vendor-mathjs.rDku6ehY.js

js holded.com collected 2026-09-24 09:10:30 UTC 678,733 bytes, 54 lines download raw bytes

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11c(t,n,e,!1)),"DenseMatrix, number | BigNumber":t.referToSelf(e=>(t,n)=>u(t,n,e,!1)),"number | Complex | Fraction | BigNumber, Array":t.referToSelf(e=>(t,n)=>u(i(n),t,e,!0).valueOf()),"number | Complex | Fraction | BigNumber, Matrix":t.referToSelf(e=>(t,n)=>a(t,0)?o(n.size(),n.storage()):n.storage()===`dense`?u(n,t,e,!0):l(n,t,e,!0))})}),ec=`cube`,tc=W(ec,[`typed`],e=>{var{typed:t}=e;return t(ec,{number:fa,Complex:function(e){return e.mul(e).mul(e)},BigNumber:function(e){return e.times(e).times(e)},bigint:function(e){return e*e*e},Fraction:function(e){return e.pow(3)},Unit:function(e){return e.pow(3)}})}),nc=`exp`,rc=W(nc,[`typed`],e=>{var{typed:t}=e;return t(nc,{number:pa,Complex:function(e){return e.exp()},BigNumber:function(e){return e.exp()}})}),ic=`expm1`,ac=W(ic,[`typed`,`Complex`],e=>{var{typed:t,Complex:n}=e;return t(ic,{number:ma,Complex:function(e){var t=Math.exp(e.re);return new n(t*Math.cos(e.im)-1,t*Math.sin(e.im))},BigNumber:function(e){return e.exp().minus(1)}})}),oc=`fix`,sc=[`typed`,`Complex`,`matrix`,`ceil`,`floor`,`equalScalar`,`zeros`,`DenseMatrix`],cc=W(oc,[`typed`,`ceil`,`floor`],e=>{var{typed:t,ceil:n,floor:r}=e;return t(oc,{number:function(e){return e>0?r(e):n(e)},"number, number":function(e,t){return e>0?r(e,t):n(e,t)}})}),lc=W(oc,sc,e=>{var{typed:t,Complex:n,matrix:r,ceil:i,floor:a,equalScalar:o,zeros:s,DenseMatrix:c}=e,l=qs({typed:t,DenseMatrix:c}),u=Js({typed:t}),d=cc({typed:t,ceil:i,floor:a});return t(`fix`,{number:d.signatures.number,"number, number | BigNumber":d.signatures[`number,number`],Complex:function(e){return new n(e.re>0?Math.floor(e.re):Math.ceil(e.re),e.im>0?Math.floor(e.im):Math.ceil(e.im))},"Complex, number":function(e,t){return new n(e.re>0?a(e.re,t):i(e.re,t),e.im>0?a(e.im,t):i(e.im,t))},"Complex, BigNumber":function(e,t){var r=t.toNumber();return new n(e.re>0?a(e.re,r):i(e.re,r),e.im>0?a(e.im,r):i(e.im,r))},BigNumber:function(e){return e.isNegative()?i(e):a(e)},"BigNumber, number | BigNumber":function(e,t){return e.isNegative()?i(e,t):a(e,t)},bigint:e=>e,"bigint, number":(e,t)=>e,"bigint, BigNumber":(e,t)=>e,Fraction:function(e){return e.s<0n?e.ceil():e.floor()},"Fraction, number | BigNumber":function(e,t){return e.s<0n?i(e,t):a(e,t)},"Unit, number, Unit":t.referToSelf(e=>function(t,n,r){var i=t.toNumeric(r);return r.multiply(e(i,n))}),"Unit, BigNumber, Unit":t.referToSelf(e=>(t,n,r)=>e(t,n.toNumber(),r)),"Array | Matrix, number | BigNumber, Unit":t.referToSelf(e=>(t,n,r)=>Xi(t,t=>e(t,n,r),!0)),"Array | Matrix | Unit, Unit":t.referToSelf(e=>(t,n)=>e(t,0,n)),"Array | Matrix":t.referToSelf(e=>t=>Xi(t,e,!0)),"Array | Matrix, number | BigNumber":t.referToSelf(e=>(t,n)=>Xi(t,t=>e(t,n),!0)),"number | Complex | Fraction | BigNumber, Array":t.referToSelf(e=>(t,n)=>u(r(n),t,e,!0).valueOf()),"number | Complex | Fraction | BigNumber, Matrix":t.referToSelf(e=>(t,n)=>o(t,0)?s(n.size(),n.storage()):n.storage()===`dense`?u(n,t,e,!0):l(n,t,e,!0))})}),uc=`floor`,dc=[`typed`,`config`,`round`,`matrix`,`equalScalar`,`zeros`,`DenseMatrix`],fc=new cr(10),pc=W(uc,[`typed`,`config`,`round`],e=>{var{typed:t,config:n,round:r}=e;function i(e){var t=Math.floor(e),i=r(e);return t===i?t:ot(e,i,n.relTol,n.absTol)&&!ot(e,t,n.relTol,n.absTol)?i:t}return t(uc,{number:i,"number, number":function(e,t){if(!G(t))throw RangeError(`number of decimals in function floor must be an integer`);if(t<0||t>15)throw RangeError(`number of decimals in floor number must be in range 0 - 15`);var n=10**t;return i(e*n)/n}})}),mc=W(uc,dc,e=>{var{typed:t,config:n,round:r,matrix:i,equalScalar:a,zeros:o,DenseMatrix:s}=e,c=Ks({typed:t,equalScalar:a}),l=qs({typed:t,DenseMatrix:s}),u=Js({typed:t}),d=pc({typed:t,config:n,round:r});function f(e){var t=(e,t)=>Lo(e,t,n.relTol,n.absTol),i=e.floor(),a=r(e);return i.eq(a)?i:t(e,a)&&!t(e,i)?a:i}return t(`floor`,{number:d.signatures.number,"number,number":d.signatures[`number,number`],Complex:function(e){return e.floor()},"Complex, number":function(e,t){return e.floor(t)},"Complex, BigNumber":function(e,t){return e.floor(t.toNumber())},BigNumber:f,"BigNumber, BigNumber":function(e,t){var n=fc.pow(t);return f(e.mul(n)).div(n)},bigint:e=>e,"bigint, number":(e,t)=>e,"bigint, BigNumber":(e,t)=>e,Fraction:function(e){return e.floor()},"Fraction, number":function(e,t){return e.floor(t)},"Fraction, BigNumber":function(e,t){return e.floor(t.toNumber())},"Unit, number, Unit":t.referToSelf(e=>function(t,n,r){var i=t.toNumeric(r);return r.multiply(e(i,n))}),"Unit, BigNumber, Unit":t.referToSelf(e=>(t,n,r)=>e(t,n.toNumber(),r)),"Array | Matrix, number | BigNumber, Unit":t.referToSelf(e=>(t,n,r)=>Xi(t,t=>e(t,n,r),!0)),"Array | Matrix | Unit, Unit":t.referToSelf(e=>(t,n)=>e(t,0,n)),"Array | Matrix":t.referToSelf(e=>t=>Xi(t,e,!0)),"Array, number | BigNumber":t.referToSelf(e=>(t,n)=>Xi(t,t=>e(t,n),!0)),"SparseMatrix, number | BigNumber":t.referToSelf(e=>(t,n)=>

