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1}e=1;c=0;while(Htc(Otc(f,2),0)){++c;f=Gtc(f,2)}e=pf(e*$wnd.Math.pow(2,Ytc(Wtc(c,Otc(c,g)))));for(d=3;Etc(d,f)<0;d+=2){c=0;while(Htc(Otc(f,d),0)){++c;f=Gtc(f,d)}e=pf(e*$wnd.Math.pow(d,Ytc(Wtc(c,Otc(c,g)))))}return e}return 1}\nfunction KLi(a,b,c,d){var e;e=a.r3(eKi(a.j,zLi(Ytc(b))),eKi(a.k,zLi(Ytc(b))));Xwi(c,new fxi((HBi(),lzi)));ysd(c.j,c.g);c.g=c.i;Etc(b,2)==0?Xwi(c,new fxi(dBi)):Xwi(c,new hxi(iAi,pe(ie($qb,1),J2n,135,0,[zLi(Ytc(b))])));ysd(c.j,c.g);c.g=c.i;Xwi(c,new hxi(Eyi,pe(ie($qb,1),J2n,135,0,[e])));e=eEi((VDi(),e),c,new ZHi);c.i=c.g=xsd(c.j);Xwi(c,new hxi(Eyi,pe(ie($qb,1),J2n,135,0,[e])));c.i=c.g=xsd(c.j);Htc(Otc(b,2),0)&&(d.n=true);return e}\nfunction XFi(a,b,c,d){var e;e=new mnd;if(aLi(a.j)>0&&aLi(a.k)<0){if(a.g){Xwi(c,new hxi((HBi(),bAi),pe(ie($qb,1),J2n,135,0,[b])))}else{Xwi(c,new hxi((HBi(),dAi),pe(ie($qb,1),J2n,135,0,[b])));Xmd(e,XMi(b,PIi(d),d))}return new hIi(e)}if(aLi(a.j)<0&&aLi(a.k)>0){if(a.g){Xwi(c,new hxi((HBi(),Jzi),pe(ie($qb,1),J2n,135,0,[b])));Xmd(e,XMi(b,PIi(d),d))}else{Xwi(c,new hxi((HBi(),Izi),pe(ie($qb,1),J2n,135,0,[b])))}return new hIi(e)}return null}\nfunction DKi(a,b){var c,d,e,f,g,h;if(!b){return null}if(a.n3()&&b.n3()){if(a.w_()3||l==0){return null}i=a;j>f&&(i=i.x3());if(l==1){g=Cwi(i.j,(vwi(),swi));i=BLi(i,g,c);i=KLi(i,2,c,d)}if(l==2){e=ZKi(iKi(i.j,i.k),null);if(!XJi(Cwi(e,(vwi(),swi)))){k=Awi(i.k,swi);i=BLi(i,k,c);g=Cwi(i.j,swi);i=BLi(i,g,c);i=KLi(i,2,c,d)}}if(l==3){g=Cwi(i.j,(vwi(),swi));i=BLi(i,g,c);while(vKi(i.k,(mij(),Fhj),b)>1){h=Dwi(i.k,Fhj);i=BLi(i,h,c)}if(vKi(i.j,Fhj,b)==3){h=Dwi(i.j,Fhj);i=BLi(i,h,c)}i=KLi(i,2,c,d)}return new iIi(i)}\nfunction UIi(a,b,c,d,e){var f,g,h,i,j,k,l,m;f=new dxi;m=new dxi;g=null;h=a;do{e.g=false;e.i=1;for(j=c,k=0,l=j.length;k1){!!ywj&&zwj(ywj,(Rwj(),Kwj),S3n+i);!!ywj&&zwj(ywj,(Rwj(),Kwj),'from: '+h);!!ywj&&zwj(ywj,(Rwj(),Kwj),'to: '+g);i.V2()?Ywi(m,bxi(f)):axi(m,h,g,f)}if(e.g||e.i>1){h=g;h.b3(0);cxi(f);break}}}while(e.g||e.i>1);a.b3(0);if(!Vb(a,g)){g.b3(0);!!d&&!!b?$wi(d,b,m,g,pe(ie($qb,1),J2n,135,0,[])):!!d&&Ywi(d,bxi(m));++e.i;return g}return a}\nfunction dCi(){dCi=iuc;aCi=new eCi('POSITIVE',0,'+');_Bi=new eCi('NEGATIVE',1,'-');ZBi=new eCi('INCREASING',2,'\\\\nearrow');YBi=new eCi('DECREASING',3,'\\\\searrow');VBi=new eCi('CONVEX',4,'\\\\smile');SBi=new eCi('CONCAVE',5,'\\\\frown');XBi=new eCi('CONVEX_INCREASING',6,'\\u2934');WBi=new eCi('CONVEX_DECREASING',7,'\\u2937');UBi=new eCi('CONCAVE_INCREASING',8,'\\\\rotatebox{90}{\\u2935}');TBi=new eCi('CONCAVE_DECREASING',9,'\\u2935');$Bi=new eCi('INVALID',10,'|');cCi=new eCi('ZERO',11,'0');bCi=new eCi('VSPACE',12,' \\\\; ')}\nfunction xwi(a,b,c){vwi();var d,e,f,g,h,i,j,k;f=me(mub,K2n,136,1+b.B.length,0,1);f[0]=a;for(h=0;h0){return -1}return a.g[0].f3(b);case 20:c=0;for(f=new CMi(a);f.gc&&(c=i)}return c;case 28:h=a.g[0].f3(b);if(h!=-1&&a.g[1].m3()){return pf(h*a.g[1].w_())}return -1;case 24:if(vKi(a,(mij(),Jhj),b)>0){return -1}g=0;for(e=new CMi(a);e.g0){Xwi(c,new hxi((HBi(),wzi),pe(ie($qb,1),J2n,135,0,[e,a.j,b])));a.g||Xmd(i,XMi(b,PIi(d),d))}else if(e.d3()){Xwi(c,new hxi((HBi(),vzi),pe(ie($qb,1),J2n,135,0,[e,a.j,b])));a.g&&Xmd(i,XMi(b,PIi(d),d))}else{a.g?NIi(d,new ZLi(e,zLi(0),false,true)):NIi(d,new ZLi(e,zLi(0),true,true));Xmd(i,XMi(b,PIi(d),d))}return new hIi(i)}k=TMi(j.getAtIndex(0));l=TMi(j.getAtIndex(1));g=cKi(e,cKi(DJi(b,GJi((mij(),yhj),k)),DJi(b,GJi(yhj,l))));h=XLi(a,g,a.k);_wi(c,a,h,(HBi(),fzi),pe(ie($qb,1),J2n,135,0,[]));return new iIi(h)}\nfunction XKi(a,b){var c,d,e,f,g,h,i,j,k,l,m,n,o;if(!b){return a}if(a.m3()&&b.m3()){return zLi($wnd.Math.floor(a.w_()/b.w_()))}if(Vb(a,b)){return zLi(1)}if(a.Bv((mij(),Jhj))){l=null;for(j=new CMi(a);j.g1){for(h=new snd(i);h.gAbn){Xwi(c,new hxi((HBi(),Qzi),pe(ie($qb,1),J2n,135,0,[h,b])));return