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guacyra

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A small and self-contained Computer Algebra System.

github.com/vinicius-mello/guacyra

vinicius-mello/guacyra

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!function(e,t){if("object"==typeof exports&&"object"==typeof module)module.exports=t();else if("function"==typeof define&&define.amd)define([],t);else{var r=t();for(var n in r)("object"==typeof exports?exports:e)[n]=r[n]}}("undefined"!=typeof self?self:this,(function(){return(()=>{"use strict";var e={150:(e,t,r)=>{const n=r(882),o=r(884),{$:a,$$:l,Form:i,ownValueSet:s,equal:u,kind:c,apply:_,match:f,Eval:p,copy:g,addRule:b,Integer:h,Plus:m,Times:d,Power:y,Sequence:I,List:L,Less:x,True:T,False:S,toString:R,mkReservedSymbol:P}=n,{gcd:w,factorization:$,binomial:v}=o,D=i("Rational"),A=i("Divide"),k=i("Complex"),C=P("I");s(C,k(0,1));const E=i("Conjugate"),q=i("Abs"),M=i("Expand"),N=i("Sqrt"),B=i("NumeratorDenominator"),O=i("Numerator"),F=i("Denominator"),X=i("Together"),H=e=>"Integer"===c(e)||"Rational"===c(e),j=e=>{if(isAtom(e))return H(e);if("Symbol"!==c(e[0]))return!1;for(let t=1;t<e.length;++t)if(!j(e[t]))return!1;return!0};b(l`Rational(a_Integer, b_Integer)`,(({a:e,b:t})=>{let r=e[1],n=t[1];const o=w(r,n);return 1==o&&n>0&&1!=n?null:(r/=o,n/=o,n<0&&(r=-r,n=-n),1==n?h(r):D(r,n))})),a`Rational : Numeric(Rational(a_Integer, b_Integer)) := True`,a`Rational : Less(a_Integer, Rational(p_Integer, q_Integer)) := a*q < p`,a`Rational : Less(Rational(p_Integer, q_Integer), a_Integer) := p < a*q`,a`Rational : Less( Rational(a_Integer, b_Integer), Rational(c_Integer, d_Integer) ) := a*d < b*c`,a`Rational : Less(a_Rational, b_) := True`,a`Rational : Less(a_, b_Rational) := False`,a`Divide(a_Integer, b_Integer) := Rational(a, b)`,a`Divide(a_, b_) := Times(a, Power(b, -1))`,a`Plus(a_Integer, Rational(b_Integer, c_Integer), d___) := Plus(Rational(a*c+b, c), d)`,a`Plus(Rational(b_Integer, c_Integer), a_Integer, d___) := Plus(Rational(a*c+b, c), d)`,a`Plus( Rational(a_Integer, b_Integer), Rational(c_Integer, d_Integer), e___) := Plus(Rational(a*d+b*c, b*d), e)`,a`Times(a_Integer, Rational(b_Integer, c_Integer), d___) := Times(Rational(a*b,c), d)`,a`Times(Rational(b_Integer, c_Integer), a_Integer, d___) := Times(Rational(a*b,c), d)`,a`Times( Rational(a_Integer, b_Integer), Rational(c_Integer, d_Integer), e___) := Times(Rational(a*c, b*d), e)`,a`Complex : Numeric(Complex(a_)) := True`,a`Complex : Less(Complex(a_, b_), Complex(c_, d_)) := If(a=c, b<d, a<c)`,a`Complex : Less(a_Complex, b_) := If(Numeric(b), False, True)`,a`Complex : Less(a_, b_Complex) := If(Numeric(a), True, False)`,a`Complex(a_, 