymbols(),le=Q.pop();Q.length;)f=Q.pop(),u=e.parse(le.getDenom()),I=e.parse(f.getDenom()),v=le.getNum(),f=f.getNum(),q=e.multiply(u.clone(),I.clone()),v=e.multiply(v,I),I=e.multiply(f,u),f=e.add(v,I),le=e.divide(f,q);return c=e.expand(le.getDenom()),(V=(V=e.expand(le.getNum())).isImaginary()&&c.isImaginary()?j.Simplify.complexSimp(V,c):e.divide(V,c)).equals(d)?d:j.Simplify.simplify(V)}return d},ratSimp:function(d){var c,u;return d.group===R&&(c=d.getDenom(),u=d.getNum().distributeMultiplier(),c=j.Simplify.fracSimp(c),u=j.Simplify.fracSimp(u),d=e.divide(u,c)),d},sqrtSimp:function(d,c){if(d.isSQRT()){var u,f,v=j.Factor.factor(d.args[0].clone()),I=e.parse(v.multiplier),q=I.sign(),V=e.sqrt(I.abs());if(Qe(V))return v.group===R?(u=new ee(1),v.each(function(Q){var le;Q.group===r&&(le=e.sqrt(Q.clone()),Qe(le))?V=e.multiply(V,le):u=e.multiply(u,Q)}),I=e.multiply(u,e.parse(q)),(f=e.sqrt(I.clone())).isImaginary&&(f=e.sqrt(e.expand(I.clone())))):f=e.sqrt(v.clone().toUnitMultiplier()),e.multiply(V,f)}else d.isComposite()&&d.isLinear()?(V=new ee(0),d.each(function(Q){V=e.add(V,j.Simplify.sqrtSimp(Q))},!0),V=e.multiply(V,e.parse(d.multiplier))):d.group===R&&(V=e.parse(d.multiplier),d.each(function(Q){Q=j.Simplify.sqrtSimp(Q),V=e.multiply(V,Q)},!0),V=e.pow(V,e.parse(d.power)));return V||e.parse(d)},patternSub:function(d){function c(v){v.each(function(I){var q;!I.symbols&&I.group!==L||(f(I)?c(I):u[I.value]||(q=t.Utils.getU(d),u[I.value]=q,d=d.sub(I.value,q)))},!0)}var u={},f=function(v){var I=!1;return v.each(function(q){q.group===_?I=!0:q.symbols&&(I=f(q))}),I};return c(d),[d,u]},simplify:function(d){var c,u,f=j.Simplify.strip(d);return d=f.pop(),(d=j.Simplify.fracSimp(d)).isConstant()||d.group===t.groups.S?f.push(d):(d=d.clone(),d=j.Simplify.trigSimp(d),d=j.Simplify.ratSimp(d),(d=j.Factor.factor(d)).group===t.groups.CP&&d.isLinear()&&(c=d.multiplier.clone(),d.toUnitMultiplier(),u=new ee(0),d.each(function(v){v=j.Simplify.simplify(v),u=e.add(u,v)}),(d=u).multiplier=u.multiplier.multiply(c))),j.Simplify.unstrip(f,d)}},Classes:{Polynomial:Oe,Factors:ut,MVTerm:at}};t.Expression.prototype.simplify=function(){return j.Simplify.simplify(this.symbol)},fr.useAlgebraDiv=function(){var d=j.divideFn=e.divide,c=0;e.divide=function(u,f){return u=++c===1?t.Algebra.divide(u,f):d(u,f),c=0,u}},fr.useParserDiv=function(){j.divideFn&&(e.divide=j.divideFn),delete j.divideFn},fr.register([{name:"factor",visible:!0,numargs:1,build:function(){return j.Factor.factor}},{name:"simplify",visible:!0,numargs:1,build:function(){return j.Simplify.simplify}},{name:"gcd",visible:!0,numargs:[1],build:function(){return j.gcd}},{name:"lcm",visible:!0,numargs:[1],build:function(){return j.lcm}},{name:"roots",visible:!0,numargs:-1,build:function(){return j.roots}},{name:"divide",visible:!0,numargs:2,build:function(){return j.divide}},{name:"div",visible:!0,numargs:2,build:function(){return j.div}},{name:"partfrac",visible:!0,numargs:[1,2],build:function(){return j.PartFrac.partfrac}},{name:"deg",visible:!0,numargs:[1,2],build:function(){return j.degree}},{name:"coeffs",visible:!0,numargs:[1,2],build:function(){return function(){var d=j.coeffs.apply(j,arguments);return new t.Vector(d)}}},{name:"line",visible:!0,numargs:[2,3],build:function(){return j.line}},{name:"sqcomp",visible:!0,numargs:[1,2],build:function(){return function(d,c){try{return c=c||de(d)[0],j.sqComplete(d.clone(),c).f}catch(u){return d}}}}]),fr.updateAPI()}(),typeof ti!="undefined"&&fr===void 0&&(fr=N0(),z0()),function(){"use strict";var t=fr.getCore(),e=t.PARSER,r=t.Frac,a=t.Settings,l=t.Utils.isSymbol,h=(t.groups.FN,t.Symbol),L=t.Utils.text,M=t.Utils.inBrackets,_=t.Utils.isInt,R=t.Utils.format,ie=t.Utils.even,K=t.Utils.evaluate,de=t.groups.N,ve=t.groups.S,De=t.groups.FN,Ie=t.groups.PL,Qe=t.groups.CP,ee=t.groups.CB,Te=t.groups.EX,ze=t.groups.P,Oe=a.LOG,ut="sqrt",at="sin",j="cos",d="tan",c="sec",u="csc",f="cot",v="asin",I="atan",q="sinh",V="cosh",Q="tanh";function le(Ue){this.message=Ue||""}le.prototype=new Error,h.prototype.hasIntegral=function(){return this.containsFunction("integrate")},h.prototype.fnTransform=function(){if(this.group!==De)return this;var Ue,Le,Ve,lt=this.args[0],Nt=new h(this.multiplier),Ct=this.clone().toUnitMultiplier();if(this.isLinear())switch(this.fname){case q:Ve=e.parse(R("(e^({0})-e^(-({0})))/2",lt));break;case V:Ve=e.parse(R("(e^({0})+e^(-({0})))/2",lt));break;case Q:Ve=e.parse(R("(e^({0})-e^(-({0})))/(e^({0})+e^(-({0})))",lt));break;case d:Ve=e.parse(R("sin({0})/cos({0})",lt));break;case u:Ve=e.parse(R("1/sin({0})",lt));break;case c:Ve=e.parse(R("1/cos({0})",lt));break;default:Ve=Ct}else if(this.power.equals(2))switch(this.fname){case at:Ve=e.parse(R("1/2-cos(2*({0}))/2",lt));break;case j:Ve=e.parse(R("1/2+cos(2*({0}))/2",lt));break;case d:Ve=e.parse(R("sin({0})^2/cos({0})^2",lt));break;case V:Ve=e.parse(R("1/2+cosh(2*({0}))/2",lt));break;case q:Ve=e.parse(R("-1/2+cosh(2*({0}))/2",lt));break;case Q:Ve=e.parse(R("(1+cosh(2*({0})))/(-1+cosh(2*({0})))",lt));break;case c:Ve=e.parse(R("(1-cos(2*({0})))/(1+cos(2*({0})))+1",lt));break;default:Ve=Ct}else this.fname===c?Ve=e.parse(R("1/cos({0})^({1})",this.args[0],this.power)):this.fname===u?Ve=e.parse(R("1/sin({0})^({1})",this.args[0],this.power)):this.fname===d?Ve=this.power.lessThan(0)?e.parse(R("cos({0})^(-({1}))/sin({0})^({1})",this.args[0],this.power.negate())):e.parse(R("sin({0})^({1})/cos({0})^({1})",this.args[0],this.power)):this.fname===at&&this.power.lessThan(0)?Ve=e.parse(R("csc({0})^(-({1}))",this.args[0],this.power.negate())):this.fname===j&&this.power.lessThan(0)?Ve=e.parse(R("sec({0})^(-({1}))",this.args[0],this.power.negate())):this.fname===at&&this.power.equals(3)?Ve=e.parse(R("(3*sin({0})-sin(3*({0})))/4",this.args[0])):this.fname===j&&this.power.equals(3)?Ve=e.parse(R("(cos(3*({0}))+3*cos({0}))/4",this.args[0])):this.fname!==j&&this.fname!==at||!ie(this.power)?Ve=Ct:(Ue=this.power/2,Le=e.pow(this.clone().toLinear(),e.parse(2)).fnTransform(),Le=e.expand(e.pow(Le,e.parse(Ue))),Ve=new h(0),Le.each(function(Xe){Xe=Xe.fnTransform(),Ve=e.add(Ve,Xe)},!0));return e.multiply(Ve,Nt)},h.prototype.hasTrig=function(){if(!this.isConstant(!0)&&this.group!==ve){if(this.fname&&(t.Utils.in_trig(this.fname)||t.Utils.in_inverse_trig(this.fname)))return!0;if(this.symbols){for(var Ue in this.symbols)if(this.symbols[Ue].hasTrig())return!0}}return!1},t.Expression.prototype.hasIntegral=function(){return this.symbol.hasIntegral()},t.Utils.toCommonDenominator=function(Ue){var Le,Ve,lt;return Ue.isComposite()&&Ue.isLinear()?(Le=new h(Ue.multiplier),Ve=new h(1),lt=new h(0),Ue.each(function(Nt){Ve=e.multiply(Ve,Nt.getDenom())},!0),Ue.each(function(Ct){var Xe=Ct.getNum(),Ct=Ct.getDenom(),Xe=e.multiply(Xe,e.divide(Ve.clone(),Ct));lt=e.add(lt,Xe)}),e.multiply(Le,t.Algebra.divide(e.expand(lt),e.expand(Ve)))):Ue},t.Utils.in_inverse_trig=function(Ue){return[v,"acos",I,"acsc","asec","acot"].indexOf(Ue)!==-1},t.Utils.in_trig=function(Ue){return[j,at,d,c,u,f].indexOf(Ue)!==-1},t.Utils.in_htrig=function(Ue){return[q,V,Q,"acsch","asech","acoth"].indexOf(Ue)!==-1},t.Matrix.jacobian=function(Ue,Le){var Ve=new t.Matrix;return(Le=Le||t.Utils.arrayGetVariables(Ue)).forEach(function(lt,Nt){Ue.forEach(function(Ct,Xe){Ct=t.Calculus.diff(Ct.clone(),lt),Ve.set(Xe,Nt,Ct)})}),Ve},t.Matrix.prototype.max=function(){var Ue=new h(0);return this.each(function(Le){Le=Le.abs(),Le.gt(Ue)&&(Ue=Le)}),Ue},t.Matrix.cMatrix=function(Ue,Le){var Ve=new t.Matrix;return Le.forEach(function(lt,Nt){Ve.set(Nt,0,e.parse(Ue))}),Ve};var ye=t.Utils.all_functions=function(Ue){for(var Le=0,Ve=Ue.length;Le<Ve;Le++)if(Ue[Le].group!==De)return!1;return!0},Ae=t.Utils.cosAsinBtranform=function(Ue,Le){return Ue=Ue.args[0],Le=Le.args[0],e.parse(R("(sin(({0})+({1}))-sin(({0})-({1})))/2",Ue,Le))},je=t.Utils.cosAsinAtranform=function(Ue,Le){return Number(Le.power)!==1?e.multiply(Ue,Le):(Le=Ue.args[0],e.parse(R("(sin(2*({0})))/2",Le)))},it=t.Utils.cosAsinBtranform=function(Ue,Le){return Ue=Ue.args[0],Le=Le.args[0],e.parse(R("(cos(({0})+({1}))-cos(({0})-({1})))/2",Ue,Le))},yt=t.Utils.trigTransform=function(Ue){for(var Le,Ve,lt,Nt,Ct={},Xe=new h(1),he=0,et=Ue.length;he<et;he++)(lt=Ue[he]).group===De?(Ve=lt.fname)===j&&Ct.sin?(Le=(Ct.sin.args[0].toString()!==lt.args[0].toString()?Ae:je)(lt,Ct.sin),delete Ct.sin,Xe=e.multiply(Xe,Le)):Ve===at&&Ct.cos?