11c(t,n,e,!1)),"DenseMatrix, number | BigNumber":t.referToSelf(e=>(t,n)=>u(t,n,e,!1)),"number | Complex | Fraction | BigNumber, Array":t.referToSelf(e=>(t,n)=>u(i(n),t,e,!0).valueOf()),"number | Complex | Fraction | BigNumber, Matrix":t.referToSelf(e=>(t,n)=>a(t,0)?o(n.size(),n.storage()):n.storage()===`dense`?u(n,t,e,!0):l(n,t,e,!0))})}),hc=W(`matAlgo02xDS0`,[`typed`,`equalScalar`],e=>{var{typed:t,equalScalar:n}=e;return function(e,r,i,a){var o=e._data,s=e._size,c=e._datatype||e.getDataType(),l=r._values,u=r._index,d=r._ptr,f=r._size,p=r._datatype||r._data===void 0?r._datatype:r.getDataType();if(s.length!==f.length)throw new ti(s.length,f.length);if(s[0]!==f[0]||s[1]!==f[1])throw RangeError(`Dimension mismatch. Matrix A (`+s+`) must match Matrix B (`+f+`)`);if(!l)throw Error(`Cannot perform operation on Dense Matrix and Pattern Sparse Matrix`);var m=s[0],h=s[1],g,_=n,v=0,y=i;typeof c==`string`&&c===p&&c!==`mixed`&&(g=c,_=t.find(n,[g,g]),v=t.convert(0,g),y=t.find(i,[g,g]));for(var b=[],x=[],S=[],C=0;C<h;C++){S[C]=x.length;for(var w=d[C],T=d[C+1],E=w;E<T;

11E++){var D=u[E],O=a?y(l[E],o[D][C]):y(o[D][C],l[E]);_(O,v)||(x.push(D),b.push(O))}}return S[h]=x.length,r.createSparseMatrix({values:b,index:x,ptr:S,size:[m,h],datatype:c===e._datatype&&p===r._datatype?g:void 0})}}),gc=W(`matAlgo03xDSf`,[`typed`],e=>{var{typed:t}=e;return function(e,n,r,i){var a=e._data,o=e._size,s=e._datatype||e.getDataType(),c=n._values,l=n._index,u=n._ptr,d=n._size,f=n._datatype||n._data===void 0?n._datatype:n.getDataType();if(o.length!==d.length)throw new ti(o.length,d.length);if(o[0]!==d[0]||o[1]!==d[1])throw RangeError(`Dimension mismatch. Matrix A (`+o+`) must match Matrix B (`+d+`)`);if(!c)throw Error(`Cannot perform operation on Dense Matrix and Pattern Sparse Matrix`);var p=o[0],m=o[1],h,g=0,_=r;typeof s==`string`&&s===f&&s!==`mixed`&&(h=s,g=t.convert(0,h),_=t.find(r,[h,h]));for(var v=[],y=0;y<p;y++)v[y]=[];for(var b=[],x=[],S=0;S<m;S++){for(var C=S+1,w=u[S],T=u[S+1],E=w;E<T;E++){var D=l[E];b[D]=i?_(c[E],a[D][S]):_(a[D][S],c[E]),x[D]=C}for(var O=0;O<p;O++)x[O]===C?v[O][S]=b[O]:v[O][S]=i?_(g,a[O][S]):_(a[O][S],g)}return e.createDenseMatrix({data:v,size:[p,m],datatype:s===e._datatype&&f===n._datatype?h:void 0})}}),_c=W(`matAlgo05xSfSf`,[`typed`,`equalScalar`],e=>{var{typed:t,equalScalar:n}=e;return function(e,r,i){var a=e._values,o=e._index,s=e._ptr,c=e._size,l=e._datatype||e._data===void 0?e._datatype:e.getDataType(),u=r._values,d=r._index,f=r._ptr,p=r._size,m=r._datatype||r._data===void 0?r._datatype:r.getDataType();if(c.length!==p.length)throw new ti(c.length,p.length);if(c[0]!==p[0]||c[1]!==p[1])throw RangeError(`Dimension mismatch. Matrix A (`+c+`) must match Matrix B (`+p+`)`);var h=c[0],g=c[1],_,v=n,y=0,b=i;typeof l==`string`&&l===m&&l!==`mixed`&&(_=l,v=t.find(n,[_,_]),y=t.convert(0,_),b=t.find(i,[_,_]));var x=a&&u?[]:void 0,S=[],C=[],w=x?[]:void 0,T=x?[]:void 0,E=[],D=[],O,k,A,j;for(k=0;k<g;k++){C[k]=S.length;var M=k+1;for(A=s[k],j=s[k+1];A<j;A++)O=o[A],S.push(O),E[O]=M,w&&(w[O]=a[A]);for(A=f[k],j=f[k+1];A<j;A++)O=d[A],E[O]!==M&&S.push(O),D[O]=M,T&&(T[O]=u[A]);if(x)for(A=C[k];A<S.length;){O=S[A];var N=E[O],P=D[O];if(N===M||P===M){var F=N===M?w[O]:y,ee=P===M?T[O]:y,te=b(F,ee);v(te,y)?S.splice(A,1):(x.push(te),A++)}}}return C[g]=S.length,e.createSparseMatrix({values:x,index:S,ptr:C,size:[h,g],datatype:l===e._datatype&&m===r._datatype?_:void 0})}}),vc=W(`matAlgo13xDD`,[`typed`],e=>{var{typed:t}=e;return function(e,r,i){var a=e._data,o=e._size,s=e._datatype,c=r._data,l=r._size,u=r._datatype,d=[];if(o.length!==l.length)throw new ti(o.length,l.length);for(var f=0;f<o.length;f++){if(o[f]!==l[f])throw RangeError(`Dimension mismatch. Matrix A (`+o+`) must match Matrix B (`+l+`)`);d[f]=o[f]}var p,m=i;typeof s==`string`&&s===u&&(p=s,m=t.find(i,[p,p]));var h=d.length>0?n(m,0,d,d[0],a,c):[];return e.createDenseMatrix({data:h,size:d,datatype:p})};function n(e,t,r,i,a,o){var s=[];if(t===r.length-1)for(var c=0;c<i;c++)s[c]=e(a[c],o[c]);else for(var l=0;l<i;l++)s[l]=n(e,t+1,r,r[t+1],a[l],o[l]);return s}});function yc(e,t){if(De(e.size(),t.size()))return[e,t];var n=Ai(e.size(),t.size());return[e,t].map(e=>bc(e,n))}function bc(e,t){return De(e.size(),t)?e:e.create(Mi(e.valueOf(),t),e.datatype())}var xc=W(`matrixAlgorithmSuite`,[`typed`,`matrix`],e=>{var{typed:t,matrix:n}=e,r=vc({typed:t}),i=Js({typed:t});return function(e){var a=e.elop,o=e.SD||e.DS,s;a?(s={"DenseMatrix, DenseMatrix":(e,t)=>r(...yc(e,t),a),"Array, Array":(e,t)=>r(...yc(n(e),n(t)),a).valueOf(),"Array, DenseMatrix":(e,t)=>r(...yc(n(e),t),a),"DenseMatrix, Array":(e,t)=>r(...yc(e,n(t)),a)},e.SS&&(s[`SparseMatrix, SparseMatrix`]=(t,n)=>e.SS(...yc(t,n),a,!1)),e.DS&&(s[`DenseMatrix, SparseMatrix`]=(t,n)=>e.DS(...yc(t,n),a,!1),s[`Array, SparseMatrix`]=(t,r)=>e.DS(...yc(n(t),r),a,!1)),o&&(s[`SparseMatrix, DenseMatrix`]=(e,t)=>o(...yc(t,e),a,!0),s[`SparseMatrix, Array`]=(e,t)=>o(...yc(n(t),e),a,!0))):(s={"DenseMatrix, DenseMatrix":t.referToSelf(e=>(t,n)=>r(...yc(t,n),e)),"Array, Array":t.referToSelf(e=>(t,i)=>r(...yc(n(t),n(i)),e).valueOf()),"Array, DenseMatrix":t.referToSelf(e=>(t,i)=>r(...yc(n(t),i),e)),"DenseMatrix, Array":t.referToSelf(e=>(t,i)=>r(...yc(t,n(i)),e))},e.SS&&(s[`SparseMatrix, SparseMatrix`]=t.referToSelf(t=>(n,r)=>