new gIi}}else{NIi(d,new ZLi(VKi(NJi((uLi(),rLi),zLi(2))),a.k,true,false));NIi(d,new ZLi(a.k,NJi(rLi,zLi(2)),true,false))}}else if(qMi(h,jgj)){if(a.k.d3()){if(a.k.w_()<0||a.k.w_()>Bbn){Xwi(c,new hxi((HBi(),Pzi),pe(ie($qb,1),J2n,135,0,[h,b])));return new gIi}}else{NIi(d,new ZLi(zLi(0),a.k,true,false));NIi(d,new ZLi(a.k,(uLi(),rLi),true,false))}}else{if(a.k.d3()){if(a.k.w_()Abn){Xwi(c,new hxi((HBi(),Rzi),pe(ie($qb,1),J2n,135,0,[h,b])));return new gIi}}else{NIi(d,new ZLi(VKi(NJi((uLi(),rLi),zLi(2))),a.k,true,false));NIi(d,new ZLi(a.k,NJi(rLi,zLi(2)),true,false))}}g=cLi(h.i);e=h.g[0];f=GJi(g,a.k);return new iIi(PLi(a,e,f))}\nfunction vDi(a,b,c,d){var e,f,g,h,i,j,k,l,m,n,o,p,q,r,s;h=ELi(a,b);if(h%2!=0||!XJi(a.k)){return null}for(i=1;ii&&(f.g+=Bid(me(sf,fXm,5,-i,15,1)));h=j.g.length;0h&&(j.g+=Bid(me(sf,fXm,5,-h,15,1)))}else{if(j.g.length!=0){Xmd(l,new gCi(j.g));i=j.g.length;0i&&(j.g+=Bid(me(sf,fXm,5,-i,15,1)));h=f.g.length;0h&&(f.g+=Bid(me(sf,fXm,5,-h,15,1)))}}g=!g}else if(d==37){++e;k=(axd(e,a.length),a.charCodeAt(e)-48);if(g){if(k>=0&&kh&&(j.g+=Bid(me(sf,fXm,5,-h,15,1)))}k>=0&&k0)&&NIi(d,new ZLi(h,zLi(0),false,false));j=NJi(DJi(GJi(yhj,f),fKi(h,zLi(2))),cKi(zLi(2),e));k=NJi(iKi(GJi(yhj,f),fKi(h,zLi(2))),cKi(zLi(2),e));Xmd(l,XMi(b,lKi(j),d));Xmd(l,XMi(b,lKi(k),d));return new hIi(l)}\nfunction bEi(a,b,c){var d,e,f;f=a.g[0];for(e=new CMi(f);e.g1){for(g=new snd(h);g.g0&&XJi(a.k)){if(a.g){if(a.i){Xwi(c,new hxi((HBi(),aAi),pe(ie($qb,1),J2n,135,0,[b])))}else{g=new VLi(a.j,a.k);Xwi(c,new hxi((HBi(),_zi),pe(ie($qb,1),J2n,135,0,[g])));return new hIi(TLi(g,b,c,new SIi))}}else{if(a.i){g=new VLi(a.j,a.k);Xwi(c,new hxi((HBi(),$zi),pe(ie($qb,1),J2n,135,0,[g])));e=TLi(g,b,c,new SIi);f=new IMi(pe(ie(mub,1),K2n,136,0,[]));for(i=e.tf();i.$i();){h=i._i();EMi(f,TMi(h))}Xmd(j,XMi(b,jKi(PIi(d),f),d))}else{Xwi(c,new hxi((HBi(),Zzi),pe(ie($qb,1),J2n,135,0,[b])));Xmd(j,XMi(b,PIi(d),d))}}return new hIi(j)}if(XJi(a.j)&&aLi(a.k)>0){if(a.g){if(a.i){g=new VLi(a.j,a.k);Xwi(c,new hxi((HBi(),GBi),pe(ie($qb,1),J2n,135,0,[g])));e=TLi(g,b,c,new SIi);f=new IMi(pe(ie(mub,1),K2n,136,0,[]));for(i=e.tf();i.$i();){h=i._i();EMi(f,TMi(h))}Xmd(j,XMi(b,jKi(PIi(d),f),d))}else{Xwi(c,new hxi((HBi(),FBi),pe(ie($qb,1),J2n,135,0,[b])));Xmd(j,XMi(b,PIi(d),d))}}else{if(a.i){Xwi(c,new hxi((HBi(),DBi),pe(ie($qb,1),J2n,135,0,[b])))}else{g=new VLi(a.j,a.k);Xwi(c,new hxi((HBi(),CBi),pe(ie($qb,1),J2n,135,0,[g])));return new hIi(TLi(g,b,c,new SIi))}}return new hIi(j)}return null}\nfunction gDi(a,b,c,d){var e,f,g,h,i,j,k,l,m,n,o,p,q;if(!pKi(a.j)||!a.k.l3(b)){return null}q=a.j;if(q.i!=(mij(),dij)){if(a.k.d3()){if(a.k.w_()<-1||a.k.w_()>1){Xwi(c,new hxi((HBi(),Szi),pe(ie($qb,1),J2n,135,0,[q,b])));return new gIi}}else{NIi(d,new ZLi(zLi(-1),a.k,true,false));NIi(d,new ZLi(a.k,zLi(1),true,false))}}j=cLi(q.i);h=q.g[0];if(qMi(q,dij)){i=DJi(GJi(j,a.k),cKi(new oLi('k',++d.i),(uLi(),rLi)));g=PLi(a,h,i);return new hIi((o=pe(ie(Itb,1),cXm,285,0,[(xIi(),qIi),mIi,NCi,rIi,OCi,LCi,_Ci,SCi,sIi,pIi,vIi,XCi,tIi,wIi,QCi,uIi,kIi,MCi,oIi,lIi,KCi,UCi,PCi,$Ci,TCi,WCi,ZCi,YCi,nIi,VCi,RCi]),VIi(g,b,c,o,d)))}f=DJi(GJi(j,a.k),cKi(bKi(2,new oLi('k',++d.i)),(uLi(),rLi)));e=new VLi(h,f);m=(p=pe(ie(Itb,1),cXm,285,0,[(xIi(),qIi),mIi,NCi,rIi,OCi,LCi,_Ci,SCi,sIi,pIi,vIi,XCi,tIi,wIi,QCi,uIi,kIi,MCi,oIi,lIi,KCi,UCi,PCi,$Ci,TCi,WCi,ZCi,YCi,nIi,VCi,RCi]),VIi(e,b,c,p,d));if(!UJi(a.k,1)&&!UJi(a.k,-1)){l=DJi(GJi(j,a.k),cKi(bKi(2,new oLi('k',++d.i)),rLi));qMi(q,Zhj)?