(Le=(Ct.cos.args[0].toString()!==lt.args[0].toString()?Ae:je)(lt,Ct.cos),delete Ct.cos,Xe=e.multiply(Xe,Le)):Ve===at&&Ct.sin?(Le=Ct.sin.args[0].toString()!==lt.args[0].toString()?it(lt,Ct.sin):e.multiply(lt,Ct.sin),delete Ct.sin,Xe=Le):Ct[Ve]=lt:Xe=e.multiply(Xe,lt);for(Nt in Ct)Xe=e.multiply(Xe,Ct[Nt]);return Xe},me=(t.Settings.integration_depth=10,t.Settings.max_lim_depth=10,t.Calculus={version:"1.4.6",sum:function(Ue,Le,Ve,lt){if(Le.group!==t.groups.S)throw new t.exceptions.NerdamerTypeError("Index must be symbol. "+L(Le)+" provided");var Nt;return Le=Le.value,t.Utils.isNumericSymbol(Ve)&&t.Utils.isNumericSymbol(lt)?(Nt=lt-Ve<200?"":"PARSE2NUMBER",Ve=Number(Ve),lt=Number(lt),t.Utils.block(Nt,function(){for(var Ct=Ue.text(),Xe={"~":!0},he=new t.Symbol(0),et=Ve;et<=lt;et++){Xe[Le]=new h(et);var Lt=e.parse(Ct,Xe),he=e.add(he,Lt)}return he})):e.symfunction("sum",arguments)},product:function(Ue,Le,Ve,lt){if(Le.group!==t.groups.S)throw new t.exceptions.NerdamerTypeError("Index must be symbol. "+L(Le)+" provided");var Nt;return Le=Le.value,t.Utils.isNumericSymbol(Ve)&&t.Utils.isNumericSymbol(lt)?(Nt=lt-Ve<200?"":"PARSE2NUMBER",t.Utils.block(Nt,function(){Ve=Number(Ve),lt=Number(lt.multiplier);for(var Ct=Ue.text(),Xe={},he=new t.Symbol(1),et=Ve;et<=lt;et++)Xe[Le]=new h(et),he=e.multiply(he,e.parse(Ct,Xe));return he})):e.symfunction("product",arguments)},diff:function(Ue,Le,Ve){var lt,Nt,Ct,Xe,he;return t.Utils.isVector(Ue)?(lt=new t.Vector([]),Ue.each(function(P){lt.elements.push(me.diff(P,Le,Ve))}),lt):t.Utils.isMatrix(Ue)?(Nt=new t.Matrix,Ue.each(function(P,B,fe){Nt.set(B,fe,me.diff(P,Le,Ve))}),Nt):(Ct=l(Le)?Le.text():Le,Ve=l(Ve)?Ve.multiplier:Ve||1,Ct===void 0&&(Ct=t.Utils.variables(Ue)[0]),Ue.group===De&&Ue.fname===ut&&(he=Ue.args[0],Xe=Ue.power.clone(),he.group===de&&he.group===ze||(he.power=l(he.power)?e.multiply(he.power,e.multiply(new h(.5)),Xe):he.power.multiply(new r(.5)).multiply(Xe),he.multiplier=he.multiplier.multiply(Ue.multiplier)),Ue=he),Ue=Ue.group!==De||l(Ue.power)?Lt(Ue):(Xe=Lt(e.parse(Ue)),he=me.diff(Ue.args[0].clone(),Ct),e.multiply(Xe,he)),1<Ve&&(Ve--,Ue=me.diff(Ue,Le,Ve)),Ue);function et(P){return P.value!==Ct&&!P.contains(Ct,!0)||(P.multiplier=P.multiplier.multiply(P.power),P.power=P.power.subtract(new r(1)),P.power.equals(0)&&(P=h(P.multiplier))),P}function Lt(P){var B,fe=P.group;if(fe===de||fe===ve&&P.value!==Ct||fe===ze)P=h(0);else if(fe===ve)P=et(P);else{if(fe===ee)return B=P.multiplier.clone(),P.toUnitMultiplier(),(st=e.multiply(function(re){for(var J=re.collectSymbols(),Ee=new h(0),xe=J.length,Ce=0;Ce<xe;Ce++){for(var Ke=me.diff(J[Ce].clone(),Ct),Ne=0;Ne<xe;Ne++)Ce!==Ne&&(Ke=e.multiply(Ke,J[Ne].clone()));Ee=e.add(Ee,Ke)}return Ee}(P),et(P))).multiplier=st.multiplier.multiply(B),st;if(fe===De&&P.power.equals(1))switch(P.fname){case Oe:pe=P.clone(),(P=P.args[0].clone()).power=P.power.negate(),P.multiplier=pe.multiplier.divide(P.multiplier);break;case j:P.fname=at,P.multiplier.negate();break;case at:P.fname=j;break;case d:P.fname=c,P.power=new r(2);break;case c:P=H(P,d);break;case u:P=H(P,"-cot");break;case f:P.fname=u,P.multiplier.negate(),P.power=new r(2);break;case v:P=e.parse("(sqrt(1-("+L(P.args[0])+")^2))^(-1)");break;case"acos":P=e.parse("-(sqrt(1-("+L(P.args[0])+")^2))^(-1)");break;case I:P=e.parse("(1+("+L(P.args[0])+")^2)^(-1)");break;case"abs":B=P.multiplier.clone(),P.toUnitMultiplier(),(se=P.args[0].clone()).toUnitMultiplier(),(P=e.parse(M(L(P.args[0]))+"/abs"+M(L(se)))).multiplier=B;break;case"parens":P=h(1);break;case"cosh":P.fname="sinh";break;case"sinh":P.fname="cosh";break;case Q:P.fname="sech",P.power=new r(2);break;case"sech":P=H(P,"-tanh");break;case"csch":var ue=String(P.args[0]);return e.parse("-coth("+ue+")*csch("+ue+")");case"coth":return ue=String(P.args[0]),e.parse("-csch("+ue+")^2");case"asinh":P=e.parse("(sqrt(1+("+L(P.args[0])+")^2))^(-1)");break;case"acosh":P=e.parse("(sqrt(-1+("+L(P.args[0])+")^2))^(-1)");break;case"atanh":P=e.parse("(1-("+L(P.args[0])+")^2)^(-1)");break;case"asech":ue=String(P.args[0]),P=e.parse("-1/(sqrt(1/("+ue+")^2-1)*("+ue+")^2)");break;case"acoth":P=e.parse("-1/(("+P.args[0]+")^2-1)");break;case"acsch":ue=String(P.args[0]),P=e.parse("-1/(sqrt(1/("+ue+")^2+1)*("+ue+")^2)");break;case"asec":ue=String(P.args[0]),P=e.parse("1/(sqrt(1-1/("+ue+")^2)*("+ue+")^2)");break;case"acsc":ue=String(P.args[0]),P=e.parse("-1/(sqrt(1-1/("+ue+")^2)*("+ue+")^2)");break;case"acot":P=e.parse("-1/(("+P.args[0]+")^2+1)");break;case"S":ue=String(P.args[0]),P=e.parse("sin((pi*("+ue+")^2)/2)");break;case"C":ue=String(P.args[0]),P=e.parse("cos((pi*("+ue+")^2)/2)");break;case"Si":ue=P.args[0],P=e.parse("sin("+ue+")/("+ue+")");break;case"Shi":ue=P.args[0],P=e.parse("sinh("+ue+")/("+ue+")");break;case"Ci":ue=P.args[0],P=e.parse("cos("+ue+")/("+ue+")");break;case"Chi":ue=P.args[0],P=e.parse("cosh("+ue+")/("+ue+")");break;case"Ei":ue=P.args[0],P=e.parse("e^("+ue+")/("+ue+")");break;case"Li":ue=P.args[0],P=e.parse("1/"+a.LOG+"("+ue+")");break;case"erf":P=e.parse("(2*e^(-("+P.args[0]+")^2))/sqrt(pi)");break;case"atan2":var pe=String(P.args[0]),ue=String(P.args[1]);P=e.parse("("+ue+")/(("+ue+")^2+("+pe+")^2)");break;case"sign":P=new h(0);break;case"sinc":P=e.parse(R("(({0})*cos({0})-sin({0}))*({0})^(-2)",P.args[0]));break;case a.LOG10:P=e.parse("1/(("+P.args[0]+")*"+a.LOG+"(10))");break;default:P=e.symfunction("diff",[P,Le])}else if(fe===Te||fe===De&&l(P.power)){var st=fe===Te?P.value:fe===De&&P.contains(Ct)?P.fname+M(L(P.args[0])):P.value+M(L(P.args[0])),se=(e.multiply(e.parse(Oe+M(st)),P.power.clone()),me.diff(e.multiply(e.parse(Oe+M(st)),P.power.clone()),Ct));P=e.multiply(P,se)}else if(fe!==De||P.power.equals(1)){if(fe===Qe||fe===Ie){var te,st=P.clone(),D=new h(0);for(te in P.symbols)D=e.add(D,me.diff(P.symbols[te].clone(),Ct));P=e.multiply(et(st),D)}}else(se=P.clone()).toLinear(),se.toUnitMultiplier(),P=e.multiply(et(P.clone()),Lt(se))}return P.updateHash(),P}function H(P,B,fe){return e.multiply(P,e.parse(B+M(fe||L(P.args[0]))))}},integration:{u_substitution:function(he,Le){function Ve(fe,pe,se){var st=me.diff(pe,Le),se=se?se(fe,pe):e.divide(fe.clone(),st);return se.contains(Le,!0)?null:se}function lt(fe,pe){return fe=me.integrate(e.symfunction(fe,[new h(H)]),H,0),(fe=fe.sub(new h(H),pe)).updateHash(),fe}var Nt,Ct,Xe=he[0].clone(),he=he[1].clone(),et=Xe.group,Lt=he.group,H="__u__";if(et===De&&Lt!==De)return(Nt=Ve(he,(P=Xe.args[0]).clone()))?e.multiply(Nt,lt(Xe.fname,P)):(Nt=Ve(he,Xe))?me.integration.poly_integrate(Xe):void 0;if(Lt===De&&et!==De)return(Nt=Ve(Xe,(P=he.args[0]).clone()))?e.multiply(Nt,lt(he.fname,P)):void 0;if(et===De&&Lt===De)return(Nt=Ve(Xe.clone(),he.clone()))||(Nt=Ve(he.clone(),Xe.clone()))?e.multiply(me.integration.poly_integrate(he),Nt):void 0;if(et!==Te||Lt===Te)return Lt===Te&&et!==Te?(Nt=Ve(Xe,(Ct=he.power).clone()),B=me.integrate(he.sub(Ct,new h(H)),H,0),e.multiply(B.sub(new h(H),Ct),Nt)):Xe.isComposite()||he.isComposite()?(P=function(fe,pe){return pe=me.diff(pe,Le),fe=t.Algebra.Factor.factor(fe),pe=t.Algebra.Factor.factor(pe),e.divide(fe,pe)},Lt=Xe.isComposite()?Xe.clone().toLinear():Xe.clone(),et=he.isComposite()?he.clone().toLinear():he.clone(),(Nt=Ve(Lt.clone(),et.clone(),P))?e.multiply(me.integration.poly_integrate(he),Nt):(Nt=Ve(et.clone(),Lt.clone(),P))?e.multiply(me.integration.poly_integrate(Xe),Nt):void 0):void 0;if(!(Nt=Ve(he,(Ct=Xe.power).clone()))){var et=me.integration.decompose_arg(Ct.clone(),Le),Lt=me.diff(et[2].clone(),Le),P=me.integration.decompose_arg(Lt.clone(),Le);if(e.multiply(et[1],P[1]).power.equals(he.power))return Lt=e.divide(et[0].clone(),P[0].clone()),he=e.multiply(Lt.clone(),e.pow(new h(Xe.value),e.multiply(et[0],new h(H)))),he=e.multiply(he,new h(H)),me.integration.by_parts(he,H,0,{}).sub(H,et[1].clone())}var B=me.integrate(Xe.sub(Ct.clone(),new h(H)),H,0);return e.multiply(B.sub(new h(H),Ct),Nt)},poly_integrate:function(lt){var Le=lt.power.toString(),Ve=lt.multiplier.toDecimal(),lt=lt.toUnitMultiplier().toLinear();return Number(Le)===-1?e.multiply(new h(Ve),e.symfunction(Oe,[lt])):e.parse(R("({0})*({1})^(({2})+1)/(({2})+1)",Ve,lt,Le))},stop:function(Ue){throw t.Utils.warn(Ue=Ue||"Unable to compute integral!"),new le(Ue)},partial_fraction:function(Ue,Le,Ve,lt){var Nt;return l(Le)||(Le=e.parse(Le)),Nt=new h(0),(Ue=t.Algebra.PartFrac.partfrac(Ue,Le)).group===ee&&Ue.isLinear()?