11e.SS(...yc(n,r),t,!1))),e.DS&&(s[`DenseMatrix, SparseMatrix`]=t.referToSelf(t=>(n,r)=>e.DS(...yc(n,r),t,!1)),s[`Array, SparseMatrix`]=t.referToSelf(t=>(r,i)=>e.DS(...yc(n(r),i),t,!1))),o&&(s[`SparseMatrix, DenseMatrix`]=t.referToSelf(e=>(t,n)=>o(...yc(n,t),e,!0)),s[`SparseMatrix, Array`]=t.referToSelf(e=>(t,r)=>o(...yc(n(r),t),e,!0))));var c=e.scalar||`any`;(e.Ds||e.Ss)&&(a?(s[`DenseMatrix,`+c]=(e,t)=>i(e,t,a,!1),s[c+`, DenseMatrix`]=(e,t)=>i(t,e,a,!0),s[`Array,`+c]=(e,t)=>i(n(e),t,a,!1).valueOf(),s[c+`, Array`]=(e,t)=>i(n(t),e,a,!0).valueOf()):(s[`DenseMatrix,`+c]=t.referToSelf(e=>(t,n)=>i(t,n,e,!1)),s[c+`, DenseMatrix`]=t.referToSelf(e=>(t,n)=>i(n,t,e,!0)),s[`Array,`+c]=t.referToSelf(e=>(t,r)=>i(n(t),r,e,!1).valueOf()),s[c+`, Array`]=t.referToSelf(e=>(t,r)=>i(n(r),t,e,!0).valueOf())));var l=e.sS===void 0?e.Ss:e.sS;return a?(e.Ss&&(s[`SparseMatrix,`+c]=(t,n)=>e.Ss(t,n,a,!1)),l&&(s[c+`, SparseMatrix`]=(e,t)=>l(t,e,a,!0))):(e.Ss&&(s[`SparseMatrix,`+c]=t.referToSelf(t=>(n,r)=>e.Ss(n,r,t,!1))),l&&(s[c+`, SparseMatrix`]=t.referToSelf(e=>(t,n)=>l(n,t,e,!0)))),a&&a.signatures&&Te(s,a.signatures),s}}),Sc=`mod`,Cc=W(Sc,[`typed`,`config`,`round`,`matrix`,`equalScalar`,`zeros`,`DenseMatrix`,`concat`],e=>{var{typed:t,config:n,round:r,matrix:i,equalScalar:a,zeros:o,DenseMatrix:s,concat:c}=e,l=mc({typed:t,config:n,round:r,matrix:i,equalScalar:a,zeros:o,DenseMatrix:s}),u=hc({typed:t,equalScalar:a}),d=gc({typed:t}),f=_c({typed:t,equalScalar:a}),p=Ks({typed:t,equalScalar:a}),m=qs({typed:t,DenseMatrix:s}),h=xc({typed:t,matrix:i,concat:c});return t(Sc,{"number, number":g,"BigNumber, BigNumber":function(e,t){return t.isZero()?e:e.sub(t.mul(l(e.div(t))))},"bigint, bigint":function(e,t){if(t===0n)return e;if(e<0){var n=e%t;return n===0n?n:n+t}return e%t},"Fraction, Fraction":function(e,t){return t.equals(0)?e:e.sub(t.mul(l(e.div(t))))}},h({SS:f,DS:d,SD:u,Ss:p,sS:m}));function g(e,t){return t===0?e:e-t*l(e/t)}}),wc=W(`matAlgo01xDSid`,[`typed`],e=>{var{typed:t}=e;return function(e,n,r,i){var a=e._data,o=e._size,s=e._datatype||e.getDataType(),c=n._values,l=n._index,u=n._ptr,d=n._size,f=n._datatype||n._data===void 0?n._datatype:n.getDataType();if(o.length!==d.length)throw new ti(o.length,d.length);if(o[0]!==d[0]||o[1]!==d[1])throw RangeError(`Dimension mismatch. Matrix A (`+o+`) must match Matrix B (`+d+`)`);if(!c)throw Error(`Cannot perform operation on Dense Matrix and Pattern Sparse Matrix`);var p=o[0],m=o[1],h=typeof s==`string`&&s!==`mixed`&&s===f?s:void 0,g=h?t.find(r,[h,h]):r,_,v,y=[];for(_=0;_<p;_++)y[_]=[];var b=[],x=[];for(v=0;v<m;v++){for(var S=v+1,C=u[v],w=u[v+1],T=C;T<w;T++)_=l[T],b[_]=i?g(c[T],a[_][v]):g(a[_][v],c[T]),x[_]=S;for(_=0;_<p;_++)x[_]===S?y[_][v]=b[_]:y[_][v]=a[_][v]}return e.createDenseMatrix({data:y,size:[p,m],datatype:s===e._datatype&&f===n._datatype?h:void 0})}}),Tc=W(`matAlgo04xSidSid`,[`typed`,`equalScalar`],e=>{var{typed:t,equalScalar:n}=e;return function(e,r,i){var a=e._values,o=e._index,s=e._ptr,c=e._size,l=e._datatype||e._data===void 0?e._datatype:e.getDataType(),u=r._values,d=r._index,f=r._ptr,p=r._size,m=r._datatype||r._data===void 0?r._datatype:r.getDataType();if(c.length!==p.length)throw new ti(c.length,p.length);if(c[0]!==p[0]||c[1]!==p[1])throw RangeError(`Dimension mismatch. Matrix A (`+c+`) must match Matrix B (`+p+`)`);var h=c[0],g=c[1],_,v=n,y=0,b=i;typeof l==`string`&&l===m&&l!==`mixed`&&(_=l,v=t.find(n,[_,_]),y=t.convert(0,_),b=t.find(i,[_,_]));var x=a&&u?[]:void 0,S=[],C=[],w=a&&u?[]:void 0,T=a&&u?[]:void 0,E=[],D=[],O,k,A,j,M;for(k=0;k<g;k++){C[k]=S.length;var N=k+1;for(j=s[k],M=s[k+1],A=j;A<M;A++)O=o[A],S.push(O),E[O]=N,w&&(w[O]=a[A]);for(j=f[k],M=f[k+1],A=j;A<M;A++)if(O=d[A],E[O]===N){if(w){var P=b(w[O],u[A]);v(P,y)?E[O]=null:w[O]=P}}else S.push(O),D[O]=N,T&&(T[O]=u[A]);if(w&&T)for(A=C[k];A<S.length;)O=S[A],E[O]===N?(x[A]=w[O],A++):D[O]===N?(x[A]=T[O],A++):S.splice(A,1)}return C[g]=S.length,e.createSparseMatrix({values:x,index:S,ptr:C,size:[h,g],datatype:l===e._datatype&&m===r._datatype?_:void 0})}}),Ec=W(`matAlgo10xSids`,[`typed`,`DenseMatrix`],e=>{var{typed:t,DenseMatrix:n}=e;return function(e,r,i,a){var o=e._values,s=e._index,c=e._ptr,l=e._size,u=e._datatype;if(!o)throw Error(`Cannot perform operation on Pattern Sparse Matrix and Scalar value`);var d=l[0],f=l[1],p,m=i;typeof u==`string`&&(p=u,r=t.convert(r,p),m=t.find(i,[p,p]));for(var h=[],g=[],_=[],v=0;v<f;v++){for(var y=v+1,b=c[v],x=c[v+1],S=b;S<x;S++){var C=s[S];g[C]=o[S],_[C]=y}for(var w=0;w<d;w++)v===0&&(h[w]=[]),_[w]===y?h[w][v]=a?m(r,g[w]):m(g[w],r):h[w][v]=r}return new n({data:h,size:[d,f],datatype:p})}});function Dc(e,t,n,r){if(!(this instanceof Dc))throw SyntaxError(`Constructor must be called with the new operator`);this.fn=e,this.count=t,this.min=n,this.max=r,this.message=`Wrong number of arguments in function `+e+` (`+t+` provided, `+n+(r==null?``:`-`+r)+` expected)`,this.stack=Error().stack}Dc.prototype=Error(),Dc.prototype.constructor=Error,Dc.prototype.name=`ArgumentsError`,Dc.prototype.isArgumentsError=!0;var Oc=`gcd`,kc=[`typed`,`config`,`round`,`matrix`,`equalScalar`,`zeros`,`BigNumber`,`DenseMatrix`,`concat`],Ac=`number | BigNumber | Fraction | Matrix | Array`,jc=`${Ac}, ${Ac}, ...${Ac}`;