(k=new VLi(iKi(rLi,h),l)):(k=new VLi(iKi(bKi(2,rLi),h),l));m.addAll((n=pe(ie(Itb,1),cXm,285,0,[qIi,mIi,NCi,rIi,OCi,LCi,_Ci,SCi,sIi,pIi,vIi,XCi,tIi,wIi,QCi,uIi,kIi,MCi,oIi,lIi,KCi,UCi,PCi,$Ci,TCi,WCi,ZCi,YCi,nIi,VCi,RCi]),VIi(k,b,c,n,d)))}return new hIi(m)}\nfunction XDi(a,b,c,d,e){var f,g,h,i,j,k,l,m,n,o,p,q,r;if(b.Bv((mij(),zhj))){o=b;f=null;n=null;m=null;for(k=new CMi(o);k.gvKi(q.j,bgj,b)&&(q=q.x3());if(vKi(q.j,bgj,b)==2){o=Dwi(q.j,bgj);q=BLi(q,o,c)}q.j.Bv(yhj)&&q.k.Bv(yhj)&&(q=ILi(q,zLi(-1),c));if(q.j.Bv(yhj)||q.k.Bv(yhj)){throw Btc((bxi(c),new nwi))}return new iIi(q)}j=new t9c;Bwi(a,j,twi);Xwi(c,new fxi((HBi(),PAi)));ysd(c.j,c.g);c.g=c.i;C=new mnd;for(i=(p=(new fmd(j.g)).g._g().tf(),new gmd(p));i.g.$i();){h=(l=i.g._i(),l.Ji());B=new VLi(h,zLi(0));Zmd(C,TLi(B,b,c,new SIi))}c.i=c.g=xsd(c.j);s=new mnd;for(w=new snd(C);w.g 0$ therefore $%1 > 0$ for all %2');vzi=new IBi('LEADING_COEFFICIENT_NEGATIVE',33,'LeadingCoefficientNegative','$a = %0 < 0$ therefore $%1 < 0$ for all %2');xzi=new IBi('LEFT_POSITIVE_RIGHT_NEGATIVE',34,'LeftPositiveRightNegative','The left hand side is always positive, the right is always negative');Pyi=new JBi('EXCLUDE_UNDEFINED_POINTS',35,'ExcludeUndefinedPoints','Exclude undefined points: %0');Xzi=new IBi('PLUG_IN_AND_CHECK',36,'PlugInAndCheck','Plug in and check if %0 is a correct solution');xxi=new IBi('CHECK_VALIDITY',37,'CheckingValidityOfSolutions','Checking validity of solutions');vBi=new IBi('VALID_SOLUTION',38,'ValidSolution','Valid Solution: %0');nzi=new IBi('INVALID_SOLUTION',39,'InvalidSolution','Invalid Solution: %0');wBi=new IBi('VALID_SOLUTION_ABS',40,V2n,'$%0 \\\\in %1$');ozi=new IBi('INVALID_SOLUTION_ABS',41,V2n,'$%0 \\\\notin %1$');hzi=new IBi('FIND_UNDEFINED_POINTS',42,'FindUndefinedPoints','Find undefined points');Gxi=new IBi('DETERMINE_THE_DEFINED_RANGE',43,'DetermineTheDefinedRange','Determine the defined range');PAi=new IBi('ROOTS_AND_SIGN_TABLE',44,'FindRootsAndCreateSignTable','Find the roots of the absolute values and create sign table');AAi=new JBi('RESOLVE_ABSOLUTE_VALUES',45,'ResolveAbsoluteValues','$\\\\left|a\\\\right| = \\\\left|b\\\\right| \\\\implies a = \\\\pm b$');szi=new JBi('IS_POSITIVE_IN',46,'IsPositiveIn','$%0 \\\\ge 0$ in %1');qzi=new JBi('IS_NEGATIVE_IN',47,'IsNegativeIn','$%0 \\\\le 0$ in %1');Hzi=new IBi(W2n,48,'NegateBothSides','Negate both sides');eBi=new IBi('SQUARE_ROOT',49,'TakeSquareRoot','Take square root of both sides');Exi=new IBi('CUBE_ROOT',50,'TakeCubeRoot','Take cube root of both sides');Tzi=new IBi('NTH_ROOT',51,'TakeNthRoot','Take %0 root of both sides');dBi=new IBi('SQUARE_BOTH_SIDES',52,'SquareBothSides','Square both sides');iAi=new IBi(X2n,53,'RaiseToPower','Raise both sides to the %0 power');mxi=new IBi('ADD_TO_BOTH_SIDES',54,'AddAToBothSides','Add %0 to both sides');nxi=new IBi('ADD_TO_BOTH_SIDES_NUM',55,'AddToBithSidesNum','Add %0 to the %1 equation');jBi=new IBi('SUBTRACT_FROM_BOTH_SIDES',56,'SubtractAFromBothSides','Subtract %0 from both sides');kBi=new IBi('SUBTRACT_FROM_BOTH_SIDES_NUM',57,'SubtractFromBothSidesNum','Subtract %0 from both sides of equation %1');Bzi=new IBi('MULTIPLY_BOTH_SIDES',58,'MultiplyBothSidesByA','Multiply both sides by %0');Czi=new IBi('MULTIPLY_BOTH_SIDES_NUM',59,'MultiplyBothSidesNum','Multiply both sides by %0 of equation %1');tyi=new IBi('DIVIDE_BOTH_SIDES',60,'DivideBothSidesByA','Divide both sides by %0');uyi=new IBi('DIVIDE_BOTH_SIDES_NUM',61,'DivideBothSidesNum','Divide both sides by %0 of equation %1');Yyi=new IBi('FACTOR_EQUATION',62,'FactorEquation','Factor equation');kAi=new IBi('RECIPROCATE_BOTH_SIDES',63,'ReciprocateBothSides','Reciprocate both sides');uBi=new IBi('USE_QUADRATIC_FORMULA',64,'UseQuadraticFormulaWithABC','Use quadratic formula with $a = %0$, $b = %1$, $c = %2$');hAi=new IBi('QUADRATIC_FORMULA',65,'QuadraticFormula','$%0 = \\\\frac{-b \\\\pm \\\\sqrt{b^2-4ac}}{2a}$');Axi=new IBi('COMPLETE_THE_CUBE',66,'CompleteCube','Complete the cube');Bxi=new IBi(Y2n,67,eFn,'Complete the square');Szi=new IBi('NO_SOLUTION_SIN_COS',68,'NoSolutionSinCos','$%0 \\\\in \\\\left[-1, 1\\\\right]$ for all $%1 \\\\in \\\\mathbb{R}$');Qzi=new IBi('NO_SOLUTION_ARCSIN',69,'NoSolutionArcsin',Z2n);Pzi=new IBi('NO_SOLUTION_ARCCOS',70,'NoSolutionArccos','$%0 \\\\in \\\\left[0, \\\\pi\\\\right]$ for all $%1 \\\\in \\\\mathbb{R}$');Rzi=new IBi('NO_SOLUTION_ARCTAN',71,'NoSolutionArctan',Z2n);zAi=new IBi('REPLACE_WITH',72,'ReplaceAWithB','Replace %0 with %1');xAi=new IBi('REPLACE_AND_REGROUP',73,'ReplaceAndRegroup','Replace %0 in %1 and regroup');yAi=new IBi('REPLACE_AND_SOLVE',74,'ReplaceAndSolve','Replace %0 with %1 in %2 and solve the equation');Ryi=new IBi($2n,75,'ExpandFractions','Expand Fractions, the common denominator is: %0');fAi=new IBi(_2n,76,'ProductIsZero','Product is zero');kzi=new JBi(a3n,77,'FractionIsZero','When the quotient of expressions equals 0, the numerator has to be 0');vAi=new IBi('REGROUP_WRAPPER',78,'RegroupExpression','Regroup Expression');SAi=new IBi('SIMPLIFICATION_WRAPPER',79,'SimplifyExpression','Simplify Expression');Cxi=new IBi('CONVERT_DECIMALS',80,'ConvertDecimals','Convert decimals to fractions');zyi=new IBi(b3n,81,'DoubleMinus','A double negative is a positive');jAi=new IBi('RATIONALIZE_DENOMINATOR',82,'RationalizeDenominator','Rationalize the denominator.');Fzi=new IBi('MULTIPLY_NUM_DENOM',83,'MultiplyNumeratorAndDenominator','Mutiply the numerator and denominator by %0');oyi=new IBi('DISTRIBUTE_POWER_FRAC',84,'DistributePowerOverFraction','Distribute power over fraction');qyi=new IBi('DISTRIBUTE_ROOT_FRAC',85,'DistributeRootOverFraction','Distribute the root over the fraction');nyi=new IBi(c3n,86,'DistributeMinus','Distribute minus');ixi=new IBi('ADD_CONSTANTS',87,'AddConstants','Add constants');yxi=new JBi('COLLECT_LIKE_TERMS',88,'CollectLikeTerms','Collect like terms: %0');kxi=new IBi(d3n,89,'AddFractions','Add fractions');lxi=new IBi(e3n,90,'AddNumerators','Add numerators');zxi=new IBi(f3n,91,'CommonFraction','Write the product as a single fraction');wxi=new JBi(g3n,92,'CancelFraction','Cancel %0 in the fraction');Azi=new IBi(h3n,93,'MultipliedByZero','Anything multiplied by zero is zero');uAi=new IBi(i3n,94,'RegroupProducts','Regroup products');Dzi=new IBi(j3n,95,'MultiplyConstants','Multiply constants');zzi=new JBi('MULTIPLIED_BY_ONE',96,'MultipliedByOne','Any expression multiplied by one is itself');Lyi=new JBi('EVEN_NUMBER_OF_NEGATIVES',97,'EvenNumberOfNegative','Multiplying an even number of negative numbers gives a positive');Uzi=new JBi('ODD_NUMBER_OF_NEGATIVES',98,'OddNumberOfNegative','Multiplying an odd number of negative numbers gives a negative');Myi=new IBi('EVEN_POWER_NEGATIVE',99,'EvenPowerNegative','An even power of a negative number is a positive');Vzi=new IBi('ODD_POWER_NEGATIVE',100,'OddPowerNegative','An odd power of a negative number is a negative');Kzi=new IBi('NEGATIVE_NUM_AND_DENOM',101,'NegativeNumeratorAndDenominator','Use $\\\\frac{-a}{-b} = \\\\frac{a}{b}$');Lzi=new IBi('NEGATIVE_NUM_OR_DENOM',102,'NegativeNumeratorOrDenominator','Use $\\\\frac{-a}{b} = \\\\frac{a}{-b} = -\\\\frac{a}{b}$');lAi=new JBi('REDUCE_ROOT_AND_POWER',103,'ReduceRootAndPower',k3n);mAi=new JBi('REDUCE_ROOT_AND_POWER_EVEN',104,'ReduceRootAndPowerEven',k3n);Gyi=new IBi('EVALUATE_FRACTION',105,'EvaluateFraction','Evaluate fraction');Iyi=new IBi('EVALUATE_POWER',106,'EvaluatePower','Evaluate powers');Jyi=new IBi('EVALUATE_ROOT',107,'EvaluateRoot','Evaluate roots');ABi=new JBi('ZEROTH_POWER',108,'ZerothPower','The zeroth power of anything is one');izi=new JBi('FIRST_POWER',109,'FirstPower','The first power of anything is itself');jzi=new JBi('FIRST_ROOT',110,'FirstRoot','The first root of anything is itself');QAi=new IBi('ROOT_OF_ONE',111,'RootOfOne','Any root of 1 is 1');Oyi=new JBi('EVEN_ROOT_OF_NEGATIVE',112,'EvenRootOfNegative','The square root of