(Ue.each(function(Ct){Ct.isLinear()||me.integration.stop()}),Ue.each(function(Ct){Nt=e.add(Nt,me.integrate(Ct,Le,Ve,lt))})):Nt=e.add(Nt,me.integrate(Ue,Le,Ve,lt)),Nt},get_udv:function(Ue){function Le(H){var P,B=H.group;B===De?(P=H.fname,t.Utils.in_trig(P)||t.Utils.in_htrig(P)?Ve[3].push(H):t.Utils.in_inverse_trig(P)?Ve[1].push(H):P===Oe?Ve[0].push(H):me.integration.stop()):B===ve||H.isComposite()&&H.isLinear()||B===ee&&H.isLinear()?Ve[2].push(H):B===Te||H.isComposite()&&!H.isLinear()?Ve[4].push(H):me.integration.stop()}var Ve=[[],[],[],[],[]];Ue.group===ee?Ue.each(function(H){Le(h.unwrapSQRT(H,!0))}):Le(Ue);for(var lt,Nt=new h(1),Ct=0;Ct<5;Ct++){var Xe=Ve[Ct],he=Xe.length;if(0<he){if(1<he)for(var et=new h(1),Lt=0;Lt<he;Lt++)et=e.multiply(et,Xe[Lt].clone());else et=Xe[0].clone();lt?Nt=e.multiply(Nt,et):(lt=et).multiplier=lt.multiplier.multiply(Ue.multiplier)}}return[lt,Nt]},trig_sub:function(Ue,et,Ve,lt,Lt,Ct){(Lt=Lt||me.integration.decompose_arg(Ue.clone().toLinear(),et))[3],Lt[2];var Xe,he,et=Lt[0],Lt=Lt[1];if(Lt.power.equals(2)&&et.greaterThan(0))return et=t.Utils.getU(Ue),Xe=e.parse(d+M(et)),he=e.parse(c+M(et)+"^2"),Ue=e.multiply(Ue.sub(Lt,Xe),he),he=me.integrate(Ue,et,Ve,lt).sub(Xe,Lt),t.Utils.clearU(Xe),he},by_parts:function(Ue,Le,Ve,lt){var Nt,Ct,Xe,he,et,Lt;return lt.previous=lt.previous||[],Ct=(Ue=me.integration.get_udv(Ue))[0],Ue=Ue[1],Xe=(Nt=h.unwrapSQRT(e.expand(me.diff(Ct.clone(),Le)),!0)).clone().stripVar(Le),Nt=e.divide(Nt,Xe.clone()),et=me.integrate(Ue.clone(),Le,Ve||0),he=(Nt=e.multiply(et.clone(),Nt)).toString(),lt.previous.indexOf(he)!==-1&&t.Utils.in_trig(Ct.fname)&&Ue.isE()?(lt.is_cyclic=!0,new h(1)):(lt.previous.push(he),Ue=e.multiply(Ct,et),he=Nt.multiplier.clone(),Nt.toUnitMultiplier(),(Ct=e.multiply(me.integrate(Nt.clone(),Le,Ve,lt),Xe)).multiplier=Ct.multiplier.multiply(he),et=e.subtract(Ue,Ct),lt.is_cyclic&&(lt.previous.pop(),lt.previous.length===0&&(et=e.expand(et),Lt=new h(0),et.each(function(H){H.contains(Le)||(Lt=e.add(Lt,H.clone()))}),et=e.divide(e.subtract(et,Lt.clone()),e.subtract(new h(1),Lt)))),et)},decompose_arg:t.Utils.decompose_fn},integrate:function(Ue,Le,Ve,lt){var Nt,Ct;return Le||(Nt=t.Utils.variables(Ue),Le=(Le=Nt.length===1?Nt[0]:Le)||"x"),t.Utils.isVector(Ue)?(Ct=new t.Vector([]),Ue.each(function(Xe){Ct.elements.push(me.integrate(Xe,Le))}),Ct):(isNaN(Le)||e.error("variable expected but received "+Le),Ue.isConstant(!0)?e.multiply(Ue.clone(),e.parse(Le)):(lt=lt||{},t.Utils.block("PARSE2NUMBER",function(){Ve=Ve||0;var Xe,he=l(Le)?Le.toString():Le,et=(A=h.unwrapSQRT(Ue.clone(),!0)).group;try{if(++Ve>t.Settings.integration_depth&&me.integration.stop("Maximum depth reached. Exiting!"),A.contains(he,!0)){if(et===ve)Xe=me.integration.poly_integrate(A,he,Ve);else if(et===Te)if(A.previousGroup===De&&A.fname!=="sqrt"&&A.fname!==a.PARENTHESIS&&me.integration.stop(),A.contains(he)&&A.previousGroup!==De)A.power.contains(he)?me.integration.stop():((dn=me.diff(A.clone().toLinear(),he)).contains(he)&&me.integration.stop(),Xe=me.integration.poly_integrate(A,he,Ve));else{if((Ce=me.diff(A.power.clone(),he)).contains(he)){var Lt=Ce.stripVar(he);if((Ke=e.divide(Ce.clone(),Lt.clone())).group===ve&&Ke.isLinear())return Lt.multiplier=Lt.multiplier.divide(new r(2)),e.parse(R("({2})*(sqrt(pi)*erf(sqrt(-{0})*{1}))/(2*sqrt(-{0}))",Lt,he,A.multiplier));me.integration.stop()}A.isE()?Ce.isLinear()?Xe=A:Ce.isE()&&Ce.power.group===ve&&Ce.power.power.equals(1)?Xe=e.multiply(e.symfunction("Ei",[A.power.clone()]),A.power):me.integration.stop():(We=e.symfunction(Oe,[e.parse(A.value)]),Xe=e.divide(A,We)),Xe=e.divide(Xe,Ce)}else if(A.isComposite()&&A.isLinear()){var H=e.parse(A.multiplier);A.toUnitMultiplier(),Xe=new h(0),A.each(function(Dt){Xe=e.add(Xe,me.integrate(Dt,he,Ve))}),Xe=e.multiply(H,Xe)}else if(et===Qe)if((A=A.power.greaterThan(1)?e.expand(A):A).power.equals(1))Xe=new h(0),A.each(function(Dt){Xe=e.add(Xe,me.integrate(Dt,he,Ve))},!0);else{var P,B,fe,pe,ue,st,se,te,D,re=Number(A.power),H=A.multiplier.clone(),J=(A.toUnitMultiplier(),A.clone().toLinear()),Ee=(N=me.integration.decompose_arg(J,he))[3],xe=N[2],Ce=N[0],Ke=N[1];if(re===-1&&Ke.group!==Ie&&Ke.power.equals(2)){var Ne,We,ae,Ge,He,ge,Je,gt,ne,Se,qe,Be=!_(Ee)||0<Ee;Xe=Ke.group===ve&&Ke.power.equals(2)&&Be?(Ne=function(tn){var hn=new h(1);return tn.each(function(pn){hn=e.multiply(hn,pn.fname==="abs"?pn.args[0]:pn)}),hn},ae=Ce.clone(),Ge=Ee.clone(),ae=e.pow(ae,new h(.5)),Ge=e.pow(Ge,new h(.5)),We=e.multiply(Ne(Ge),Ne(ae)),ct=e.symfunction(I,[e.divide(e.multiply(Ce,Ke.toLinear()),We.clone())]),e.divide(ct,We)):Ke.group===ve&&Ke.isLinear()?e.divide(me.integration.poly_integrate(A),Ce):Ke.power.equals(4)?(qe=M,ae=e.parse(ut+qe(Ce)+"*"+he+"^2"),Ge=e.parse(ut+qe(2)+"*"+qe(Ce)+"^"+qe("1/4")+"*"+qe(Ee)+"^"+qe("1/4")+"*"+he),He=e.parse(ut+qe(Ee)),Mt=e.add(e.add(ae.clone(),Ge.clone()),He.clone()),nt=e.add(e.subtract(ae,Ge),He),ge=e.parse(ut+qe(2)+"*"+qe(Ee)+"^"+qe("3/4")),Je=e.parse(ut+qe(Ee)+"*"+qe(Ee)+"^"+qe("1/4")+"*"+he),gt=e.parse("2*"+qe(Ee)+"*"+ut+qe(2)+"*"+qe(Ee)+"^"+qe("1/4")),ne=e.divide(e.subtract(ge.clone(),Je.clone()),e.multiply(gt.clone(),nt)),Se=e.divide(e.add(ge,Je),e.multiply(gt,Mt.clone())),e.add(me.integrate(ne,he,Ve,lt),me.integrate(Se,he,Ve,lt))):me.integration.partial_fraction(A,he,Ve)}else if(re===-.5)Ke.group===ve&&Ke.power.equals(2)&&xe.multiplier.lessThan(0)&&!Ee.multiplier.lessThan(0)?(Ce.negate(),Xe=Ee.isConstant()&&Ce.isConstant()?(We=e.symfunction(ut,[Ce.clone()]),P=e.symfunction(ut,[e.multiply(Ce.clone(),Ee)]),e.divide(e.symfunction(v,[e.divide(xe.toLinear(),P)]),We)):(B=e.symfunction(ut,[Ce]),fe=e.multiply(B.clone(),Ke.clone().toLinear()),e.divide(e.symfunction(I,[e.divide(fe,e.symfunction(ut,[J.clone()]))]),B))):me.integration.stop();else if(re===.5&&Ke.power.equals(2)&&Ce.greaterThan(0))me.integration.stop();else if(Ke.isLinear()&&Ke.group!==Ie)Xe=e.divide(me.integration.poly_integrate(A),Ce);else{if(Ke.power.equals(2)&&Ce.greaterThan(0))return pe=e.parse(ut+M(Ce)),ue=e.parse(ut+M(Ee)),st=e.multiply(pe.clone(),ue.clone()).invert(),se=e.pow(Ee,new h(A.power)),te=t.Utils.getU(A),Bt=e.multiply(st,Ke.clone().toLinear()),D=e.parse(I+M(Bt)),rt=2*(Math.abs(A.power)-1),Jt=me.integrate(e.parse(j+M(te)+"^"+rt)),t.Utils.clearU(te),e.multiply(Jt.sub(te,D),se);if(A.group===ee||A.power.lessThan(0)){var ct=A.clone().toLinear(),wt=t.Algebra.Factor.factor(ct).toString()!==ct.toString();if(t.Algebra.degree(ct,e.parse(he)).equals(2)&&!wt)try{var Mt,qt,Ft=t.Algebra.sqComplete(ct,he);Bt=t.Utils.getU(ct),Mt=Ft.f.sub(Ft.a,Bt),qt=e.pow(Mt,e.parse(A.power)),Xe=me.integrate(qt,Bt).sub(Bt,Ft.a)}catch(tn){me.integration.stop()}else Xe=me.integration.partial_fraction(A,he,Ve,lt)}else Xe=me.integration.by_parts(A,he,Ve,lt)}Xe.multiplier=Xe.multiplier.multiply(H)}else if(et===De){var Tt=A.args[0],H=A.multiplier.clone();A.toUnitMultiplier();var Ze,ht,Et,Pt,Ye,nt,O,Z,g,Ce=(N=me.integration.decompose_arg(Tt,he))[0],Ke=N[1],E=A.fname;if(E===Oe||E===v||E==="acos"||E===I&&Ke.isLinear()){var T,re=A.power.toString();_(re)&&(Ve-=re),Xe=Tt.isComposite()?(Bt=t.Utils.getU(A),ct=e.pow(e.parse(Oe+M(Bt)),new h(re)),un=me.diff(Tt,he),T=e.multiply(ct,un),Jt=me.integrate(T,Bt,Ve,lt),e.multiply(e.parse(H),Jt.sub(Bt,Tt))):e.multiply(e.parse(H),me.integration.by_parts(A,he,Ve,lt))}else{if(E===d&&A.power.lessThan(0))return(en=A.clone()).power.negate(),en.fname=f,e.multiply(e.parse(H),me.integrate(en,he,Ve));if(!Ce.contains(he,!0)&&A.isLinear())if(E==="abs")(Ke=e.divide(Tt.clone(),Ce.clone())).group!==ve||Ke.power.lessThan(0)?me.integration.stop():Xe=t.Utils.even(Ke.power)?me.integrate(Tt,he,Ve):((g=me.integrate(Ke,he,Ve)).power=g.power.subtract(new r(1)),e.multiply(e.multiply(e.symfunction("abs",[Ke.toLinear()]),g),Ce));else{var s=A.args[0].group,x=me.integration.decompose_arg(Tt,he);switch((s!==Qe&&s!==ve&&s!