0) := a`,a`Conjugate(Complex(a_, b_)) := Complex(a, -b)`,a`Abs(a_Integer) := If(a<0, -a, a); Abs(Rational(a_Integer, b_Integer)) := Rational(Abs(a), b)`,a`Abs(Complex(a_, b_)) := Sqrt(a^2+b^2)`,a`Plus(n_Integer, Complex(a_, b_), c___) := Plus(Complex(a+n, b), c)`,a`Plus(p_Rational, Complex(a_, b_), c___) := Plus(Complex(a+p, b), c)`,a`Plus(Complex(a_, b_), Complex(c_, d_), e___) := Plus(Complex(a+c, b+d), e)`,a`Times(n_Integer, Complex(a_, b_), c___) := Times(Complex(n*a, n*b), c)`,a`Times(p_Rational, Complex(a_, b_), c___) := Times(Complex(Times(p, a), Times(p, b)), c)`,a`Times(Complex(a_, b_), Complex(c_, d_), e___) := Times(Complex(a*c-b*d, a*d+b*c), e)`,a`Times(-1, Plus(a__)) := Map(x => Times(-1, x), Plus(a))`;const G=(e,t,r)=>{const n=R(t);return e[n]?(e[n][1].push(r),!0):(e[n]=[t,I(r)],!1)};b(l`Plus(c__)`,(({c:e})=>{const t=m();let r=!1;const n={};for(let t=1;t<e.length;++t){const o={};r=f(e[t],l`Times(a_Integer, b_)`,o)||f(e[t],l`Times(a_Integer, b__)`,o)||f(e[t],l`Times(a_Rational, b_)`,o)||f(e[t],l`Times(a_Rational, b__)`,o)||f(e[t],l`Times(a_Complex, b_)`,o)||f(e[t],l`Times(a_Complex, b__)`,o)?G(n,o.b,o.a)||r:f(e[t],l`Times(b__)`,o)?G(n,o.b,h(1))||r:G(n,e[t],h(1))||r}if(r){for(let e in n){const r=n[e];_("Plus",r[1]),t.push(d(r[1],r[0]))}return t}return null})),b(l`Times(c__)`,(({c:e})=>{const t=d();let r=!1;const n={};for(let t=1;t<e.length;++t){const o={};r=f(e[t],l`Power(a_Integer, b_Rational)`,o)?G(n,y(o.a,o.b),h(1))||r:f(e[t],l`Power(a_, b_)`,o)?G(n,o.a,o.b)||r:G(n,e[t],h(1))||r}if(r){for(let e in n){const r=n[e];_("Plus",r[1]),t.push(y(r[0],r[1]))}return t}return null})),b(l`Times(c__)`,(({c:e})=>{const t=d();let r=!1;const n={};for(let t=1;t<e.length;++t){const o={};f(e[t],l`Power(a_Integer, b_)`,o)?r=G(n,o.b,o.a)||r:G(n,h(1),e[t])}if(r){for(let e in n){const r=n[e];_("Times",r[1]),t.push(y(r[1],r[0]))}return t}return null})),a`Power(a_Integer, b_Integer) := Rational(1, a^(-b))`,a`Power(Rational(a_Integer, b_Integer), c_Integer) := If(c<0, Rational(b^(-c), a^(-c)), Rational(a^c, b^c))`;const U=(e,t,r)=>{let[n,o]=[1,1];for(let a=0;a<e.length;++a){const l=e[a][1]*t,i=e[a][0],s=Math.floor(l/r),u=l-s*r;n*=Math.pow(i,s),o*=Math.pow(i,u)}return[n,o]};b(l`Power(a_Integer, b_Rational)`,(({a:e,b:t})=>{if(e[1]<0)return null;const r=$(e[1]);if(t[1][1]>0){const[e,n]=U(r,t[1][1],t[2][1]);return 1==e&&1==t[1][1]?null:d(e,y(n,D(1,t[2][1])))}{const n=-t[1][1],o=Math.floor(n/t[2][1]),a=n-o*t[2][1],[l,i]=U(r,t[2][1]-a,t[2][1]);return d(D(l,Math.pow(e[1],o+1)),y(i,D(1,t[2][1])))}})),a`Power(Rational(a_Integer, b_Integer), c_Rational) := a^(c)*b^(-c)`,a`Power(Power(a_, b_), c_Integer) := Power(a, Times(b, c))`,a`Power(Times(a__), b_Integer) := Map( x => x^b, Times(a))`,a`Sqrt(a_) := Power(a, Rational(1, 2))`,b(l`Power(z_Complex, n_Integer)`,(({z:e,n:t})=>{let