a negative number is undefined in the set of the real numbers');Wzi=new IBi('ODD_ROOT_OF_NEGATIVE',113,'OddRootOfNegative','An odd root of a negative radicand is always negative');RAi=new IBi(l3n,114,'RootOfRoot','Use $\\\\sqrt[m]{\\\\sqrt[n]{a}} \\\\equiv \\\\sqrt[mn]{a}$ to simplify the expression');IAi=new IBi('REWRITE_DECIMAL_AS_COMMON_FRACTION',115,'RewriteDecimalAsCommonFraction','Rewrite decimal as common fraction');bBi=new IBi(m3n,116,'SplitProducts','Split products for factoring');$Ai=new IBi(n3n,117,'SplitFractions','Split fractions');aBi=new JBi('SPLIT_POWERS',118,'SplitPowers',o3n);cBi=new JBi(p3n,119,'SplitRoots','The root of a product is equal to the product of the roots of each factor');Ayi=new IBi(q3n,120,'EliminateOpposites','Eliminate the opposites');Vyi=new IBi(r3n,121,'ExponentialOfLog','Exponential of logarithm');EBi=new IBi('ZERO_IN_ADDITION',122,'AddingOrSubtractionZero','When adding or subtracting zero, the quantity does not change');BBi=new JBi('ZERO_DIVIDED',123,'ZeroDivided','Zero divided by anything is zero');Fyi=new JBi('EVALUATE_DIVISION',124,'EvaluateDivision','Evaluate the division');ryi=new JBi('DIVIDED_BY_ITSELF',125,'DividedByItself','Any expression divided by itself equals 1');syi=new JBi('DIVIDED_BY_ZERO',126,'DividedByZero','Any expression divided by zero is undefined');wyi=new JBi('DIVIDE_BY_ONE',127,'DividedByOne','Any expression divided by one remains the same');vyi=new JBi('DIVIDE_BY_NEGATVE_ONE',128,'DividedByNegativeOne','Any expression divided by negative one negates the expression');BAi=new IBi('REWRITE_AS',129,'RewriteAAsB',o3n);DAi=new IBi('REWRITE_COMPLEX_FRACTION',130,'RewriteComplexFraction','Rewrite complex fraction');eAi=new IBi(s3n,131,'MultiplyExponents','Simplify the expression by multiplying the exponents');Mzi=new JBi('NEGATIVE_POWER',132,'NegativePower','Express with a positive exponent using $a^{-n} \\\\equiv \\\\frac{1}{a^n}$');gzi=new IBi('FACTOR_SQUARE',133,'FactorSquare','Factor out the perfect square');Uyi=new JBi('EXPAND_SUM_TIMES_SUM',134,'ExpandSumTimesSum','Multiply everything in the first parentheses with everything in the second parentheses');Tyi=new JBi('EXPAND_SIMPLE_TIMES_SUM',135,'ExpandSimpleTimesSum','Multiply %0 with everything in the parentheses');txi=new IBi('BINOM_SQUARED_SUM',136,t3n,'Use $(a+b)^2 \\\\equiv a^2 + 2ab + b^2$ to expand');rxi=new IBi('BINOM_SQUARED_DIFF',137,u3n,'Use $(a-b)^2 \\\\equiv a^2 - 2ab + b^2$ to expand');oxi=new IBi('BINOM_CUBED',138,v3n,'Use $(a+b)^3 \\\\equiv a^3 + 3a^2b + 3ab^2 + b^3$ to expand');qBi=new IBi('TRINOM_SQUARED',139,'TrinomSquared','Use $(a+b+c)^2 \\\\equiv a^2 + b^2 + c^2 + 2ab + 2bc + 2ac$ to expand');Ixi=new IBi('DIFFERENCE_OF_SQUARES',140,'DifferenceOfSquares','Use $(a+b)(a-b) \\\\equiv a^2-b^2$ to expand');Zyi=new IBi(w3n,141,'FactorFractions','Factor fractions');lBi=new IBi('SUM_OF_CUBES',142,'SumOfCubes','Use $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ to factor');uxi=new IBi('BINOM_SQUARED_SUM_FACTOR',143,t3n,'Use $a^2 + 2ab + b^2 \\\\equiv (a+b)^2$ to factor');sxi=new IBi('BINOM_SQUARED_DIFF_FACTOR',144,u3n,'Use $a^2 - 2ab + b^2 \\\\equiv (a-b)^2$ to factor');Hxi=new IBi('DIFFERENCE_OF_CUBES_FACTOR',145,'DifferenceOfCubes','Use $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ to factor');Jxi=new IBi('DIFFERENCE_OF_SQUARES_FACTOR',146,'DifferenceOfSquaresFactor','Use $a^2-b^2 \\\\equiv (a+b)(a-b)$ to factor');qxi=new IBi('BINOM_CUBED_SUM_FACTOR',147,v3n,'Use $a^3 + 3a^2b + 3ab^2 + b^3 \\\\equiv (a+b)^3$ to factor');pxi=new IBi('BINOM_CUBED_DIFF_FACTOR',148,v3n,'Use $a^3 - 3a^2b + 3ab^2 - b^3 \\\\equiv (a+b)^3$ to factor');tzi=new IBi('IS_POSITIVE_IN_INEQUALITY',149,'IsPositiveInInequality','%0 is positive in %1, because there are an even number