==ee||!x[1].power.equals(1)||Tt.hasFunc())&&me.integration.stop(),E){case j:Xe=e.symfunction(at,[Tt]);break;case at:(Xe=e.symfunction(j,[Tt])).negate();break;case d:Xe=e.parse(R(a.LOG+"(sec({0}))",Tt));break;case c:Xe=e.parse(R(a.LOG+"(tan({0})+sec({0}))",Tt));break;case u:Xe=e.parse(R("-"+a.LOG+"(csc({0})+cot({0}))",Tt));break;case f:Xe=e.parse(R(a.LOG+"(sin({0}))",Tt));break;case q:Xe=e.symfunction(V,[Tt]);break;case V:Xe=e.symfunction(q,[Tt]);break;case Q:Xe=e.parse(R(a.LOG+"(cosh({0}))",Tt));break;case"asec":case"acsc":case"acot":case"asech":case"acsch":case"acoth":Xe=me.integration.by_parts(A,he,Ve,lt);break;case"sech":Xe=e.parse(R("atan(sinh({0}))",Tt));break;case"csch":Xe=e.parse(R(a.LOG+"(tanh(({0})/2))",Tt));break;case"coth":Xe=e.parse(R(a.LOG+"(sinh({0}))",Tt));break;case"exp":Xe=me.integrate(e.parse(R("e^({0})",Tt)),he,Ve);break;case"S":var Tt=A.args[0].clone(),C=(kt=me.integration.decompose_arg(Tt,he))[1],U=kt[0],G=kt[3];Xe=e.parse(R("(cos((1/2)*pi*(({1})+({0})*({2}))^2)+pi*(({1})+({0})*({2}))*S(({1})+({0})*({2})))/(({0})*pi)",U,G,Ke));break;case"C":Tt=A.args[0].clone(),C=(kt=me.integration.decompose_arg(Tt,he))[1],U=kt[0],G=kt[3],Xe=e.parse(R("(pi*(({1})+({0})*({2}))*C(({1})+({0})*({2}))-sin((1/2)*pi*(({1})+({0})*({2}))^2))/(({0})*pi)",U,G,C));break;case"erf":Tt=A.args[0].clone(),C=(kt=me.integration.decompose_arg(Tt,he))[1],U=kt[0],Xe=e.parse(R("e^(-(({2}))^2)/(({0})*sqrt(pi))+(1/({0})+({1}))*erf(({2}))",U,C,Tt));break;case"sign":Xe=e.multiply(A.clone(),Tt.clone());break;default:me.integration.stop()}Xe=e.divide(Xe,Ce)}else Ke.isLinear()?E===j||E===at?(re=Number(A.power),Xe=re<0?(A.fname=E===at?u:c,A.invert().updateHash(),me.integrate(A,he,Ve)):(Tt=A.args[0],Ze=A.clone(),ht=A.clone(),y=new h((re-1)/re),Et=e.multiply(Ce.clone(),new h(re)).invert(),Ze.power=Ze.power.subtract(new r(1)),ht.power=ht.power.subtract(new r(2)),dn=e.symfunction(E===j?at:j,[Tt.clone()]),E===at&&dn.negate(),e.add(e.multiply(e.multiply(Et,Ze),dn),e.multiply(y,me.integrate(e.parse(ht),he,Ve))))):E===d||E===f?A.args[0].isLinear(he)&&(rt=A.power.subtract(new r(1)).toString(),sn=A.clone().toUnitMultiplier(),Z=e.parse(R((E===f?"-":"")+"1/({2}*{0})*{3}({1})^({0})",rt,Tt,Ce,E)),sn.power=sn.power.subtract(new r(2)),sn.power.equals(0)&&(sn=e.parse(sn)),Xe=e.subtract(Z,me.integrate(sn,he,Ve))):E===c||E===u?(Pt=A.power.subtract(new r(1)).toString(),Ye=A.power.subtract(new r(2)).toString(),nt=E===c?d:f,sn=A.clone().toUnitMultiplier(),O=R((E===u?"-":"")+"1/({0}*{1})*{4}({3})^({2})*{5}({3})",Ce,Pt,Ye,Tt,E,nt),Z=e.parse(O),sn.power=sn.power.subtract(new r(2)),sn.power.equals(0)&&(sn=e.parse(sn)),Xe=e.add(Z,e.multiply(new h(Ye/Pt),me.integrate(sn,he,Ve)))):E!==V&&E!==q||!A.power.equals(2)?me.integration.stop():Xe=me.integrate(A.fnTransform(),he,Ve):me.integration.stop();Xe.multiplier=Xe.multiplier.multiply(H)}}else if(et===Ie)Xe=me.integration.partial_fraction(A,he,Ve);else if(et===ee){var Y=(A=A.getDenom().group===ve?e.expand(A):A).stripVar(he),ce=e.divide(A.clone(),Y.clone());if(Y.contains(he)&&(ce=e.multiply(ce,Y),Y=new h(1)),ce.group!==ee){if(ce.equals(1))return me.integrate(e.expand(A),he,Ve);ce.clone().toLinear().isPoly(!0)&&1<t.Utils.variables(ce).length&&(ce=t.Algebra.Factor.factor(ce)),Xe=me.integrate(ce,he,Ve)}else{var Me=ce.collectSymbols().sort(function(Dt,tn){return Dt.group===tn.group?Number(Dt.power)===Number(tn.power)?Dt<tn?1:-1:tn.power-Dt.power:tn.group-Dt.group}).map(function(Dt){return Dt=h.unwrapSQRT(Dt,!0),Dt.fname==="exp"?e.parse(R("({1})*e^({0})",Dt.args[0],Dt.multiplier)):Dt}),dt=Me.length;if(A.power<0){if(dt===2)return me.integrate(e.expand(A),he,Ve,lt)}else if(dt===2){try{Xe=me.integration.u_substitution(Me,he)}catch(Dt){}if(!Xe){var _t,$t,i,S,A,W,ke,Fe,ft,St,Vt,zt,oe,$,Ot,kt,xt,At,Gt,Kt,Jt,cn,nn,un,o,y,F,X,w,b,z,_e=Me[0].group,tt=Me[1].group,be=Me[0],$e=Me[1],pt=be.fname,vt=$e.fname;if(A=e.multiply(be.clone(),$e.clone()),_e===De&&tt===De)if(pt===Oe||vt===Oe)Xe=me.integration.by_parts(A.clone(),he,Ve,lt);else{Me.sort(function(Dt,tn){return tn.fname>Dt.fname});var p=be.args[0];p.isLinear()&&(p.group===Qe||p.group===ee||p.group===ve)||me.integration.stop(),Ke=(N=me.integration.decompose_arg(p,he))[1],Ce=N[0],Ke.isLinear()||me.integration.stop();var N,we,Re=$e.args[0];if(p.equals(Re))if(pt===at&&vt===j||pt===j&&vt===at)if(be.power.lessThan(0)&&me.integration.stop(),pt===at&&be.power.add($e.power).equals(0))be.fname=d,be.updateHash(),Xe=me.integrate(be,he,Ve);else if(ie(be.power)&&vt===j&&$e.power.lessThan(0)){var rt=Number(be.power)/2,mt=e.parse(R("(1-cos({0})^2)^({1})",be.args[0],rt));Xe=me.integrate(e.expand(e.multiply(mt,$e.clone())),he,Ve,lt)}else if(ie(be.power)&&vt===at&&$e.power.lessThan(0))rt=Number(be.power)/2,mt=e.parse(R("(1-sin({0})^2)^({1})",be.args[0],rt)),Xe=me.integrate(e.expand(e.multiply(mt,$e.clone())),he,Ve,lt);else{var It,Bt,Rt,jt,Ut,en,Wt=t.Utils.even(be.power),Qt=t.Utils.even($e.power);if(Xe=new h(0),Wt&&Qt)return Ce=(It=function(hn){var tn=hn.power/2,hn=hn.fname===j?"((1/2)+(cos(2*("+hn.args[0]+"))/2))^"+tn:"((1/2)-(cos(2*("+hn.args[0]+"))/2))^"+tn;return e.parse(hn)})(be),Ee=It($e),dn=e.multiply(Ce,Ee),(en=e.expand(dn)).each(function(Dt){Xe=e.add(Xe,me.integrate(Dt,he,Ve))}),e.multiply(Xe,Y);sn=Wt?(Bt=be,$e):(Bt=$e,be),Rt=Bt.fname===j?-1:1,jt=((rt=sn.power)-1)/2,Ut=e.parse("(1-"+Bt.fname+t.Utils.inBrackets(p)+"^2)^"+jt),(en=e.expand(e.multiply(new h(Rt),e.multiply(Bt.clone(),Ut)))).each(function(Dt){Xe=e.add(Xe,me.integration.poly_integrate(Dt.clone()))})}else pt===c&&vt===d&&Ke.isLinear()&&$e.isLinear()?Xe=e.parse(R("sec({0})^({1})/({1})",be.args[0],be.power)):pt===d&&vt===c&&Ke.isLinear()?be.isLinear()&&$e.isLinear()?Xe=e.divide(e.symfunction(c,[p.clone()]),Ce):ie(be.power)?(re=Number(be.power)/2,dn=e.parse(R("(sec({0})^2-1)^({1})",be.args[0],re)),Xe=me.integrate(e.expand(e.multiply(dn,$e)),he,Ve)):me.integration.stop():Xe=pt===c&&vt===j?(be.fname=j,be.invert().updateHash(),me.integrate(e.multiply(be,$e),he,Ve)):pt===at&&vt===u?($e.fname=at,$e.invert().updateHash(),me.integrate(e.multiply(be,$e),he,Ve)):(dn=pt!==d||vt!==j&&vt!==at||!$e.power.lessThan(0)?e.multiply(be.fnTransform(),$e.fnTransform()):e.multiply(be.fnTransform(),$e),me.integrate(e.expand(dn),he,Ve));else pt!==at&&pt!==j||vt!==at&&vt!==j?me.integration.stop():be.isLinear()&&$e.isLinear()?Xe=be.args[0].isLinear()&&$e.args[0].isLinear()?(vt===at?(xe=be.args[0],we=$e.args[0]):(we=be.args[0],xe=$e.args[0]),ct=e.parse(R("(sin(({1})+({0}))+sin(({1})-({0})))/2",xe.toString(),we.toString())),me.integrate(ct,he,Ve)):(vn=yt(Me),me.integrate(e.expand(vn),he,Ve)):(vn=new h(1),Me.map(function(Dt){Dt=Dt.fnTransform(),vn=e.multiply(vn,Dt)}),dn=e.expand(vn),(Xe=me.integrate(dn,he,Ve)).hasIntegral()&&(Xe=me.integrate(yt(vn.collectSymbols()),he,Ve)))}else 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h(he),xt)]))):me.integration.partial_fraction(A,he,Ve,lt)):W&&(Xe=me.integration.partial_fraction(A,he,Ve))):be.isComposite()&&$e.isComposite()?(Xe=new h(0),be.power.greaterThan(0)&&$e.power.greaterThan(0)?(en=e.expand(A)).each(function(Dt){Xe=e.add(Xe,me.integrate(Dt,he,Ve))},!0):(cn=Number(be.power),nn=Number($e.power),cn<0&&0<nn&&(dn=be,be=$e,$e=dn),cn===-1&&nn===-1?Xe=me.integration.partial_fraction(A,he):be.each(function(Dt){Dt=e.multiply(Dt,$e.clone()),Dt=me.integrate(Dt,he,Ve),Xe=e.add(Xe,Dt)}))):_e===Qe&&Me[0].power.greaterThan(0)?(be=e.expand(be),Xe=new h(0),be.each(function(Dt){Xe=e.add(Xe,me.integrate(e.multiply(Dt,$e.clone()),he,Ve))},!0)):_e===De&&tt===Te&&t.Utils.in_htrig(be.fname)?(be=be.fnTransform(),Xe=me.integrate(e.expand(e.multiply(be,$e)),he,Ve)):_e===De&&tt===Qe||tt===De&&_e===Qe?(tt===De&&_e===Qe&&(dn=be,be=$e,$e=dn),un=h.unwrapSQRT(me.diff(be.clone(),he),!0),o=h.unwrapSQRT($e,!0),un.power.equals(o.power)?(re=new h($e.power),F=un.clone().toLinear(),X=$e.clone().toLinear(),(y=t.Algebra.divide(F.toLinear(),X)).isConstant()&&(w=e.pow(y,re.negate()),Xe=e.multiply(w,me.integration.poly_integrate(be.clone())))):Xe=me.integration.by_parts(A,he,Ve,lt)):(b=be.clone().toLinear(),z=$e.clone().toLinear(),Xe=_e===Te&&tt===Te&&be.power.contains(he)&&$e.power.contains(he)&&!b.contains(he)&&!z.contains(he)?e.parse(R("(({0})^(({2})*({4}))*({1})^(({3})*({4})))/(log(({0})^({2}))+log(({1})^({3})))",b.toString(),z.toString(),be.power.multiplier.toString(),$e.power.multiplier.toString(),he)):me.integration.by_parts(A,he,Ve,lt))}}else if(dt===3&&(Me[2].group===ve&&Me[2].power.lessThan(2)||Me[0].group===Qe)){var sn,ln=Me[0];ln.group===Qe?(ln.power.greaterThan(1)&&(ln=e.expand(ln)),sn=e.multiply(Me[1],Me[2]),Xe=new h(0),ln.each(function(Dt){Dt=e.multiply(Dt,sn.clone()),Dt=me.integrate(Dt,he,Ve),Xe=e.add(Xe,Dt)},!0)):Xe=me.integration.by_parts(A,he,Ve,lt)}else if(ye(Me)){for(var dn=new h(1),En=0,dt=Me.length;En<dt;En++)dn=e.multiply(dn,Me[En].fnTransform());dn=e.expand(dn),Xe=me.integrate(dn,he,Ve)}else{var vn=yt(Me);Xe=me.integrate(e.expand(vn),he,Ve)}}Xe=e.multiply(Xe,Y)}}else Xe=e.multiply(A.clone(),e.parse(he));if(Xe)return Xe}catch(Dt){if(!