11function Mc(e){return!e.some(e=>Array.isArray(e))}var Nc=W(Oc,kc,e=>{var{typed:t,matrix:n,config:r,round:i,equalScalar:a,zeros:o,BigNumber:s,DenseMatrix:c,concat:l}=e,u=Cc({typed:t,config:r,round:i,matrix:n,equalScalar:a,zeros:o,DenseMatrix:c,concat:l}),d=wc({typed:t}),f=Tc({typed:t,equalScalar:a}),p=Ec({typed:t,DenseMatrix:c}),m=xc({typed:t,matrix:n,concat:l});return t(Oc,{"number, number":h,"BigNumber, BigNumber":g,"Fraction, Fraction":(e,t)=>e.gcd(t)},m({SS:f,DS:d,Ss:p}),{[jc]:t.referToSelf(e=>(t,n,r)=>{for(var i=e(t,n),a=0;a<r.length;a++)i=e(i,r[a]);return i}),Array:t.referToSelf(e=>t=>{if(t.length===1&&Array.isArray(t[0])&&Mc(t[0]))return e(...t[0]);if(Mc(t))return e(...t);throw new Dc(`gcd() supports only 1d matrices!`)}),Matrix:t.referToSelf(e=>t=>e(t.toArray()))});function h(e,t){if(!G(e)||!G(t))throw Error(`Parameters in function gcd must be integer numbers`);for(var n;t!==0;)n=u(e,t),e=t,t=n;return e<0?-e:e}function g(e,t){if(!e.isInt()||!t.isInt())throw Error(`Parameters in function gcd must be integer numbers`);for(var n=new s(0);!t.isZero();){var r=u(e,t);e=t,t=r}return e.lt(n)?e.neg():e}}),Pc=W(`matAlgo06xS0S0`,[`typed`,`equalScalar`],e=>{var{typed:t,equalScalar:n}=e;return function(e,r,i){var a=e._values,o=e._size,s=e._datatype||e._data===void 0?e._datatype:e.getDataType(),c=r._values,l=r._size,u=r._datatype||r._data===void 0?r._datatype:r.getDataType();if(o.length!==l.length)throw new ti(o.length,l.length);if(o[0]!==l[0]||o[1]!==l[1])throw RangeError(`Dimension mismatch. Matrix A (`+o+`) must match Matrix B (`+l+`)`);var d=o[0],f=o[1],p,m=n,h=0,g=i;typeof s==`string`&&s===u&&s!==`mixed`&&(p=s,m=t.find(n,[p,p]),h=t.convert(0,p),g=t.find(i,[p,p]));for(var _=a&&c?[]:void 0,v=[],y=[],b=_?[]:void 0,x=[],S=[],C=0;C<f;C++){y[C]=v.length;var w=C+1;if($i(e,C,x,b,S,w,v,g),$i(r,C,x,b,S,w,v,g),b)for(var T=y[C];T<v.length;){var E=v[T];if(S[E]===w){var D=b[E];m(D,h)?v.splice(T,1):(_.push(D),T++)}else v.splice(T,1)}else for(var O=y[C];O<v.length;)S[v[O]]===w?O++:v.splice(O,1)}return y[f]=v.length,e.createSparseMatrix({values:_,index:v,ptr:y,size:[d,f],datatype:s===e._datatype&&u===r._datatype?p:void 0})}}),Fc=`lcm`,Ic=W(Fc,[`typed`,`matrix`,`equalScalar`,`concat`],e=>{var{typed:t,matrix:n,equalScalar:r,concat:i}=e,a=hc({typed:t,equalScalar:r}),o=Pc({typed:t,equalScalar:r}),s=Ks({typed:t,equalScalar:r}),c=xc({typed:t,matrix:n,concat:i}),l=`number | BigNumber | Fraction | Matrix | Array`,u={};return u[`${l}, ${l}, ...${l}`]=t.referToSelf(e=>(t,n,r)=>{for(var i=e(t,n),a=0;a<r.length;a++)i=e(i,r[a]);return i}),t(Fc,{"number, number":ga,"BigNumber, BigNumber":d,"Fraction, Fraction":(e,t)=>e.lcm(t)},c({SS:o,DS:a,Ss:s}),u);function d(e,t){if(!e.isInt()||!t.isInt())throw Error(`Parameters in function lcm must be integer numbers`);if(e.isZero())return e;if(t.isZero())return t;for(var n=e.times(t);!t.isZero();){var r=t;t=e.mod(r),e=r}return n.div(e).abs()}});function Lc(e,t,n,r){return function(i){if(i>0||n.predictable){if(i<=0)return NaN;var a=i.toString(16),o=a.substring(0,15);return e*(a.length-o.length)+t(Number(`0x`+o))}return r(i.toNumber())}}var Rc=`log10`,zc=[`typed`,`config`,`Complex`],Bc=va(16),Vc=W(Rc,zc,e=>{var{typed:t,config:n,Complex:r}=e;function i(e){return e.log().div(Math.LN10)}function a(e){return i(new r(e,0))}return t(Rc,{number:function(e){return e>=0||n.predictable?va(e):a(e)},bigint:Lc(Bc,va,n,a),Complex:i,BigNumber:function(e){return!e.isNegative()||n.predictable?e.log():a(e.toNumber())},"Array | Matrix":t.referToSelf(e=>t=>Xi(t,e))})}),Hc=`log2`,Uc=W(Hc,[`typed`,`config`,`Complex`],e=>{var{typed:t,config:n,Complex:r}=e;function i(e){return a(new r(e,0))}return t(Hc,{number:function(e){return e>=0||n.predictable?ya(e):i(e)},bigint:Lc(4,ya,n,i),Complex:a,BigNumber:function(e){return!e.isNegative()||n.predictable?e.log(2):i(e.toNumber())},"Array | Matrix":t.referToSelf(e=>t=>Xi(t,e))});function a(e){var t=Math.sqrt(e.re*e.re+e.im*e.im);return new r(Math.log2?Math.log2(t):Math.log(t)/Math.LN2,Math.atan2(e.im,e.re)/Math.LN2)}}),Wc=W(`multiplyScalar`,[`typed`],e=>{var{typed:t}=e;return t(`multiplyScalar`,{"number, number":sa,"Complex, Complex":function(e,t){return e.mul(t)},"BigNumber, BigNumber":function(e,t){return e.times(t)},"bigint, bigint":function(e,t){return e*t},"Fraction, Fraction":function(e,t){return e.mul(t)},"number | Fraction | BigNumber | Complex, Unit":(e,t)=>t.multiply(e),"Unit, number | Fraction | BigNumber | Complex | Unit":(e,t)=>e.multiply(t)})}),Gc=`multiply`,Kc=W(Gc,[`typed`,`matrix`,`addScalar`,`multiplyScalar`,`equalScalar`,`dot`],e=>{var{typed:t,matrix:n,addScalar:r,multiplyScalar:i,equalScalar:a,dot:o}=e,s=Ks({typed:t,equalScalar:a}),c=Js({typed:t});function l(e,t){switch(e.length){case 1:switch(t.length){case 1:if(e[0]!==t[0])throw RangeError(`Dimension mismatch in multiplication. 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11var p=t(`_multiplyMatrixVector`,{"DenseMatrix, any":h,"SparseMatrix, any":v}),m=t(`_multiplyMatrixMatrix`,{"DenseMatrix, DenseMatrix":g,"DenseMatrix, SparseMatrix":_,"SparseMatrix, DenseMatrix":y,"SparseMatrix, SparseMatrix":b});function h(e,n){var a=e._data,o=e._size,s=e._datatype||e.getDataType(),c=n._data,l=n._datatype||n.getDataType(),u=o[0],d=o[1],f,p=r,m=i;s&&l&&s===l&&typeof s==`string`&&s!