of negative values in the product');rzi=new IBi('IS_NEGATIVE_IN_INEQUALITY',150,'IsNegativeInInequality','%0 is negative in %1, because there are an odd number of negative values in the product');uzi=new IBi('IS_ZERO_IN',151,'IsZeroIn','%0 is zero in %1, because at least one of the multiplicands is zero');pzi=new IBi('IS_INVALID_IN',152,'IsInvalidIn','%0 is invalid in %1, because there is a zero in the denominator');fzi=new JBi('FACTOR_QUADRATIC',153,'FactorQuadratic','Use $ax^2+bx+c = a\\\\left(x - x_{1}\\\\right)\\\\left(x - x_{2}\\\\right)$ to factor the expression');bzi=new JBi('FACTOR_OUT',154,'FactorOutA','Factor out %0');Xyi=new IBi(x3n,155,'FactorCommon','Factor common');ezi=new IBi(y3n,156,'FactorPolynomial','Factor polynomial');$yi=new IBi('FACTOR_FROM_PAIR',157,'FactorOutAFromEveryPair','Factor out %0 from every pair');azi=new IBi('FACTOR_MINUS',158,'FactorMinus','Factor out the minus sign');_yi=new IBi('FACTOR_GCD',159,'FactorGCD','Factor out the greatest common divisor of %0 and %1: %2');wAi=new IBi('REORGANIZE_EXPRESSION',160,'ReorganizeExpression','Reorganize expression');CAi=new IBi('REWRITE_AS_MULTIPLICATION',161,'RewriteAsMultiplication','Rewrite as multiplication');pyi=new IBi(z3n,162,'DistributePowerOverProduct','Distribute power over product');fBi=new IBi(A3n,163,'SquareRootMultipliedByItself','When the square root of an expression in multiplied by itself, the result is that expression');Syi=new IBi(B3n,164,'ExpandRoot','Using $\\\\sqrt[n]{a} \\\\equiv \\\\sqrt[mn]{a^m}$, expand the expression');gAi=new IBi('PRODUCT_OF_ROOTS',165,'ProductOfRoots','The product of roots with the same index is equal to the root of the product');Yzi=new IBi('POLYNOMIAL_DIVISION',166,'DivideAByBToGetC','Divide %0 by %1 to get %2');Kyi=new IBi('EVALUATE_TRIGO',167,'EvaluateTrigo','Evaluate trigonometric function');oBi=new JBi('TRIGO_ODD_SIN',168,'TrigoOddSin','$\\\\sin(-x) = -\\\\sin(x)$');nBi=new JBi('TRIGO_EVEN_COS',169,'TrigoEvenCos','$\\\\cos(-x) = \\\\cos(x)$');pBi=new JBi('TRIGO_ODD_TAN',170,'TrigoOddTan','$\\\\tan(-x) = \\\\tan(x)$');czi=new IBi('FACTOR_OUT_2PI',171,C3n,'Factor out $2 \\\\pi$ where possible');dzi=new IBi('FACTOR_OUT_PI',172,C3n,'Factor out $\\\\pi$ where possible');Cyi=new JBi('ELIMINATE_THE_PERIOD_SIN',173,D3n,'$\\\\sin(x + k \\\\cdot 2 \\\\pi) = \\\\sin(x)$, for any $k \\\\in \\\\mathbb{Z}$');Byi=new JBi('ELIMINATE_THE_PERIOD_COS',174,D3n,'$\\\\cos(x + k \\\\cdot 2 \\\\pi) = \\\\cos(x)$, for any $k \\\\in \\\\mathbb{Z}$');Dyi=new JBi('ELIMINATE_THE_PERIOD_TAN',175,D3n,'$\\\\tan(x + k \\\\cdot \\\\pi) = \\\\tan(x)$, for any $k \\\\in \\\\mathbb{Z}$');qAi=new JBi('REDUCE_TO_FRIST_QUADRANT_SIN_II',176,'ReduceToFirstQuadrantSinII','Use $\\\\sin(x) = \\\\sin(\\\\pi - x)$');rAi=new JBi('REDUCE_TO_FRIST_QUADRANT_SIN_III',177,'ReduceToFirstQuadrantSinIII','Use $\\\\sin(x) = -\\\\sin(x - \\\\pi)$');sAi=new JBi('REDUCE_TO_FRIST_QUADRANT_SIN_IV',178,'ReduceToFirstQuadrantSinIV','Use $\\\\sin(x) = -\\\\sin(2 \\\\pi - x)$');nAi=new JBi('REDUCE_TO_FRIST_QUADRANT_COS_II',179,'ReduceToFirstQuadrantCosII','Use $\\\\cos(x) = -\\\\cos(\\\\pi - x)$');oAi=new JBi('REDUCE_TO_FRIST_QUADRANT_COS_III',180,'ReduceToFirstQuadrantCosIII','Use $\\\\cos(x) = -\\\\cos(x - \\\\pi)$');pAi=new JBi('REDUCE_TO_FRIST_QUADRANT_COS_IV',181,'ReduceToFirstQuadrantCosIV','Use $\\\\cos(x) = \\\\cos(2 \\\\pi - x)$');tAi=new JBi('REDUCE_TO_FRIST_QUADRANT_TAN',182,'ReduceToFirstQuadrantTan','Use $\\\\tan(x) = -\\\\tan(\\\\pi - x)$');_Ai=new IBi(E3n,183,'SplitFractionsWithPi','Split fractions with $\\\\pi$');MAi=new JBi('REWRITE_SIN_PI_POSITIVE',184,'RewriteSinPiPositive','$\\\\sin(x + \\\\pi) = -\\\\sin(x)$');LAi=new JBi('REWRITE_SIN_PI_NEGATIVE',185,'RewriteSinPiNegative','$\\\\sin(\\\\pi - x) = \\\\sin(x)$');HAi=new