(Dt instanceof le||Dt instanceof t.exceptions.DivisionByZero))throw Dt}return e.symfunction("integrate",[Ue,Le])},!1)))},defint:function(Ue,Le,Ve,lt){lt=lt||"x";function Nt(et,Lt,H){try{return e.parse(et,Lt)}catch(P){return me.Limit.limit(et,lt,H)}}var Ct,Xe=t.Utils.variables(Ue),he=Ue.hasTrig();return Xe.length!==1||lt||(lt=Xe[0]),he||(Ct=me.integrate(Ue,lt)),he||Ct.hasIntegral()?Xe.length===1&&Le.isConstant()&&Ve.isConstant()?(he=t.Utils.build(Ue),new h(t.Math2.num_integrate(he,Number(Le),Number(Ve)))):e.symfunction("defint",[Ue,Le,Ve,lt]):(Xe={},(he={})[lt]=Ve,Xe[lt]=Le,Ue=Nt(Ct,he,Ve),he=Nt(Ct,Xe,Le),e.subtract(Ue,he))},Limit:{interval:function(Ue,Le){return e.parse(R("[{0}, {1}]",Ue,Le))},diverges:function(){return me.Limit.interval("-Infinity","Infinity")},divide:function(Ue,Le,Ve,lt,Nt){if(!(Nt++>a.max_lim_depth)){Ue.clone();var Ct=Le.clone();if(Le.fname==="abs"){var Xe=Ue.sign(),he=lt.sign();if(lt.isInfinity)return e.multiply(new h(Xe),new h(he));if(lt.equals(0))return Xe=e.parse(Ue.multiplier),he=e.parse(Le.multiplier),e.divide(e.multiply(Xe,me.Limit.interval("-1","1")),he);me.Limit.diverges()}var et=function(ue){if(t.Utils.isVector(ue)){for(var st=0;st<ue.elements.length;st++)if(!ue.elements[st].isInfinity)return!1;return!0}return ue.isInfinity},Lt=function(ue,st){return!t.Utils.isVector(ue)&&ue.equals(st)};do var H,P,B=K(me.Limit.limit(Ue.clone(),Ve,lt,Nt)),fe=K(me.Limit.limit(Le.clone(),Ve,lt,Nt)),pe=et(B)&&et(fe)||Lt(B,0)&&Lt(fe,0);while(pe&&(P=me.diff(Ue.clone(),Ve),H=me.diff(Le.clone(),Ve),Ue=(P=e.expand(e.divide(P,H))).getNum(),Le=P.getDenom()),pe);return Xe=fe.equals(0),he=Number(Ct.power),lt.isConstant(!0)&&Xe?h.infinity(t.Utils.even(he)&&B.lessThan(0)?-1:void 0):Xe?me.Limit.diverges():e.divide(B,fe)}},rewriteToLog:function(Ue){var Le=Ue.power.clone();return Ue.toLinear(),e.pow(new h("e"),e.multiply(Le,e.symfunction(a.LOG+"",[Ue])))},getSubbed:function(Ue,Le,Ve){var lt;Ue.group===Te&&(Ue=me.rewriteToLog(Ue));try{lt=Ue.sub(Le,Ve)}catch(Nt){lt=Ue}return lt},isInterval:function(Ue){return t.Utils.isVector(Ue)},isConvergent:function(Ue){return!(me.Limit.isInterval(Ue)&&Ue.elements[0].isInfinity&&Ue.elements[1].isInfinity||Ue.containsFunction("limit"))},limit:function(Ue,Le,Ve,lt){var Nt;if(Ue.isLinear()&&Ue.isComposite())return Nt=new h(0),Ue.each(function(Be){Nt=e.add(Nt,me.Limit.limit(Be,Le,Ve,lt))},!0),Nt;if(Ue=t.Algebra.Simplify.simplify(Ue),lt=lt||1,!(lt++>a.max_lim_depth)){var Ct=e.parse(Ue.multiplier);Ue.toUnitMultiplier();try{if(Ue.isConstant(!0))ue=Ue;else{var Xe={};Xe[Le]=Ve;try{var he=e.parse(Ue.sub(Le,Ve),Xe);(he.isConstant(!0)||he.isInfinity)&&(ue=he)}catch(Be){}if(!ue){var et=Ue.getNum(),Lt=Ue.getDenom();if(Lt.isConstant(!0)){if(Ue.group===Te){var H,P,B,fe,pe,ue,st=Ue.clone().toLinear(),se=(Ue.power.clone(),st.getNum()),te=st.getDenom(),D=t.Utils.decompose_fn(te,Le,!0);ue=se.group===ve&&se.multiplier.isOne()&&D.ax.group===ve&&D.b.isConstant(!0)&&D.a.isOne()&&D.b.isConstant(!0)?e.parse(R("(1/e^({0}))",D.b)):(P=(H=me.Limit.rewriteToLog(Ue.clone())).power.clone(),B=H.clone().toLinear(),fe=me.Limit.limit(B,Le,Ve,lt),pe=me.Limit.limit(P,Le,Ve,lt),e.pow(fe,pe))}else if(Ue.group===De&&Ue.args.length===1){var re,J=me.Limit.limit(Ue.args[0],Le,Ve,lt);if(t.Utils.isVector(J))return ue=J.map(function(Be){return Ue.clone().args[0]=Be,me.Limit.limit(e.symfunction(Ue.fname,[Be]),Le,Ve,lt)}),e.multiply(Ct,ue);if(J.isConstant(!0)){var Ee=e.symfunction(Ue.fname,[J]);try{K(Ee),re=!0}catch(Be){re=!1}}if(re)ue=Ee;else if(me.Limit.isConvergent(J))if(Ue.fname===Oe)switch(J.toString()){case"0":ue=h.infinity().negate();break;case"Infinity":case"-Infinity":ue=h.infinity()}else 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at(f,v){if(v.isConstant()&&f.isConstant()&&!f.equals(v)||f.equals(e.Settings.IMAGINARY)&&v.isConstant(!0)||v.equals(e.Settings.IMAGINARY)&&f.isConstant(!0))throw new e.exceptions.NerdamerValueError(f.toString()+" does not equal "+v.toString());this.LHS=f,this.RHS=v}e.Settings.SOLVE_RADIUS=1e3,e.Settings.ROOTS_PER_SIDE=10,e.Settings.make_pi_conversions=!1,e.Settings.STEP_SIZE=.1,e.Settings.EPSILON=1e-13,e.Settings.MAX_NEWTON_ITERATIONS=200,e.Settings.MAX_NON_LINEAR_TRIES=12,e.Settings.NON_LINEAR_JUMP_AT=50,e.Settings.NON_LINEAR_JUMP_SIZE=100,e.Settings.NON_LINEAR_START=.01,e.Settings.NEWTON_SLICES=200,e.Settings.NEWTON_EPSILON=2*Number.EPSILON,e.Settings.SOLUTION_PROXIMITY=1e-14,e.Settings.FILTER_SOLUTIONS=!0,e.Settings.MAX_SOLVE_DEPTH=10,e.Settings.ZERO_EPSILON=1e-9,e.Settings.MAX_BISECTION_ITER=2e3,e.Settings.BI_SECTION_EPSILON=1e-12,e.Symbol.prototype.hasTrig=function(){return this.containsFunction(["cos","sin","tan","cot","csc","sec"])},e.Symbol.prototype.hasNegativeTerms=function(){if(this.isComposite())for(var f in this.symbols){var v=this.symbols[f];if(v.group===Ie&&v.hasNegativeTerms()||this.symbols[f].power.lessThan(0))return!0}return!1},at.prototype={toString:function(){return this.LHS.toString()+"="+this.RHS.toString()},text:function(f){return this.LHS.text(f)+"="+this.RHS.text(f)},toLHS:function(f){var I=(v=(f=f===void 0)?this.removeDenom():this.clone()).LHS,v=v.RHS,I=(I.isConstant(!0)&&!v.isConstant(!0)&&([I,v]=[v,I]),r.subtract(I,v));return new at(f?r.expand(I):I,new K(0)).removeDenom().LHS},removeDenom:function(){var f=this.LHS.clone(),v=this.RHS.clone(),I=r.multiply(f.getDenom(),v.getDenom());if(f=r.expand(r.multiply(f,I.clone())),(v=r.expand(r.multiply(v,I))).group===ee&&v.group!==ee&&(q=f,f=v,v=q),f.group===Qe){var q=new K(f.multiplier),V=v.clone();f.each(function(Ae){Ae.power.lessThan(0)?V=r.divide(V,Ae):q=r.multiply(q,Ae)}),f=q,v=V}else 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I=[],q=e.Algebra.Factor.factor(q);return q.group===Qe&&q.each(function(V){V=K.unwrapPARENS(V),I=I.concat(u(V,v))}),I},csolve:function(f,v){return e.Utils.block("IGNORE_E",function(){var I=[],q=e.Utils.decompose_fn(f,v,!0);if(q.x.group===De)for(var V,Q=r.parse(q.x.power),le=Number(Q),q=r.pow(r.divide(q.b.negate(),q.a),Q.invert()),ye=(q=K.toPolarFormArray(q))[0],Ae=(q[1],ye.toString()),je=(Q.toString(),0);je<le;je++)V=_("({0})*e^(2*{1}*pi*{2}*{3})",Ae,je,Q,e.Settings.IMAGINARY),V=r.parse(V),I.push(V);return I},!0)},getPoints:function(Ae,v,I){v=v||.01,I=I||[];function q(it,yt){for(var me,Ue,Le,Ve=[],lt=0,Nt=it.length;lt<Nt;lt++)me=it[lt],Le=(Ue=V(me))/Math.abs(Ue),isNaN(Ue)||!isFinite(Ue)||Ve.length>yt||(Le!==Q&&Ve.push(me),Q=Le);I=I.concat(Ve)}var 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st=pe,se=l.diff(je.clone()),te=R(se);for(ue=0;ue<st.length;ue++)he=st[ue],He(c.Newton(he,fe,te),Lt);I.sort()}catch(Se){console.log(Se)}else if(!je.hasFunc(v)&&je.isComposite())try{if((Ct=e.Algebra.Factor.factor(je.clone())).group===Qe)Ct.each(function(Se){He(u(Se,v))});else{switch(Xe=(Nt=e.Utils.getCoeffs(je,v)).length-1){case 0:var D,re,J,Ee=(D=ne(je))[0],xe=D[1];Ee.group===e.groups.EX&&(J=`${re=e.Settings.LOG}((${xe})/(${Ee.multiplier}))/${re}(${Ee.value})/`+Ee.power.multiplier,He(r.parse(J)));break;case 1:He(r.divide(Nt[0],Nt[1].negate()));break;case 2:He(c.quad.apply(void 0,Nt));break;case 3:He(c.cubic.apply(void 0,Nt));break;case 4:He(c.quartic.apply(void 0,Nt));break;default:He(c.csolve(je,v)),I.length===0&&He(c.divideAndConquer(je,v))}I.length===0&&He(u(Ct,v,I,q))}}catch(Se){}else try{var Ce,Ke=c.rewrite(je,null,v),Ee=Ke[0],xe=Ke[1];if(Ee.group===Te)Ee.fname==="abs"?He([xe.clone(),xe.negate()]):Ee.fname==="sin"?He(c.inverseFunctionSolve("asin",Ee,xe)):Ee.fname==="cos"?He(c.inverseFunctionSolve("acos",Ee,xe)):Ee.fname==="tan"?He(c.inverseFunctionSolve("atan",Ee,xe)):Ee.fname===e.Settings.LOG?(lt=(Ce=h(Ee.args[0],v))[1]).group===De&&(je=new at(lt,xe=r.divide(r.subtract(r.pow(1<Ee.args.length?Ee.args[1]:new K("e"),r.divide(xe,r.parse(Ee.multiplier))),Ce[3]),Ce[0])).toLHS(),He(u(je,v))):He(r.subtract(Ee,xe));else{var Ne=new at(Ee,xe).toLHS();if(Ne.equals(je))throw new Error("Stopping. 