==`mixed`&&(f=s,p=t.find(r,[f,f]),m=t.find(i,[f,f]));for(var h=[],g=0;g<u;g++){for(var _=a[g],v=m(_[0],c[0]),y=1;y<d;y++)v=p(v,m(_[y],c[y]));h[g]=v}return e.createDenseMatrix({data:h,size:[u],datatype:s===e._datatype&&l===n._datatype?f:void 0})}function g(e,n){var a=e._data,o=e._size,s=e._datatype||e.getDataType(),c=n._data,l=n._size,u=n._datatype||n.getDataType(),d=o[0],f=o[1],p=l[1],m,h=r,g=i;s&&u&&s===u&&typeof s==`string`&&s!==`mixed`&&s!==`mixed`&&(m=s,h=t.find(r,[m,m]),g=t.find(i,[m,m]));for(var _=[],v=0;v<d;v++){var y=a[v];_[v]=[];for(var b=0;b<p;b++){for(var x=g(y[0],c[0][b]),S=1;S<f;S++)x=h(x,g(y[S],c[S][b]));_[v][b]=x}}return e.createDenseMatrix({data:_,size:[d,p],datatype:s===e._datatype&&u===n._datatype?m:void 0})}function _(e,n){var o=e._data,s=e._size,c=e._datatype||e.getDataType(),l=n._values,u=n._index,d=n._ptr,f=n._size,p=n._datatype||n._data===void 0?n._datatype:n.getDataType();if(!l)throw Error(`Cannot multiply Dense Matrix times Pattern only Matrix`);var m=s[0],h=f[1],g,_=r,v=i,y=a,b=0;c&&p&&c===p&&typeof c==`string`&&c!==`mixed`&&(g=c,_=t.find(r,[g,g]),v=t.find(i,[g,g]),y=t.find(a,[g,g]),b=t.convert(0,g));for(var x=[],S=[],C=[],w=n.createSparseMatrix({values:x,index:S,ptr:C,size:[m,h],datatype:c===e._datatype&&p===n._datatype?g:void 0}),T=0;T<h;T++){C[T]=S.length;var E=d[T],D=d[T+1];if(D>E)for(var O=0,k=0;k<m;k++){for(var A=k+1,j=void 0,M=E;M<D;M++){var N=u[M];O===A?j=_(j,v(o[k][N],l[M])):(j=v(o[k][N],l[M]),O=A)}O===A&&!y(j,b)&&(S.push(k),x.push(j))}}return C[h]=S.length,w}function v(e,n){var o=e._values,s=e._index,c=e._ptr,l=e._datatype||e._data===void 0?e._datatype:e.getDataType();if(!o)throw Error(`Cannot multiply Pattern only Matrix times Dense Matrix`);var u=n._data,d=n._datatype||n.getDataType(),f=e._size[0],p=n._size[0],m=[],h=[],g=[],_,v=r,y=i,b=a,x=0;l&&d&&l===d&&typeof l==`string`&&l!==`mixed`&&(_=l,v=t.find(r,[_,_]),y=t.find(i,[_,_]),b=t.find(a,[_,_]),x=t.convert(0,_));var S=[],C=[];g[0]=0;for(var w=0;w<p;w++){var T=u[w];if(!b(T,x))for(var E=c[w],D=c[w+1],O=E;O<D;O++){var k=s[O];C[k]?S[k]=v(S[k],y(T,o[O])):(C[k]=!0,h.push(k),S[k]=y(T,o[O]))}}for(var A=h.length,j=0;j<A;j++)m[j]=S[h[j]];return g[1]=h.length,e.createSparseMatrix({values:m,index:h,ptr:g,size:[f,1],datatype:l===e._datatype&&d===n._datatype?_:void 0})}function y(e,n){var o=e._values,s=e._index,c=e._ptr,l=e._datatype||e._data===void 0?e._datatype:e.getDataType();if(!o)throw Error(`Cannot multiply Pattern only Matrix times Dense Matrix`);var u=n._data,d=n._datatype||n.getDataType(),f=e._size[0],p=n._size[0],m=n._size[1],h,g=r,_=i,v=a,y=0;l&&d&&l===d&&typeof l==`string`&&l!==`mixed`&&(h=l,g=t.find(r,[h,h]),_=t.find(i,[h,h]),v=t.find(a,[h,h]),y=t.convert(0,h));for(var b=[],x=[],S=[],C=e.createSparseMatrix({values:b,index:x,ptr:S,size:[f,m],datatype:l===e._datatype&&d===n._datatype?h:void 0}),w=[],T=[],E=0;E<m;E++){S[E]=x.length;for(var D=E+1,O=0;O<p;O++){var k=u[O][E];if(!v(k,y))for(var A=c[O],j=c[O+1],M=A;M<j;M++){var N=s[M];T[N]===D?w[N]=g(w[N],_(k,o[M])):(T[N]=D,x.push(N),w[N]=_(k,o[M]))}}for(var P=S[E],F=x.length,ee=P;ee<F;ee++)b[ee]=w[x[ee]]}return S[m]=x.length,C}function b(e,n){var a=e._values,o=e._index,s=e._ptr,c=e._datatype||e._data===void 0?e._datatype:e.getDataType(),l=n._values,u=n._index,d=n._ptr,f=n._datatype||n._data===void 0?n._datatype:n.getDataType(),p=e._size[0],m=n._size[1],h=a&&l,g,_=r,v=i;c&&f&&c===f&&typeof c==`string`&&c!==`mixed`&&(g=c,_=t.find(r,[g,g]),v=t.find(i,[g,g]));for(var y=h?[]:void 0,b=[],x=[],S=e.createSparseMatrix({values:y,index:b,ptr:x,size:[p,m],datatype:c===e._datatype&&f===n._datatype?g:void 0}),C=h?[]:void 0,w=[],T,E,D,O,k,A,j,M,N=0;N<m;N++){x[N]=b.length;var P=N+1;for(k=d[N],A=d[N+1],O=k;O<A;O++)if(M=u[O],h)for(E=s[M],D=s[M+1],T=E;T<D;T++)j=o[T],w[j]===P?C[j]=_(C[j],v(l[O],a[T])):(w[j]=P,b.push(j),C[j]=v(l[O],a[T]));else for(E=s[M],D=s[M+1],T=E;T<D;T++)j=o[T],w[j]!==P&&(w[j]=P,b.push(j));if(h)for(var F=x[N],ee=b.length,te=F;te<ee;te++)y[te]=C[b[te]]}return x[m]=b.length,S}return t(Gc,i,{"Array, Array":t.referTo(`Matrix, Matrix`,e=>(t,r)=>{l(ri(t),ri(r));var i=e(n(t),n(r));return O(i)?i.valueOf():i}),"Matrix, Matrix":function(e,t){var n=e.size(),r=t.size();return l(n,r),n.length===1?r.length===1?u(e,t,n[0]):d(e,t):r.length===1?p(e,t):m(e,t)},"Matrix, Array":t.referTo(`Matrix,Matrix`,e=>(t,r)=>e(t,n(r))),"Array, Matrix":t.referToSelf(e=>(t,r)=>e(n(t,r.storage()),r)),"SparseMatrix, any":function(e,t){return s(e,t,i,!1)},"DenseMatrix, 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11),qc=`nthRoot`,Jc=W(qc,[`typed`,`matrix`,`equalScalar`,`BigNumber`,`concat`],e=>{var{typed:t,matrix:n,equalScalar:r,BigNumber:i,concat:a}=e,o=wc({typed:t}),s=hc({typed:t,equalScalar:r}),c=Pc({typed:t,equalScalar:r}),l=Ks({typed:t,equalScalar:r}),u=xc({typed:t,matrix:n,concat:a});function d(){throw Error(`Complex number not supported in function nthRoot. Use nthRoots instead.