JBi('REWRITE_COS_PI_POSITIVE',186,'RewriteCosPiPositive','$\\\\cos(x + \\\\pi) = -\\\\cos(x)$');GAi=new JBi('REWRITE_COS_PI_NEGATIVE',187,'RewriteCosPiNegative','$\\\\cos(\\\\pi - x) = -\\\\cos(x)$');KAi=new JBi('REWRITE_SIN_PI_HALF_POSITIVE',188,'RewriteSinPiHalfPositive','$\\\\sin\\\\left(x + \\\\frac{\\\\pi}{2}\\\\right) = \\\\cos(x)$');JAi=new JBi('REWRITE_SIN_PI_HALF_NEGATIVE',189,'RewriteSinPiHalfNegative','$\\\\sin\\\\left(\\\\frac{\\\\pi}{2} - x\\\\right) = \\\\cos(x)$');FAi=new JBi('REWRITE_COS_PI_HALF_POSITIVE',190,'RewriteCosPiHalfPositive','$\\\\cos\\\\left(x + \\\\frac{\\\\pi}{2}\\\\right) = -\\\\sin(x)$');EAi=new JBi('REWRITE_COS_PI_HALF_NEGATIVE',191,'RewriteCosPiHalfNegative','$\\\\cos\\\\left(\\\\frac{\\\\pi}{2} - x\\\\right) = \\\\sin(x)$');OAi=new JBi('REWRITE_TAN_PI_HALF_POSITIVE',192,'RewriteTanPiHalfPositive','$\\\\tan\\\\left(x + \\\\frac{\\\\pi}{2}\\\\right) = -\\\\frac{1}{\\\\tan(x)}$');NAi=new JBi('REWRITE_TAN_PI_HALF_NEGATIVE',193,'RewriteTanPiHalfNegative','$\\\\tan\\\\left(\\\\frac{\\\\pi}{2} - x\\\\right) = \\\\frac{1}{\\\\tan(x)}$');Hyi=new IBi('EVALUATE_INVERSE_TRIGO',194,'EvaluateInverseTrigo','Evaluate inverse trigonometric function');cAi=new JBi('POSITIVE_UNDER_ABSOLUTE_VALUE',195,'PositiveUnderAbsoluteValue','The absolute value of a positive value is itself');Nzi=new JBi('NEGATIVE_UNDER_ABSOLUTE_VALUE',196,'NegativeUnderAbsoluteValue','The absolute value of a negative value is the negation of itself');Nyi=new JBi(F3n,197,'EvenPowerOfAbsoluteValue','An even power of an absolute value is already positive');Kxi=new IBi('DIFFERENTIATE',198,'Differentiate','Differentiate %0');jyi=new JBi('DIFF_SUM',199,'SumRule','$\\\\frac{d}{dx} \\\\left[f(x) + g(x)\\\\right] = \\\\frac{d}{dx}f(x) + \\\\frac{d}{dx}g(x)$');Rxi=new IBi('DIFF_CONSTANT',200,'ConstantRule','The derivative of a constant is zero');Sxi=new JBi('DIFF_CONSTANT_COEFFICIENT',201,'ConstantCoefficientRule','$\\\\frac{d}{dx} \\\\left[k \\\\cdot f(x) \\\\right] = k \\\\cdot \\\\frac{d}{dx} f(x)$');eyi=new JBi('DIFF_PRODUCT',202,'ProductRule','$\\\\frac{d}{dx}\\\\left[f(x) \\\\cdot g(x)\\\\right] = \\\\frac{d}{dx} f(x) \\\\cdot g(x) + f(x) \\\\cdot \\\\frac{d}{dx} g(x)$');Zxi=new JBi('DIFF_FRACTION',203,'QuotientRule','$\\\\frac{d}{dx} \\\\frac{f(x)}{g(x)} = \\\\frac{\\\\frac{d}{dx} f(x) \\\\cdot g(x) - f(x) \\\\cdot \\\\frac{d}{dx} g(x)}{(g(x))^2}$');myi=new JBi('DIFF_VARIABLE',204,'DifferentiateVariable','$\\\\frac{d}{dx} x = 1$');cyi=new JBi('DIFF_POWER',205,'PowerRule','$\\\\frac{d}{dx} x^n = n x^{n-1}$');Xxi=new JBi('DIFF_EXPONENTIAL_E',206,'ExponentialRuleE','$\\\\frac{d}{dx} e^x = e^x$');Vxi=new JBi('DIFF_EXPONENTIAL',207,'ExponentialRule','$\\\\frac{d}{dx} a^x = \\\\ln(a) a^x$');fyi=new JBi('DIFF_ROOT',208,'RootRule','$\\\\frac{d}{dx} \\\\sqrt[n]{x} = \\\\frac{1}{n \\\\sqrt[n]{x^{n-1}}}$');$xi=new JBi('DIFF_LOG',209,'LogRule','$\\\\frac{d}{dx} \\\\( \\\\log_{a} \\\\left(x\\\\right) \\\\) = \\\\frac{1}{\\\\ln(a) \\\\cdot x}$');ayi=new JBi('DIFF_NATURAL_LOG',210,'NaturalLogRule','$\\\\frac{d}{dx} \\\\ln(x) = \\\\frac{1}{x}$');hyi=new JBi('DIFF_SIN',211,'SinRule','$\\\\frac{d}{dx} sin(x) = cos(x)$');Txi=new JBi('DIFF_COS',212,'CosRule','$\\\\frac{d}{dx} cos(x) = -sin(x)$');kyi=new JBi('DIFF_TAN',213,'TanRule','$\\\\frac{d}{dx} tan(x) = \\\\frac{1}{cos^2(x)}$');Nxi=new JBi('DIFF_ARCSIN',214,'ArcsinRule','$\\\\frac{d}{dx} arcsin(x) = \\\\frac{1}{\\\\sqrt{1-x^2}}$');Lxi=new JBi('DIFF_ARCCOS',215,'ArccosRule','$\\\\frac{d}{dx} arccos(x) = -\\\\frac{1}{\\\\sqrt{1-x^2}}$');Pxi=new JBi('DIFF_ARCTAN',216,'ArctanRule','$\\\\frac{d}{dx} arctan(x) = \\\\frac{1}{x^2+1}$');dyi=new JBi('DIFF_POWER_CHAIN',217,'PowerRuleChain','$\\\\frac{d}{dx} (u(x))^n = n (u(x))^{n-1} \\\\cdot \\\\frac{d}{dx} u(x)$');Yxi=new