r=k(1,0);const n=Math.abs(t[1]);for(let t=0;t<n;++t)r=p(d(r,e));return t[1]<0?d(E(r),A(1,y(q(r),2))):r})),b(l`Numerator(a_Integer)`,l`a`),b(l`Numerator(Rational(a_Integer, b_Integer))`,l`a`),b(l`Numerator(a_)`,(({a:e})=>p(B(e))[1])),b(l`Denominator(a_Integer)`,l`1`),b(l`Denominator(a_Rational)`,(({a:e})=>h(e[2][1]))),b(l`Denominator(a_)`,(({a:e})=>p(B(e))[2])),b(l`NumeratorDenominator(a_Integer)`,(({a:e})=>L(e,h(1)))),b(l`NumeratorDenominator(a_Rational)`,(({a:e})=>L(h(e[1][1]),h(e[2][1])))),b(l`NumeratorDenominator(Power(a_, n_Integer))`,(({a:e,n:t})=>t[1]<0?L(1,y(e,-t[1])):L(y(e,t),1))),b(l`NumeratorDenominator(Power(a_, 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d(e)})),b(l`Expand(Power(Plus(a_, b__), n_Integer))`,(({a:e,b:t,n:r})=>{let n=m();for(let o=0;o<=r[1];++o)n.push(M(d(v(r[1],o),y(e,r[1]-o),M(y(m(t),o)))));return n})),b(l`Expand(Plus(a_, b__))`,(({a:e,b:t})=>m(M(e),M(m(t))))),b(l`Expand(List(a__))`,l`Map(Expand,List(a))`),b(l`Expand(a_)`,(({a:e})=>e));const z={};z.Rational=D,z.Divide=A,z.Complex=k,z.I=C,z.Conjugate=E,z.Abs=q,z.Expand=M,z.Sqrt=N,z.NumeratorDenominator=B,z.Numerator=O,z.Denominator=F,z.Together=X,z.isNumeric=H,z.isNumericEx=j,e.exports=z},613:(e,t,r)=>{const n=r(882),{$$:o,Form:a,mkReservedSymbol:l,Cons:i,has:s,subst:u,Eval:c,addRule:_,Integer:f,Str:p,Plus:g,Times:b,Power:h,Sqrt:m,Divide:d,Subtract:y,toString:I}=n,L=r(762),{equal:x}=r(882),{latex:T}=L,S=a("Diff"),R=a("Derivative"),P=a("Log"),w=a("Exp"),$=a("Sin"),v=a("Cos"),D=l("Pi");_(o`Log(1)`,o`0`),_(o`Exp(0)`,o`1`),_(o`Sin(Pi)`,o`0`),_(o`Sin(0)`,o`0`),_(o`Sin(Times(n_Integer, Pi))`,o`0`),_(o`Sin(Times(Rational(a_Integer, b_Integer), 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A={Diff:S,Derivative:R,Sin:$,Cos:v,Pi:D,Log:P,Exp:w};e.exports=A},762:(e,t,r)=>{const n=r(882),o=r(150),a=r(986),{$$:l,Form:i,equal:s,kind:u,Eval:c,addRule:_,Integer:f,Str:p,Plus:g,Times:b,Power:h,isAtom:m,toString:d}=n,{isNumeric:y,NumeratorDenominator:I}=o,{size:L,reducedRowEchelonSteps:x,rowEchelonSteps:T,buildTensor:S,forEachEntry:R}=a,P=i("LaTeX"),w=i("Output"),v=e=>"Integer"===u(e)?e[1]:e[1][1]/e[2][1],D=e=>c(P(e))[1],A=e=>c(w(e))[1],k=(i("Display"),i("RowReduceSteps"),i("GaussianEliminationSteps"),e=>"Symbol"===e||"Literal"===e),C=(e,t)=>{const r=u(e),n=u(t);if(y(e)&&y(t))return v(e)<v(t);if(k(r)&&k(n))return e[1]<t[1];if("Plus"===r&&"Plus"===n||"Times"===r&&"Times"===n){let r=e.length-1,n=t.length-1;for(;r>=1&&n>=1;){if(!s(e[r],t[n]))return C(e[r],t[n]);r-=1,n-=1}return r<n}if("Power"===r&&"Power"===n)return s(e[2],t[2])?C(e[1],t[1]):C(t[2],e[2]);if(r===n){let r=e.length,n=t.length,o=1;for(;o<r&&o<n;){if(!s(e[o],t[o]))return C(e[o],t[o]);o+=1}return 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