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t=fr.getCore(),e=t.PARSER,r=t.Symbol,a=t.Utils.format,l=t.Utils.isVector,h=t.Utils.isArray,L=(t.Vector,t.groups.S),M=(t.groups.EX,t.groups.CP),_=t.groups.CB,R=t.groups.FN,ie=(t.Settings.Laplace_integration_depth=40,r.prototype.findFunction=function(K){if(this.group===R&&this.fname===K)return this.clone();var de;if(this.symbols){for(var ve in this.symbols)if(de=this.symbols[ve].findFunction(K))break}return de},t.Extra={version:"1.4.2",LaPlace:{transform:function(K,de,ve){K=K.clone(),de=de.toString();var De=(K=r.unwrapSQRT(K,!0)).stripVar(de),Ie=K.group;if((K=e.divide(K,De.clone())).isConstant()||!K.contains(de,!0))Qe=e.parse(a("({0})/({1})",K,ve));else if(Ie===L&&t.Utils.isInt(K.power))var Ie=String(K.power),Qe=e.parse(a("factorial({0})/({1})^({0}+1)",Ie,ve));else if(K.group===L&&K.power.equals(.5))Qe=e.parse(a("sqrt(pi)/(2*({0})^(3/2))",ve));else if(K.isComposite())Qe=new r(0),K.each(function(ze){Qe=e.add(Qe,ie.LaPlace.transform(ze,de,ve))},!0);else if(!K.isE()||K.power.group!==L&&K.power.group!==_)if(K.group!==R||["sin","cos","sinh","cosh"].indexOf(K.fname)===-1||K.args[0].group!==L&&K.args[0].group!==_){var ee,Ie=t.Settings.integration_depth<t.Settings.Laplace_integration_depth;Ie&&(ee=t.Settings.integration_depth,t.Settings.integration_depth=t.Settings.Laplace_integration_depth),t.Utils.block("PARSE2NUMBER",function(){var Oe=de,ut=K.sub(de,Oe),ut=e.parse("e^(-"+ve+"*"+Oe+")*"+ut);if((Qe=t.Calculus.integrate(ut,Oe)).hasIntegral())return e.symfunction("laplace",arguments);Qe=Qe.sub(de,0),Qe=(Qe=e.expand(e.multiply(Qe,new r(-1)))).sub(Oe,de)},!1),Qe=t.Utils.block("PARSE2NUMBER",function(){return e.parse(Qe)},!0),Ie&&(t.Settings.integration_depth=ee)}else switch(Te=K.args[0].stripVar(de),K.fname){case"sin":Qe=e.parse(a("({0})/(({1})^2+({0})^2)",Te,ve));break;case"cos":Qe=e.parse(a("({1})/(({1})^2+({0})^2)",Te,ve));break;case"sinh":Qe=e.parse(a("({0})/(({1})^2-({0})^2)",Te,ve));break;case"cosh":Qe=e.parse(a("({1})/(({1})^2-({0})^2)",Te,ve))}else{var Te=K.power.stripVar(de);Qe=e.parse(a("1/(({1})-({0}))",Te,ve))}return e.multiply(Qe,De)},inverse:function(K,de,ve){var De=K.clone();return t.Utils.block("POSITIVE_MULTIPLIERS",function(){if((K=K.group===_?t.Algebra.PartFrac.partfrac(e.expand(K),de):K).group===L||K.group===_||K.isComposite()){var Ie,Qe,ee,Te,ze,Oe,ut,at,j,d,c,u,f,v,I=function(){(ze=e.multiply(ze,Ie)).multiplier=ze.multiplier.multiply(K.multiplier),ze=e.divide(ze,ee.a)},q=K.multiplier.clone();if(K.toUnitMultiplier(),Ie=K.getNum(),(at=K.getDenom().toUnitMultiplier()).group===M?(Te=at.power.clone(),at.toLinear()):Te=new t.Frac(1),Qe=de.toString(),ee=t.Utils.decompose_fn(at,Qe,!0),t.Utils.decompose_fn(e.expand(Ie.clone()),Qe,!0),Ie.multiplier=Ie.multiplier.multiply(q),(at.group===L||at.group===_)&&ee.x.value===Qe&&ee.b.equals(0)&&t.Utils.isInt(ee.x.power))d=ee.x.power-1,c=t.Math2.factorial(d),ze=e.divide(e.pow(ve,new r(d)),new r(c)),I();else if(at.group===M&&Te.equals(1))ee.x.group===t.groups.PL&&t.Algebra.degree(at).equals(2)?(j=t.Algebra.sqComplete(at,Qe),at=t.Utils.getU(at),f=t.Utils.decompose_fn(j.a,Qe,!0).b,j=ie.LaPlace.inverse(e.parse(`1/((${at})^2+(${j.c}))`),at,ve),ze=e.multiply(j,e.parse(`(${q})*e^(-(${f})*(${ve}))`))):ee.x.isLinear()&&!Ie.contains(Qe)?(ve=e.divide(ve,ee.a.clone()),c=(d=Te-1)===0||d===1?"1":`(${Te}-1)!`,ze=e.parse(a("(({0})^({3}-1)*e^(-(({2})*({0}))/({1})))/(({4})*({1})^({3}))",ve,ee.a,ee.b,Te,c)),I()):ee.x.group===L&&ee.x.power.equals(2)&&(Ie.contains(Qe)?(f=new r(1),Ie.group===_&&(Oe=new 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V=e.divide(Ie.clone(),e.parse("sqrt(pi)"));ze=e.parse(a("(2*({2})*sqrt({0}))/({1})",ve,ee.a,V,Ie))}else if(Te.equals(2)&&ee.x.power.equals(2))if(Ie.contains(Qe))if((ut=t.Utils.decompose_fn(e.expand(Ie.clone()),Qe,!0)).x.isComposite()){var Q=[],le=Ie.collectSymbols(function(je){je=r.unwrapPARENS(je);var it=t.Utils.decompose_fn(je,Qe,!0);return it.symbol=je,it}).sort(function(je,it){return je=je.x.value!==Qe?0:je.x.power,(it.x.value!==Qe?0:it.x.power)-je});f=new r(-1);for(var ye=0;ye<le.length;ye++){var Ae=le[ye];Ae.x.value===Qe?Q.push(Ae):f=e.multiply(f,Ae.symbol)}Q[0].x.power.equals(2)&&Q[1].x.power.equals(1)&&Q[1].b.equals(0)&&!Q[0].b.equals(0)&&(V=Q[0].a.negate(),ze=e.parse(a("-(({1})*({2})*({5})*({0})*sin((sqrt(({4})*({5}))*({0}))/({4})))/(2*({4})^2*sqrt(({4})*({5})))-(({1})*({3})*({0})*sin((sqrt(({4})*({5}))*({0}))/({4})))/(2*({4})*sqrt(({4})*({5})))+(({1})*({2})*cos((sqrt(({4})*({5}))*({0}))/({4})))/({4})^2",ve,f,V,Q[0].b,ee.a,ee.b)))}else ut.x.isLinear()?(f=e.divide(ut.a,new 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r(0),K.each(function(je){ze=e.add(ze,ie.LaPlace.inverse(je,de,ve))},!0)))}return ze=ze||e.symfunction("ilt",[De,de,ve])},!0)}},Statistics:{frequencyMap:function(K){for(var de={},ve=0,De=K.length;ve<De;ve++){var Ie=K[ve].toString();de[Ie]||(de[Ie]=0),de[Ie]++}return de},sort:function(K){return K.sort(function(de,ve){return de.isConstant()&&ve.isConstant()||e.error("Unable to sort! 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De?(Ie=De[Qe],h(Ie)?Ie.push(ve):De[Qe]=[ve,De[Qe]]):De[Qe]=ve}var K=De[Math.max.apply(null,t.Utils.keys(De))],ee=h(K)?e.symfunction("mode",K.sort()):e.parse(K)}return ee},gVariance:function(K,De){var ve=ie.Statistics.mean.apply(ie.Statistics,De),De=ie.Statistics.sum(De,ve);return e.multiply(K,De)},variance:function(){var K,de=[].slice.call(arguments);return l(de[0])?ie.Statistics.variance.apply(this,de[0].elements):(K=e.divide(new r(1),ie.Statistics.count(de)),ie.Statistics.gVariance(K,de))},sampleVariance:function(){var K,de=[].slice.call(arguments);return l(de[0])?ie.Statistics.sampleVariance.apply(this,de[0].elements):(K=e.divide(new r(1),e.subtract(ie.Statistics.count(de),new r(1))),ie.Statistics.gVariance(K,de))},standardDeviation:function(){var K=[].slice.call(arguments);return l(K[0])?ie.Statistics.standardDeviation.apply(this,K[0].elements):e.pow(ie.Statistics.variance.apply(ie.Statistics,K),new r(.5))},sampleStandardDeviation:function(){var K=[].slice.call(arguments);return l(K[0])?ie.Statistics.sampleStandardDeviation.apply(this,K[0].elements):e.pow(ie.Statistics.sampleVariance.apply(ie.Statistics,K),new r(.5))},zScore:function(K,de,ve){return e.divide(e.subtract(K,de),ve)}},Units:{table:{foot:"12 inch",meter:"100 cm",decimeter:"10 cm"}}});fr.register([{name:"laplace",visible:!0,numargs:3,build:function(){return ie.LaPlace.transform}},{name:"ilt",visible:!0,numargs:3,build:function(){return ie.LaPlace.inverse}},{name:"mean",visible:!0,numargs:-1,build:function(){return ie.Statistics.mean}},{name:"median",visible:!0,numargs:-1,build:function(){return ie.Statistics.median}},{name:"mode",visible:!0,numargs:-1,build:function(){return ie.Statistics.mode}},{name:"smpvar",visible:!0,numargs:-1,build:function(){return ie.Statistics.sampleVariance}},{name:"variance",visible:!0,numargs:-1,build:function(){return ie.Statistics.variance}},{name:"smpstdev",visible:!0,numargs:-1,build:function(){return ie.Statistics.sampleStandardDeviation}},{name:"stdev",visible:!0,numargs:-1,build:function(){return ie.Statistics.standardDeviation}},{name:"zscore",visible:!0,numargs:3,build:function(){return ie.Statistics.zScore}}]),fr.updateAPI()}(),typeof ti!="undefined"&&(ti.exports=fr)});var R7=an((qS,Mo)=>{typeof Mo!="undefined"&&(Q2=N0(),V0(),z0());var Q2;(function(){"use strict";var t=Q2.getCore(),e=t.PARSER,r=t.Symbol,a=t.Utils.format,l=t.Utils.isVector,h=t.Utils.isArray,L=t.Vector,M=t.groups.S,_=t.groups.EX,R=t.groups.CP,ie=t.groups.CB,K=t.groups.FN;t.Settings.Laplace_integration_depth=40,r.prototype.findFunction=function(ve){if(this.group===K&&this.fname===ve)return this.clone();var De;if(this.symbols){for(var Ie in this.symbols)if(De=this.symbols[Ie].findFunction(ve),De)break}return De};var de=t.Extra={version:"1.4.2",LaPlace:{transform:function(ve,De,Ie){ve=ve.clone(),De=De.toString(),ve=r.unwrapSQRT(ve,!0);var Qe,ee=ve.stripVar(De),Te=ve.group;if(ve=e.divide(ve,ee.clone()),ve.isConstant()||!ve.contains(De,!0))Qe=e.parse(a("({0})/({1})",ve,Ie));else if(Te===M&&t.Utils.isInt(ve.power)){var ze=String(ve.power);Qe=e.parse(a("factorial({0})/({1})^({0}+1)",ze,Ie))}else if(ve.group===M&&ve.power.equals(1/2))Qe=e.parse(a("sqrt(pi)/(2*({0})^(3/2))",Ie));else if(ve.isComposite())Qe=new r(0),ve.each(function(d){Qe=e.add(Qe,de.LaPlace.transform(d,De,Ie))},!0);else if(ve.isE()&&(ve.power.group===M||ve.power.group===ie)){var Oe=ve.power.stripVar(De);Qe=e.parse(a("1/(({1})-({0}))",Oe,Ie))}else{var ut=["sin","cos","sinh","cosh"];if(ve.group===K&&ut.indexOf(ve.fname)!