`)}return t(qc,{number:Sa,"number, number":Sa,BigNumber:e=>f(e,new i(2)),"BigNumber, BigNumber":f,Complex:d,"Complex, number":d,Array:t.referTo(`DenseMatrix,number`,e=>t=>e(n(t),2).valueOf()),DenseMatrix:t.referTo(`DenseMatrix,number`,e=>t=>e(t,2)),SparseMatrix:t.referTo(`SparseMatrix,number`,e=>t=>e(t,2)),"SparseMatrix, SparseMatrix":t.referToSelf(e=>(t,n)=>{if(n.density()===1)return c(t,n,e);throw Error(`Root must be non-zero`)}),"DenseMatrix, SparseMatrix":t.referToSelf(e=>(t,n)=>{if(n.density()===1)return o(t,n,e,!1);throw Error(`Root must be non-zero`)}),"Array, SparseMatrix":t.referTo(`DenseMatrix,SparseMatrix`,e=>(t,r)=>e(n(t),r)),"number | BigNumber, SparseMatrix":t.referToSelf(e=>(t,n)=>{if(n.density()===1)return l(n,t,e,!0);throw Error(`Root must be non-zero`)})},u({scalar:`number | BigNumber`,SD:s,Ss:l,sS:!1}));function f(e,t){var n=i.precision,r=i.clone({precision:n+2}),a=new i(0),o=new r(1),s=t.isNegative();if(s&&(t=t.neg()),t.isZero())throw Error(`Root must be non-zero`);if(e.isNegative()&&!t.abs().mod(2).equals(1))throw Error(`Root must be odd when a is negative.`);if(e.isZero())return s?new r(1/0):0;if(!e.isFinite())return s?a:e;var c=e.abs().pow(o.div(t));return c=e.isNeg()?c.neg():c,new i((s?o.div(c):c).toPrecision(n))}}),Yc=`sign`,Xc=W(Yc,[`typed`,`BigNumber`,`Fraction`,`complex`],e=>{var{typed:t,BigNumber:n,complex:r,Fraction:i}=e;return t(Yc,{number:Ca,Complex:function(e){return e.im===0?r(Ca(e.re)):e.sign()},BigNumber:function(e){return new n(e.cmp(0))},bigint:function(e){return e>0n?1n:e<0n?-1n:0n},Fraction:function(e){return e.n===0n?new i(0):new i(e.s)},"Array | Matrix":t.referToSelf(e=>t=>Xi(t,e,!0)),Unit:t.referToSelf(e=>n=>{if(!n._isDerived()&&n.units[0].unit.offset!==0)throw TypeError(`sign is ambiguous for units with offset`);return t.find(e,n.valueType())(n.value)})})}),Zc=W(`sqrt`,[`config`,`typed`,`Complex`],e=>{var{config:t,typed:n,Complex:r}=e;return n(`sqrt`,{number:i,Complex:function(e){return e.sqrt()},BigNumber:function(e){return!e.isNegative()||t.predictable?e.sqrt():i(e.toNumber())},Unit:function(e){return e.pow(.5)}});function i(e){return isNaN(e)?NaN:e>=0||t.predictable?Math.sqrt(e):new r(e,0).sqrt()}}),Qc=`square`,$c=W(Qc,[`typed`],e=>{var{typed:t}=e;return t(Qc,{number:Ta,Complex:function(e){return e.mul(e)},BigNumber:function(e){return e.times(e)},bigint:function(e){return e*e},Fraction:function(e){return e.mul(e)},Unit:function(e){return e.pow(2)}})}),el=`subtract`,tl=W(el,[`typed`,`matrix`,`equalScalar`,`subtractScalar`,`unaryMinus`,`DenseMatrix`,`concat`],e=>{var{typed:t,matrix:n,equalScalar:r,subtractScalar:i,unaryMinus:a,DenseMatrix:o,concat:s}=e,c=wc({typed:t}),l=gc({typed:t}),u=_c({typed:t,equalScalar:r}),d=Ec({typed:t,DenseMatrix:o}),f=qs({typed:t,DenseMatrix:o}),p=xc({typed:t,matrix:n,concat:s});return t(el,{"any, any":i},p({elop:i,SS:u,DS:c,SD:l,Ss:f,sS:d}))}),nl=`xgcd`,rl=W(nl,[`typed`,`config`,`matrix`,`BigNumber`],e=>{var{typed:t,config:n,matrix:r,BigNumber:i}=e;return t(nl,{"number, number":function(e,t){var i=Ea(e,t);return n.matrix===`Array`?i:r(i)},"BigNumber, BigNumber":a});function a(e,t){var a,o,s,c=new i(0),l=new i(1),u=c,d=l,f=l,p=c;if(!e.isInt()||!t.isInt())throw Error(`Parameters in function xgcd must be integer numbers`);for(;!t.isZero();)o=e.div(t).floor(),s=e.mod(t),a=u,u=d.minus(o.times(u)),d=a,a=f,f=p.minus(o.times(f)),p=a,e=t,t=s;var m=e.lt(c)?[e.neg(),d.neg(),p.neg()]:[e,e.isZero()?0:d,p];return n.matrix===`Array`?m:r(m)}}),il=`invmod`,al=W(il,[`typed`,`config`,`BigNumber`,`xgcd`,`equal`,`smaller`,`mod`,`add`,`isInteger`],e=>{var{typed:t,config:n,BigNumber:r,xgcd:i,equal:a,smaller:o,mod:s,add:c,isInteger:l}=e;return t(il,{"number, number":u,"BigNumber, BigNumber":u});function u(e,t){if(!l(e)||!l(t))throw Error(`Parameters in function invmod must be integer numbers`);if(e=s(e,t),a(t,0))throw Error(`Divisor must be non zero`);var n=i(e,t);n=n.valueOf();var[u,d]=n;return a(u,r(1))?(d=s(d,t),o(d,r(0))&&(d=c(d,t)),d):NaN}}),ol=W(`matAlgo09xS0Sf`,[`typed`,`equalScalar`],e=>{var{typed:t,equalScalar:n}=e;return function(e,r,i){var a=e._values,o=e._index,s=e._ptr,c=e._size,l=e._datatype||e._data===void 0?e._datatype:e.getDataType(),u=r._values,d=r._index,f=r._ptr,p=r._size,m=r._datatype||r._data===void 0?r._datatype:r.getDataType();if(c.length!==p.length)throw new ti(c.length,p.length);if(c[0]!==p[0]||c[1]!==p[1])throw RangeError(`Dimension mismatch. Matrix A (`+c+`) must match Matrix B (`+p+`)`);var h=c[0],g=c[1],_,v=n,y=0,b=i;typeof l==`string`&&l===m&&l!==`mixed`&&(_=l,v=t.find(n,[_,_]),y=t.convert(0,_),b=t.find(i,[_,_]));var x=a&&u?[]:void 0,S=[],C=[],w=x?[]:void 0,T=[],E,D,O,k,A;for(D=0;D<g;D++){C[D]=S.length;var j=D+1;if(w)for(k=f[D],A=f[D+1],O=k;O<A;O++)E=d[O],T[E]=j,w[E]=u[O];for(k=s[D],A=s[D+1],O=k;O<A;O++)if(E=o[O],w){var M=T[E]===j?w[E]:y,N=b(a[O],M);v(N,y)||(S.push(E),x.push(N))}else S.push(E)}return C[g]=S.length,e.createSparseMatrix({values:x,index:S,ptr:C,size:[h,g],datatype:l===e._datatype&&m===r._datatype?_:void 0})}}),sl=`dotMultiply`,cl=W(sl,[`typed`,`matrix`,`equalScalar`,`multiplyScalar`,`concat`],e=>