JBi('DIFF_EXPONENTIAL_E_CHAIN',218,'ExponentialRuleEChain','$\\\\frac{d}{dx} a^{u(x)} = \\\\ln(a) a^{u(x)} \\\\cdot \\\\frac{d}{dx} u(x)$');Wxi=new JBi('DIFF_EXPONENTIAL_CHAIN',219,'ExponentialRuleChain','$\\\\frac{d}{dx} e^{u(x)} = e^{u(x)} \\\\cdot \\\\frac{d}{dx} u(x)$');gyi=new JBi('DIFF_ROOT_CHAIN',220,'RootRuleChain','$\\\\frac{d}{dx} \\\\sqrt[n]{u(x)} = \\\\frac{1}{n \\\\sqrt[n]{(u(x))^{n-1}}} \\\\cdot \\\\frac{d}{dx} u(x)$');_xi=new JBi('DIFF_LOG_CHAIN',221,'LogRuleChain','$\\\\frac{d}{dx} \\\\log_{a}(u(x)) = \\\\frac{1}{\\\\ln(a) \\\\cdot u(x)} \\\\cdot \\\\frac{d}{dx} u(x)$');byi=new JBi('DIFF_NATURAL_LOG_CHAIN',222,'NaturalLogRuleChain','$\\\\frac{d}{dx} \\\\ln(u(x)) = \\\\frac{1}{u(x)} \\\\cdot \\\\frac{d}{dx} u(x)$');iyi=new JBi('DIFF_SIN_CHAIN',223,'SinRuleChain','$\\\\frac{d}{dx} sin(u(x)) = cos(u(x)) \\\\cdot \\\\frac{d}{dx} u(x)$');Uxi=new JBi('DIFF_COS_CHAIN',224,'CosRuleChain','$\\\\frac{d}{dx} cos(u(x)) = -sin(u(x)) \\\\cdot \\\\frac{d}{dx} u(x)$');lyi=new JBi('DIFF_TAN_CHAIN',225,'TanRuleChain','$\\\\frac{d}{dx} tan(u(x)) = \\\\frac{1}{cos^2(u(x))} \\\\cdot \\\\frac{d}{dx} u(x)$');Oxi=new JBi('DIFF_ARCSIN_CHAIN',226,'ArcsinRuleChain','$\\\\frac{d}{dx} arcsin(u(x)) = \\\\frac{1}{\\\\sqrt{1-(u(x))^2}} \\\\cdot \\\\frac{d}{dx} u(x)$');Mxi=new JBi('DIFF_ARCCOS_CHAIN',227,'ArccosRuleChain','\\\\frac{d}{dx} arccos(u(x)) = -\\\\frac{1}{\\\\sqrt{1-(u(x))^2}} \\\\cdot \\\\frac{d}{dx} u(x)');Qxi=new JBi('DIFF_ARCTAN_CHAIN',228,'ArctanRuleChain','\\\\frac{d}{dx} arctan(u(x)) = \\\\frac{1}{(u(x))^2+1} \\\\cdot \\\\frac{d}{dx} u(x)');jxi=new IBi('ADD_EQUATIONS',229,'AddEquations','Add the equations to eliminate %0');sBi=new IBi('USE_CRAMERS_RULE',230,'UseCramersRule',\"Use Cramer's rule to solve the equation system\");Fxi=new IBi('DETERMINANTS',231,'','$D = %3$, $D_{1} = %0$, $D_{2} = %1$, $D_{3} = %2$');Dxi=new IBi('CRAMER_VARIABLE',232,'','$%0 = \\\\frac{D_{%1}}{D} = \\\\frac{%2}{%3}$');tBi=new JBi('USE_LEIBNIZ_FORMULA',233,'UseLeibnizFormula','Use the Leibniz formula to evaluate the determinant');vxi=new IBi('CALCULATE_DETERINANT',234,'CalculateDeterminant','Calculate the determinant %0');yBi=new IBi('WRITE_IN_MATRIX_FORM',235,'WriteInMatrixForm','Write the equation system in matrix form');zBi=new IBi('WRITE_IN_SYSTEM_FORM',236,'WriteInSystemForm','Write the matrix in equation system form');Gzi=new IBi('MULTIPLY_ROW_AND_ADD',237,'MultiplyRowAndAdd','Multiply row %0 by %1 and add it to row %2');Ezi=new IBi('MULTIPLY_EACH_ELEMENT_AND_ADD',238,'MultiplyEachElementAndAdd','Multiply each element in row %0 by %1 and add that product to row %2');yyi=new IBi('DIVIDE_ROW',239,'DivideRow','Divide row %0 by %1');xyi=new IBi('DIVIDE_EACH_ELEMENT',240,'DivideEachElement','Divide each element in row %0 by %1')}\nvar J2n={3:1,4:1,7:1,76:1},K2n={3:1,4:1,8:1,7:1,76:1,153:1},L2n='EXPAND',M2n='FACTOR',N2n='PositiveGEZero',O2n='The statement is true for all values of %0',P2n='PositiveGTZero',Q2n='The statement is true, except when %0',R2n='PositiveLEZero',S2n='The statement is only true when %0',T2n='PositiveLTZero',U2n='The statement is false for all values of %0',V2n='ValidSolutionAbs',W2n='NEGATE_BOTH_SIDES',X2n='RAISE_TO_POWER',Y2n='COMPLETE_THE_SQUARE',Z2n='$%0 \\\\in \\\\left[-\\\\frac{\\\\pi}{2}, \\\\frac{\\\\pi}{2}\\\\right]$ for all $%1 \\\\in \\\\mathbb{R}$',$2n='EXPAND_FRACTIONS',_2n='PRODUCT_IS_ZERO',a3n='FRACTION_IS_ZERO',b3n='DOUBLE_MINUS',c3n='DISTRIBUTE_MINUS',d3n='ADD_FRACTIONS',e3n='ADD_NUMERATORS',f3n='COMMON_FRACTION',g3n='CANCEL_FRACTION',h3n='MULTIPLIED_BY_ZERO',i3n='REGROUP_PRODUCTS',j3n='MULTIPLY_CONSTANTS',k3n='Reduce the root and power by: %0',l3n='ROOT_OF_ROOT',m3n='SPLIT_PRODUCTS',n3n='SPLIT_FRACTIONS',o3n='Rewrite %0 as 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