==-1&&(ve.args[0].group===M||ve.args[0].group===ie)){var Oe=ve.args[0].stripVar(De);switch(ve.fname){case"sin":Qe=e.parse(a("({0})/(({1})^2+({0})^2)",Oe,Ie));break;case"cos":Qe=e.parse(a("({1})/(({1})^2+({0})^2)",Oe,Ie));break;case"sinh":Qe=e.parse(a("({0})/(({1})^2-({0})^2)",Oe,Ie));break;case"cosh":Qe=e.parse(a("({1})/(({1})^2-({0})^2)",Oe,Ie));break}}else{var at=t.Settings.integration_depth<t.Settings.Laplace_integration_depth;if(at){var j=t.Settings.integration_depth;t.Settings.integration_depth=t.Settings.Laplace_integration_depth}t.Utils.block("PARSE2NUMBER",function(){var d=De,c=ve.sub(De,d),u=e.parse("e^(-"+Ie+"*"+d+")*"+c);if(Qe=t.Calculus.integrate(u,d),Qe.hasIntegral())return e.symfunction("laplace",arguments);Qe=Qe.sub(De,0),Qe=e.expand(e.multiply(Qe,new r(-1))),Qe=Qe.sub(d,De)},!1),Qe=t.Utils.block("PARSE2NUMBER",function(){return e.parse(Qe)},!0),at&&(t.Settings.integration_depth=j)}}return e.multiply(Qe,ee)},inverse:function(ve,De,Ie){var Qe=ve.clone();return t.Utils.block("POSITIVE_MULTIPLIERS",function(){if(ve.group===ie&&(ve=t.Algebra.PartFrac.partfrac(e.expand(ve),De)),ve.group===M||ve.group===ie||ve.isComposite()){var ee=function(){ut=e.multiply(ut,Te),ut.multiplier=ut.multiplier.multiply(ve.multiplier),ut=e.divide(ut,at.a)},Te,ze,Oe,ut,at,j,d,c,u;if(d=ve.multiplier.clone(),ve.toUnitMultiplier(),Te=ve.getNum(),ze=ve.getDenom().toUnitMultiplier(),ze.group===R?(c=ze.power.clone(),ze.toLinear()):c=new t.Frac(1),Oe=De.toString(),at=t.Utils.decompose_fn(ze,Oe,!0),u=t.Utils.decompose_fn(e.expand(Te.clone()),Oe,!0),Te.multiplier=Te.multiplier.multiply(d),(ze.group===M||ze.group===ie)&&at.x.value===Oe&&at.b.equals(0)&&t.Utils.isInt(at.x.power)){var f,j;j=at.x.power-1,f=t.Math2.factorial(j),ut=e.divide(e.pow(Ie,new r(j)),new r(f)),ee()}else if(ze.group===R&&c.equals(1)){if(at.x.group===t.groups.PL&&t.Algebra.degree(ze).equals(2)){var v=t.Algebra.sqComplete(ze,Oe),I=t.Utils.getU(ze),q=t.Utils.decompose_fn(v.a,Oe,!0).b,V=de.LaPlace.inverse(e.parse(`1/((${I})^2+(${v.c}))`),I,Ie);ut=e.multiply(V,e.parse(`(${d})*e^(-(${q})*(${Ie}))`))}else if(at.x.isLinear()&&!Te.contains(Oe)){Ie=e.divide(Ie,at.a.clone());var j=c-1,f=j===0||j===1?"1":`(${c}-1)!`;ut=e.parse(a("(({0})^({3}-1)*e^(-(({2})*({0}))/({1})))/(({4})*({1})^({3}))",Ie,at.a,at.b,c,f)),ee()}else if(at.x.group===M&&at.x.power.equals(2))if(!Te.contains(Oe))ut=e.parse(a("(({1})*sin((sqrt(({2})*({3}))*({0}))/({2})))/sqrt(({2})*({3}))",Ie,Te,at.a,at.b));else{var q=new r(1);if(Te.group===ie){var Q=new r(1);Te.each(function(B){B.contains(Oe)?Q=e.multiply(Q,B):q=e.multiply(q,B)}),Te=Q}var le=t.Utils.decompose_fn(Te,Oe,!0),ye,Ae,je,it,yt,me;if(ye=le.a,Ae=le.b,je=ye.containsFunction("sin"),yt=ye.containsFunction("cos"),it=Ae.containsFunction("cos"),me=Ae.containsFunction("sin"),le.x.value===Oe&&le.x.isLinear()&&!(je&&it||yt||me))ut=e.parse(a("(({1})*cos((sqrt(({2})*({3}))*({0}))/({2})))/({2})",Ie,le.a,at.a,at.b));else if(je&&it){var Ue,Le;if(Ue=ye.findFunction("sin"),Le=Ae.findFunction("cos"),Ue.args[0].equals(Le.args[0])&&!Ue.args[0].contains(Oe)){var Ve,lt,Nt,Ct;Ve=e.divide(Ae,Le.toUnitMultiplier()).toString(),lt=Ue.args[0].toString(),Nt=at.b,Ct=e.divide(ye,Ue.toUnitMultiplier()),Xe="(({1})*({2})*cos({3})*sin(sqrt({4})*({0})))/sqrt({4})+({1})*sin({3})*({5})*cos(sqrt({4})*({0}))",ut=e.parse(a(Xe,Ie,q,Ve,lt,Nt,Ct))}}}}else if(at.x.power.num&&at.x.power.num.equals(3)&&at.x.power.den.equals(2)&&Te.contains("sqrt(pi)")&&!Te.contains(Oe)&&Te.isLinear()){var Ve=e.divide(Te.clone(),e.parse("sqrt(pi)"));ut=e.parse(a("(2*({2})*sqrt({0}))/({1})",Ie,at.a,Ve,Te))}else if(c.equals(2)&&at.x.power.equals(2)){var q,Nt,Xe;if(!Te.contains(Oe))q=e.divide(Te,new r(2)),Xe="(({1})*sin((sqrt(({2})*({3}))*({0}))/({2})))/(({3})*sqrt(({2})*({3})))-(({1})*({0})*cos((sqrt(({2})*({3}))*({0}))/({2})))/(({2})*({3}))",ut=e.parse(a(Xe,Ie,q,at.a,at.b));else if(le=t.Utils.decompose_fn(e.expand(Te.clone()),Oe,!0),le.x.isComposite()){var he=[],et=Te.collectSymbols(function(fe){fe=r.unwrapPARENS(fe);var pe=t.Utils.decompose_fn(fe,Oe,!0);return pe.symbol=fe,pe}).sort(function(fe,pe){var ue,st;return ue=fe.x.value!==Oe?0:fe.x.power,st=pe.x.value!==Oe?0:pe.x.power,st-ue});q=new r(-1);for(var Lt=0;Lt<et.length;Lt++){var H=et[Lt];H.x.value===Oe?he.push(H):q=e.multiply(q,H.symbol)}he[0].x.power.equals(2)&&he[1].x.power.equals(1)&&he[1].b.equals(0)&&!he[0].b.equals(0)&&(Ve=he[0].a.negate(),Xe="-(({1})*({2})*({5})*({0})*sin((sqrt(({4})*({5}))*({0}))/({4})))/(2*({4})^2*sqrt(({4})*({5})))-(({1})*({3})*({0})*sin((sqrt(({4})*({5}))*({0}))/({4})))/(2*({4})*sqrt(({4})*({5})))+(({1})*({2})*cos((sqrt(({4})*({5}))*({0}))/({4})))/({4})^2",ut=e.parse(a(Xe,Ie,q,Ve,he[0].b,at.a,at.b)))}else le.x.isLinear()?(q=e.divide(le.a,new r(2)),Xe="(({1})*({0})*sin((sqrt(({2})*({3}))*({0}))/({2})))/(({2})*sqrt(({2})*({3})))",ut=e.parse(a(Xe,Ie,q,at.a,at.b))):le.x.power.equals(2)&&(le.b.equals(0)?(q=e.divide(le.a,new r(2)),Xe="(({1})*sin((sqrt(({2})*({3}))*({0}))/({2})))/(({2})*sqrt(({2})*({3})))+(({1})*({0})*cos((sqrt(({2})*({3}))*({0}))/({2})))/({2})^2",ut=e.parse(a(Xe,Ie,q,at.a,at.b))):(q=e.divide(le.a,new r(2)),Nt=le.b.negate(),Xe="-((({2})*({4})-2*({1})*({3}))*sin((sqrt(({2})*({3}))*({0}))/({2})))/(2*({2})*({3})*sqrt(({2})*({3})))+(({4})*({0})*cos((sqrt(({2})*({3}))*({0}))/({2})))/(2*({2})*({3}))+(({1})*({0})*cos((sqrt(({2})*({3}))*({0}))/({2})))/({2})^2",ut=e.parse(a(Xe,Ie,q,at.a,at.b,Nt))))}else ve.isComposite()&&(c.equals(2)&&at.x.group===M?ut=e.parse(`(${d})*(${Ie})*e^(-(${at.b})*(${Ie}))`):(ut=new r(0),ve.each(function(P){ut=e.add(ut,de.LaPlace.inverse(P,De,Ie))},!0)))}return ut||(ut=e.symfunction("ilt",[Qe,De,Ie])),ut},!0)}},Statistics:{frequencyMap:function(ve){for(var De={},Ie=0,Qe=ve.length;Ie<Qe;Ie++){var ee=ve[Ie],Te=ee.toString();De[Te]||(De[Te]=0),De[Te]++}return De},sort:function(ve){return ve.sort(function(De,Ie){return(!De.isConstant()||!Ie.isConstant())&&e.error("Unable to sort! 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Ie){var Te=Ie[ee];if(!(Te in Qe))Qe[Te]=ee;else{var ze=Qe[Te];h(ze)?ze.push(ee):Qe[Te]=[ee,Qe[Te]]}}var Oe=Qe[Math.max.apply(null,t.Utils.keys(Qe))];h(Oe)?De=e.symfunction("mode",Oe.sort()):De=e.parse(Oe)}return De},gVariance:function(ve,De){var Ie=de.Statistics.mean.apply(de.Statistics,De),Qe=de.Statistics.sum(De,Ie);return e.multiply(ve,Qe)},variance:function(){var ve=[].slice.call(arguments);if(l(ve[0]))return de.Statistics.variance.apply(this,ve[0].elements);var De=e.divide(new r(1),de.Statistics.count(ve));return de.Statistics.gVariance(De,ve)},sampleVariance:function(){var ve=[].slice.call(arguments);if(l(ve[0]))return de.Statistics.sampleVariance.apply(this,ve[0].elements);var De=e.divide(new r(1),e.subtract(de.Statistics.count(ve),new r(1)));return de.Statistics.gVariance(De,ve)},standardDeviation:function(){var ve=[].slice.call(arguments);return l(ve[0])?de.Statistics.standardDeviation.apply(this,ve[0].elements):e.pow(de.Statistics.variance.apply(de.Statistics,ve),new 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de.Statistics.variance}},{name:"smpstdev",visible:!0,numargs:-1,build:function(){return de.Statistics.sampleStandardDeviation}},{name:"stdev",visible:!0,numargs:-1,build:function(){return de.Statistics.standardDeviation}},{name:"zscore",visible:!0,numargs:3,build:function(){return de.Statistics.zScore}}]),Q2.updateAPI()})();typeof Mo!="undefined"&&(Mo.exports=Q2)});var U7=an((US,q7)=>{typeof q7!