11{var{typed:t,matrix:n,equalScalar:r,multiplyScalar:i,concat:a}=e,o=hc({typed:t,equalScalar:r}),s=ol({typed:t,equalScalar:r}),c=Ks({typed:t,equalScalar:r});return t(sl,xc({typed:t,matrix:n,concat:a})({elop:i,SS:s,DS:o,Ss:c}))});function ll(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw Error(`Integers expected in function bitAnd`);var n=e.constructor;if(e.isNaN()||t.isNaN())return new n(NaN);if(e.isZero()||t.eq(-1)||e.eq(t))return e;if(t.isZero()||e.eq(-1))return t;if(!e.isFinite()||!t.isFinite()){if(!e.isFinite()&&!t.isFinite())return e.isNegative()===t.isNegative()?e:new n(0);if(!e.isFinite())return t.isNegative()?e:e.isNegative()?new n(0):t;if(!t.isFinite())return e.isNegative()?t:t.isNegative()?new n(0):e}return fl(e,t,function(e,t){return e&t})}function ul(e){if(e.isFinite()&&!e.isInteger())throw Error(`Integer expected in function bitNot`);var t=e.constructor,n=t.precision;t.config({precision:1e9});var r=e.plus(new t(1));return r.s=-r.s||null,t.config({precision:n}),r}function dl(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw Error(`Integers expected in function bitOr`);var n=e.constructor;if(e.isNaN()||t.isNaN())return new n(NaN);var r=new n(-1);return e.isZero()||t.eq(r)||e.eq(t)?t:t.isZero()||e.eq(r)?e:!e.isFinite()||!t.isFinite()?!e.isFinite()&&!e.isNegative()&&t.isNegative()||e.isNegative()&&!t.isNegative()&&!t.isFinite()?r:e.isNegative()&&t.isNegative()?e.isFinite()?e:t:e.isFinite()?t:e:fl(e,t,function(e,t){return e|t})}function fl(e,t,n){var r=e.constructor,i,a,o=+(e.s<0),s=+(t.s<0);if(o){i=pl(ul(e));for(var c=0;c<i.length;++c)i[c]^=1}else i=pl(e);if(s){a=pl(ul(t));for(var l=0;l<a.length;++l)a[l]^=1}else a=pl(t);var u,d,f;i.length<=a.length?(u=i,d=a,f=o):(u=a,d=i,f=s);var p=u.length,m=d.length,h=n(o,s)^1,g=new r(h^1),_=new r(1),v=new r(2),y=r.precision;for(r.config({precision:1e9});p>0;)n(u[--p],d[--m])===h&&(g=g.plus(_)),_=_.times(v);for(;m>0;)n(f,d[--m])===h&&(g=g.plus(_)),_=_.times(v);return r.config({precision:y}),h===0&&(g.s=-g.s),g}function pl(e){for(var t=e.d,n=t[0]+``,r=1;r<t.length;++r){for(var i=t[r]+``,a=7-i.length;a--;)i=`0`+i;n+=i}for(var o=n.length;n.charAt(o)===`0`;)o--;var s=e.e,c=n.slice(0,o+1||1),l=c.length;if(s>0)if(++s>l)for(s-=l;s--;)c+=`0`;else s<l&&(c=c.slice(0,s)+`.`+c.slice(s));for(var u=[0],d=0;d<c.length;){for(var f=u.length;f--;)u[f]*=10;u[0]+=parseInt(c.charAt(d++));for(var p=0;p<u.length;++p)u[p]>1&&((u[p+1]===null||u[p+1]===void 0)&&(u[p+1]=0),u[p+1]+=u[p]>>1,u[p]&=1)}return u.reverse()}function ml(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw Error(`Integers expected in function bitXor`);var n=e.constructor;if(e.isNaN()||t.isNaN())return new n(NaN);if(e.isZero())return t;if(t.isZero())return e;if(e.eq(t))return new n(0);var r=new n(-1);return e.eq(r)?ul(t):t.eq(r)?ul(e):!e.isFinite()||!t.isFinite()?!e.isFinite()&&!t.isFinite()?r:new n(e.isNegative()===t.isNegative()?1/0:-1/0):fl(e,t,function(e,t){return e^t})}function hl(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw Error(`Integers expected in function leftShift`);var n=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new n(NaN):e.isZero()||t.isZero()?e:!e.isFinite()&&!t.isFinite()?new n(NaN):t.lt(55)?e.times(2**t.toNumber()+``):e.times(new n(2).pow(t))}function gl(e,t){if(e.isFinite()&&!e.isInteger()||t.isFinite()&&!t.isInteger())throw Error(`Integers expected in function rightArithShift`);var n=e.constructor;return e.isNaN()||t.isNaN()||t.isNegative()&&!t.isZero()?new n(NaN):e.isZero()||t.isZero()?e:t.isFinite()?t.lt(55)?e.div(2**t.toNumber()+``).floor():e.div(new n(2).pow(t)).floor():e.isNegative()?new n(-1):e.isFinite()?new n(0):new n(NaN)}var _l=`bitAnd`,vl=W(_l,[`typed`,`matrix`,`equalScalar`,`concat`],e=>{var{typed:t,matrix:n,equalScalar:r,concat:i}=e,a=hc({typed:t,equalScalar:r}),o=Pc({typed:t,equalScalar:r}),s=Ks({typed:t,equalScalar:r}),c=xc({typed:t,matrix:n,concat:i});return t(_l,{"number, number":Ma,"BigNumber, BigNumber":ll,"bigint, bigint":(e,t)=>e&t},c({SS:o,DS:a,Ss:s}))}),yl=`bitNot`,bl=W(yl,[`typed`],e=>{var{typed:t}=e;return t(yl,{number:Na,BigNumber:ul,bigint:e=>~e,"Array | Matrix":t.referToSelf(e=>t=>Xi(t,e))})}),xl=`bitOr`,Sl=W(xl,[`typed`,`matrix`,`equalScalar`,`DenseMatrix`,`concat`],e=>{var{typed:t,matrix:n,equalScalar:r,DenseMatrix:i,concat:a}=e,o=wc({typed:t}),s=Tc({typed:t,equalScalar:r}),c=Ec({typed:t,DenseMatrix:i}),l=xc({typed:t,matrix:n,concat:a});return t(xl,{"number, number":Pa,"BigNumber, BigNumber":dl,"bigint, bigint":(e,t)=>e|t},l({SS:s,DS:o,Ss:c}))}),Cl=W(`matAlgo07xSSf`,[`typed`,`SparseMatrix`],e=>{var{typed:t,SparseMatrix:n}=e;return function(e,i,a){var o=e._size,s=e._datatype||e._data===void 0?e._datatype:e.getDataType(),c=i._size,l=i._datatype||i._data===void 0?i._datatype:i.getDataType();if(o.length!==c.length)throw new ti(o.length,c.length);if(o[0]!==c[0]||o[1]!==c[1])throw RangeError(`Dimension mismatch. Matrix A (`+o+`) must match Matrix B (`+c+`)`);var u=o[0],d=o[1],f,p=0,m=a;typeof s==`string`&&s===l&&s!==`mixed`&&(f=s,p=t.convert(0,f),m=t.find(a,[f,f]));for(var h=[],g=[],_=Array(d+1).fill(0),v=[],y=[],b=[],x=[],S=0;S<d;S++){var C=S+1,w=0;r(e,S,b,v,C),r(i,S,x,y,C);for(var T=0;T<u;T++){var E=b[T]===C?v[T]:p,D=x[T]===C?y[T]:p,O=m(E,D);O!==0&&O!==!1&&(g.push(T),h.push(O),w++)}_[S+1]=_[S]+w}return new n({values:h,index:g,ptr:_,size:[u,d],datatype:s===e._datatype&&l===i._datatype?f:void 0})};function r(e,t,n,r,i){for(var a=e._values,o=e._index,s=e._ptr,c=s[t],l=s[t+1];c<l;c++){var u=o[c];n[u]=i,r[u]=a[c]}}}),wl=`bitXor`,Tl=W(wl,[`typed`,`matrix`,`DenseMatrix`,`concat`,`SparseMatrix`],e=>{var{typed:t,matrix:n,DenseMatrix:r,concat:i,SparseMatrix:a}=e,o=gc({typed:t}),s=Cl({typed:t,SparseMatrix:a}),c=qs({typed:t,DenseMatrix:r}