="undefined"&&(J2=N0(),V0(),z0());var J2;(function(){var t=J2.getCore(),e=t.PARSER,r=t.Algebra,a=t.Calculus,l=a.integration.decompose_arg,h=t.Utils.evaluate,L=t.Utils.remove,M=t.Utils.format,_=t.Utils.build,R=t.Utils.knownVariable,ie=t.Symbol,K=t.Utils.isSymbol,de=t.Utils.variables,ve=t.groups.S,De=t.groups.PL,Ie=t.groups.CB,Qe=t.groups.CP,ee=t.groups.FN,Te=t.Settings,ze=t.Utils.range,Oe=t.Utils.isArray;t.Settings.SOLVE_RADIUS=1e3,t.Settings.ROOTS_PER_SIDE=10,t.Settings.make_pi_conversions=!1,t.Settings.STEP_SIZE=.1,t.Settings.EPSILON=1e-13,t.Settings.MAX_NEWTON_ITERATIONS=200,t.Settings.MAX_NON_LINEAR_TRIES=12,t.Settings.NON_LINEAR_JUMP_AT=50,t.Settings.NON_LINEAR_JUMP_SIZE=100,t.Settings.NON_LINEAR_START=.01,t.Settings.NEWTON_SLICES=200,t.Settings.NEWTON_EPSILON=Number.EPSILON*2,t.Settings.SOLUTION_PROXIMITY=1e-14,t.Settings.FILTER_SOLUTIONS=!0,t.Settings.MAX_SOLVE_DEPTH=10,t.Settings.ZERO_EPSILON=1e-9,t.Settings.MAX_BISECTION_ITER=2e3,t.Settings.BI_SECTION_EPSILON=1e-12,t.Symbol.prototype.hasTrig=function(){return this.containsFunction(["cos","sin","tan","cot","csc","sec"])},t.Symbol.prototype.hasNegativeTerms=function(){if(this.isComposite())for(var u in this.symbols){var f=this.symbols[u];if(f.group===De&&f.hasNegativeTerms()||this.symbols[u].power.lessThan(0))return!0}return!1};function ut(u,f){if(f.isConstant()&&u.isConstant()&&!u.equals(f)||u.equals(t.Settings.IMAGINARY)&&f.isConstant(!0)||f.equals(t.Settings.IMAGINARY)&&u.isConstant(!0))throw new t.exceptions.NerdamerValueError(u.toString()+" does not equal "+f.toString());this.LHS=u,this.RHS=f}ut.prototype={toString:function(){return this.LHS.toString()+"="+this.RHS.toString()},text:function(u){return this.LHS.text(u)+"="+this.RHS.text(u)},toLHS:function(u){u=typeof u=="undefined";var f;u?f=this.removeDenom():f=this.clone();var v=f.LHS,I=f.RHS;v.isConstant(!0)&&!I.isConstant(!0)&&([v,I]=[I,v]);var q=e.subtract(v,I),V=u?e.expand(q):q;return V=new ut(V,new ie(0)).removeDenom().LHS,V},removeDenom:function(){var u=this.LHS.clone(),f=this.RHS.clone(),v=e.multiply(u.getDenom(),f.getDenom());if(u=e.expand(e.multiply(u,v.clone())),f=e.expand(e.multiply(f,v)),f.group===Qe&&f.group!==Qe){var I=u;u=f,f=I}if(u.group===Ie){var I=new ie(u.multiplier),q=f.clone();u.each(function(je){je.power.lessThan(0)?q=e.divide(q,je):I=e.multiply(I,je)}),u=I,f=q}else if(u.group===Qe)for(var V in u.symbols){var Q=u.symbols[V];if(Q.group===Ie)for(var le in Q.symbols){var ye=Q.symbols[le];if(ye.power.lessThan(0))return new ut(e.expand(e.multiply(ye.clone().toLinear(),u)),e.expand(e.multiply(ye.clone().toLinear(),f)))}}return new ut(u,f)},clone:function(){return new ut(this.LHS.clone(),this.RHS.clone())},sub:function(u,f){var v=this.clone();return v.LHS=v.LHS.sub(u.clone(),f.clone()),v.RHS=v.RHS.sub(u.clone(),f.clone()),v},isZero:function(){return t.Utils.evaluate(this.toLHS()).equals(0)},latex:function(u){return[this.LHS.latex(u),this.RHS.latex(u)].join("=")}},e.equals=function(u,f){return new ut(u,f)},function(){var u=e.functions.simplify[0];e.functions.simplify[0]=function(f){return f instanceof ut?(f.LHS=u(f.LHS),f.RHS=u(f.RHS),f):u(f)}}(),t.Expression.prototype.equals=function(u){u instanceof t.Expression&&(u=u.symbol);var f=new ut(this.symbol,u);return f},t.Expression.prototype.solveFor=function(u){var f;if(this.symbol instanceof ut){if(this.symbol.LHS.isConstant()&&this.symbol.RHS.equals(u))return new t.Expression(this.symbol.LHS);if(this.symbol.RHS.isConstant()&&this.symbol.LHS.equals(u))return new t.Expression(this.symbol.RHS);f=this.symbol.toLHS()}else f=this.symbol;return c(f,u).map(function(v){return new t.Expression(v)})},t.Expression.prototype.expand=function(){if(this.symbol instanceof ut){var u=this.symbol.clone();return u.RHS=e.expand(u.RHS),u.LHS=e.expand(u.LHS),new t.Expression(u)}return new t.Expression(e.expand(this.symbol))},t.Expression.prototype.variables=function(){return this.symbol instanceof 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v=[],I=t.Algebra.Factor.factor(u);return I.group===Ie&&I.each(function(q){q=ie.unwrapPARENS(q),v=v.concat(c(q,f))}),v},csolve:function(u,f){return t.Utils.block("IGNORE_E",function(){var v,I,q,V,Q,le,ye,Ae,je,it;if(it=[],v=t.Utils.decompose_fn(u,f,!0),v.x.group===ve){I=e.parse(v.x.power),q=Number(I),V=e.pow(e.divide(v.b.negate(),v.a),I.invert()),Q=ie.toPolarFormArray(V),le=Q[0],ye=Q[1],Ae=le.toString(),je=I.toString();for(var yt,me,Ue,Le=0;Le<q;Le++)yt=Le,Ue=M("({0})*e^(2*{1}*pi*{2}*{3})",Ae,yt,I,t.Settings.IMAGINARY),me=e.parse(Ue),it.push(me)}return it},!0)},getPoints:function(u,f,v){f=f||.01,v=v||[];var I=_(u),q=0,V=Math.round(q),Q=I(V),le=Q/Math.abs(Q),ye=t.Settings.ROOTS_PER_SIDE,Ae=ye;v.push(Math.floor(V/2)),v.push(Math.abs(V)),v.push(V),u.each(function(me){me.containsFunction(t.Settings.LOG)&&v.push(.1)});var je=ze(-t.Settings.SOLVE_RADIUS,V,f),it=ze(V,t.Settings.SOLVE_RADIUS,f),yt=function(me,Ue){for(var Le,Ve,lt,Nt=[],Ct=0,Xe=me.length;Ct<Xe;Ct++)Le=me[Ct],Ve=I(Le),lt=Ve/Math.abs(Ve),!(isNaN(Ve)||!isFinite(Ve)||Nt.length>Ue)&&(lt!==le&&Nt.push(Le),le=lt);v=v.concat(Nt)};return yt(je,Ae),yt(it,ye),v},bisection:function(u,f){var v=u-1,I=u+1;if(Math.sign(f(v))!==Math.sign(f(I))){var q=0,V,Q;do{if(V=Math.abs(I-v),q++>t.Settings.MAX_BISECTION_ITER||isNaN(V))return;Q=(v+I)/2,f(v)*f(Q)>0?v=Q:I=Q}while(V>=Te.EPSILON);var le=(v+I)/2,ye=f(le);if(!isNaN(ye)&&Math.abs(ye)<=t.Settings.BI_SECTION_EPSILON)return t.Utils.round(le,13)}},Newton:function(u,f,v){var I=t.Settings.MAX_NEWTON_ITERATIONS,q=0,V=u,Q;do{var le=f(V);if(V===0&&le===0){Q=0;break}if(q++,q>I)return;Q=V-le/v(V);var ye=Math.abs(Q-V);V=Q}while(ye>Te.NEWTON_EPSILON);if(Math.abs(f(Q))<=Te.EPSILON)return Q},rewrite:function(u,f,v){if(f=f||new ie(0),u.isComposite()&&u.isLinear()){var I=[],q=[];u.each(function(Ae){Ae=Ae.clone(),Ae.fname==="sqrt"&&Ae.contains(v)?I.push(Ae):q.push(Ae)},!0),I.length===1&&(f=e.expand(e.pow(e.subtract(f,t.Utils.arraySum(q)),new ie(2))),u=e.expand(e.pow(ie.unwrapSQRT(I[0]),new ie(2))))}else u=ie.unwrapSQRT(e.expand(u));var V=0,Q=u.length;if(u.group===Qe&&u.contains(v)&&u.isLinear()){u.distributeMultiplier();var le=new ie(0);return u.each(function(Ae){Ae.contains(v)?(V++,le=e.add(le,Ae.clone())):f=e.subtract(f,Ae.clone())}),u=le,V!==Q?d.rewrite(u,f,v):[u,f]}else if(u.group===Ie&&u.contains(v)&&u.isLinear()){if(u.multiplier.lessThan(0)&&(u.multiplier=u.multiplier.multiply(new t.Frac(-1)),f.multiplier=f.multiplier.multiply(new t.Frac(-1))),f.equals(0))return new ie(0);var le=new ie(1);return u.each(function(je){je.contains(v)?le=e.multiply(le,je.clone()):f=e.divide(f,je.clone())}),u=le,d.rewrite(u,f,v)}else if(!u.isLinear()&&u.contains(v)){var ye=e.parse(u.power.clone().invert());return 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Be=K(Se);if(!(Se===void 0||typeof Se=="number"&&isNaN(Se))){if(Oe(Se))Se.forEach(function(Tt){le(Tt)});else if(Se.valueOf()!=="null"){if(typeof t.Settings.PRE_ADD_SOLUTION=="function"&&(Se=t.Settings.PRE_ADD_SOLUTION(Se)),Be||(Se=e.parse(Se)),t.Settings.make_pi_conversions&&qe){var ct=e.divide(Se.clone(),new ie(Math.PI)),wt=ct.multiplier,Mt=Math.abs(wt.num),qt=Math.abs(wt.den);Mt<10&&qt<10&&(Se=e.multiply(ct,new ie("pi")))}var Ft=Se.toString();V[Ft]||v.push(Se),V[Ft]=!0}}};if(u.group===ve&&u.contains(f)){try{var ye={};ye[f]=0,h(q,ye,"numer"),le(new ie(0))}catch(Se){}return v}if(u.group===Ie){var Ae=u.getNum();if(Ae.group===Ie){var je=String(f);return Ae.each(function(Se){Se.contains(je)&&c(Se,f,v,I,u)}),v}return c(Ae,f,v,I,q)}u.group===ee&&u.fname==="sqrt"&&(u=e.pow(ie.unwrapSQRT(u),new ie(2)));var it=(t.Utils.isSymbol(u)?u:d.toLHS(u,!1)).getNum(),yt=t.Utils.variables(it),me=yt.length;if(t.Utils.isInt(it.power)&&it.power>0&&(it=e.parse(it).toLinear()),it.group===ve||it.group===Ie&&it.contains(f))return[new ie(0)];var Ue={},Le,Ve=function(Se){Se=e.expand(Se,{expand_denominator:!0,expand_functions:!0});var qe=Se.clone();if(Se.symbols)for(var Be in Se.symbols){var ct=Se.symbols[Be],wt=ct.getDenom();if(!wt.isConstant(!0)&&Se.isComposite()){var Mt=new ie(0);return Se.each(function(nt){Mt=e.add(Mt,e.multiply(nt,wt.clone()))}),Ve(e.multiply(e.parse(Se.multiplier),Mt))}var qt=l(ct,f),Ft=qt[1].fname===t.Settings.SQRT,Tt=ie.unwrapSQRT(qt[1]),Ze=Tt.power.clone();if(!K(Ze)&&!Ze.equals(1/2)){if(Ze.den.gt(1)){if(Ft)return Se=e.subtract(Se,ct.clone()),Se=e.add(Se,e.multiply(qt[0].clone(),Tt)),Ve(Se);var ht=Ue[Ze.den];Ue[Ze.den]=ht?ht++:1}else if(Ze.sign()===-1){var Et=e.parse(f+"^"+Math.abs(Ze));return 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/**
* @license React
* react-dom.production.min.js
*
* Copyright (c) Facebook, Inc. and its affiliates.
*
* This source code is licensed under the MIT license found in the
* LICENSE file in the root directory of this source tree.
*/
/**
* @license React
* react.production.min.js
*
* Copyright (c) Facebook, Inc. and its affiliates.
*
* This source code is licensed under the MIT license found in the
* LICENSE file in the root directory of this source tree.
*/
/**
* @license React
* scheduler.production.min.js
*
* Copyright (c) Facebook, Inc. and its affiliates.
*
* This source code is licensed under the MIT license found in the
* LICENSE file in the root directory of this source tree.
*/
/* nosourcemap */
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