11),l=xc({typed:t,matrix:n,concat:i});return t(wl,{"number, number":Fa,"BigNumber, BigNumber":ml,"bigint, bigint":(e,t)=>e^t},l({SS:s,DS:o,Ss:c}))}),El=`arg`,Dl=W(El,[`typed`],e=>{var{typed:t}=e;return t(El,{number:function(e){return Math.atan2(0,e)},BigNumber:function(e){return e.constructor.atan2(0,e)},Complex:function(e){return e.arg()},"Array | Matrix":t.referToSelf(e=>t=>Xi(t,e))})}),Ol=`conj`,kl=W(Ol,[`typed`],e=>{var{typed:t}=e;return t(Ol,{"number | BigNumber | Fraction":e=>e,Complex:e=>e.conjugate(),Unit:t.referToSelf(e=>t=>new t.constructor(e(t.toNumeric()),t.formatUnits())),"Array | Matrix":t.referToSelf(e=>t=>Xi(t,e))})}),Al=`im`,jl=W(Al,[`typed`],e=>{var{typed:t}=e;return t(Al,{number:()=>0,"BigNumber | Fraction":e=>e.mul(0),Complex:e=>e.im,"Array | Matrix":t.referToSelf(e=>t=>Xi(t,e))})}),Ml=`re`,Nl=W(Ml,[`typed`],e=>{var{typed:t}=e;return t(Ml,{"number | BigNumber | Fraction":e=>e,Complex:e=>e.re,"Array | Matrix":t.referToSelf(e=>t=>Xi(t,e))})}),Pl=`not`,Fl=W(Pl,[`typed`],e=>{var{typed:t}=e;return t(Pl,{"null | undefined":()=>!0,number:qa,Complex:function(e){return e.re===0&&e.im===0},BigNumber:function(e){return e.isZero()||e.isNaN()},bigint:e=>!e,Unit:t.referToSelf(e=>n=>t.find(e,n.valueType())(n.value)),"Array | Matrix":t.referToSelf(e=>t=>Xi(t,e))})}),Il=`nullish`,Ll=W(Il,[`typed`,`matrix`,`size`,`flatten`,`deepEqual`],e=>{var{typed:t,matrix:n,size:r,flatten:i,deepEqual:a}=e,o=gc({typed:t}),s=Js({typed:t}),c=vc({typed:t});return t(Il,{"number|bigint|Complex|BigNumber|Fraction|Unit|string|boolean|SparseMatrix, any":(e,t)=>e,"null, any":(e,t)=>t,"undefined, any":(e,t)=>t,"SparseMatrix, Array | Matrix":(e,t)=>{var n=r(e),i=r(t);if(a(n,i))return e;throw new ti(n,i)},"DenseMatrix, DenseMatrix":t.referToSelf(e=>(t,n)=>c(t,n,e)),"DenseMatrix, SparseMatrix":t.referToSelf(e=>(t,n)=>o(t,n,e,!1)),"DenseMatrix, Array":t.referToSelf(e=>(t,r)=>c(t,n(r),e)),"DenseMatrix, any":t.referToSelf(e=>(t,n)=>s(t,n,e,!1)),"Array, Array":t.referToSelf(e=>(t,r)=>c(n(t),n(r),e).valueOf()),"Array, DenseMatrix":t.referToSelf(e=>(t,r)=>c(n(t),r,e)),"Array, SparseMatrix":t.referToSelf(e=>(t,r)=>o(n(t),r,e,!1)),"Array, any":t.referToSelf(e=>(t,r)=>s(n(t),r,e,!1).valueOf())})}),Rl=`or`,zl=W(Rl,[`typed`,`matrix`,`equalScalar`,`DenseMatrix`,`concat`],e=>{var{typed:t,matrix:n,equalScalar:r,DenseMatrix:i,concat:a}=e,o=gc({typed:t}),s=_c({typed:t,equalScalar:r}),c=qs({typed:t,DenseMatrix:i}),l=xc({typed:t,matrix:n,concat:a});return t(Rl,{"number, number":Ja,"Complex, Complex":function(e,t){return e.re!==0||e.im!==0||t.re!==0||t.im!==0},"BigNumber, BigNumber":function(e,t){return!e.isZero()&&!e.isNaN()||!t.isZero()&&!t.isNaN()},"bigint, bigint":Ja,"Unit, Unit":t.referToSelf(e=>(t,n)=>e(t.value||0,n.value||0))},l({SS:s,DS:o,Ss:c}))}),Bl=`xor`,Vl=W(Bl,[`typed`,`matrix`,`DenseMatrix`,`concat`,`SparseMatrix`],e=>{var{typed:t,matrix:n,DenseMatrix:r,concat:i,SparseMatrix:a}=e,o=gc({typed:t}),s=Cl({typed:t,SparseMatrix:a}),c=qs({typed:t,DenseMatrix:r}),l=xc({typed:t,matrix:n,concat:i});return t(Bl,{"number, number":Ya,"Complex, Complex":function(e,t){return(e.re!==0||e.im!==0)!=(t.re!==0||t.im!==0)},"bigint, bigint":Ya,"BigNumber, BigNumber":function(e,t){return(!e.isZero()&&!e.isNaN())!=(!t.isZero()&&!t.isNaN())},"Unit, Unit":t.referToSelf(e=>(t,n)=>e(t.value||0,n.value||0))},l({SS:s,DS:o,Ss:c}))}),Hl=`concat`,Ul=W(Hl,[`typed`,`matrix`,`isInteger`],e=>{var{typed:t,matrix:n,isInteger:r}=e;return t(Hl,{"...Array | Matrix | number | BigNumber":function(e){var t,i=e.length,a=-1,o,s=!1,c=[];for(t=0;t<i;t++){var l=e[t];if(O(l)&&(s=!0),b(l)||x(l)){if(t!==i-1)throw Error(`Dimension must be specified as last argument`);if(o=a,a=l.valueOf(),!r(a))throw TypeError(`Integer number expected for dimension`);if(a<0||t>0&&a>o)throw new ni(a,o+1)}else{var u=V(l).valueOf(),d=ri(u);if(c[t]=u,o=a,a=d.length-1,t>0&&a!==o)throw new ti(o+1,a+1)}}if(c.length===0)throw SyntaxError(`At least one matrix expected`);for(var f=c.shift();c.length;)f=ki(f,c.shift(),a);return s?n(f):f},"...string":function(e){return e.join(``)}})}),Wl=`column`,Gl=W(Wl,[`typed`,`Index`,`matrix`,`range`],e=>{var{typed:t,Index:n,matrix:r,range:i}=e;return t(Wl,{"Matrix, number":a,"Array, number":function(e,t){return a(r(V(e)),t).valueOf()}});function a(e,t){if(e.size().length!==2)throw Error(`Only two dimensional matrix is supported`);si(t,e.size()[1]);

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14forEach(e){this.params.forEach((t,n)=>e(t,`params[`+n+`]`,this),this)}map(e){return new r(this.conditionals.slice(),this.params.map((t,n)=>this._ifNode(e(t,`params[`+n+`]`,this)),this))}clone(){return new r(this.conditionals,this.params)}_toString(e){for(var t=e&&e.parenthesis?e.parenthesis:`keep`,r=lh(this,t,e&&e.implicit),i=this.params.map(function(n,i){var a=lh(n,t,e&&e.implicit);return t===`all`||a!==null&&a<=r?`(`+n.toString(e)+`)`:n.toString(e)}),a=i[0],o=0;o<this.conditionals.length;o++)a+=` `+n[this.conditionals[o]],a+=` `+i[o+1];return a}toJSON(){return{mathjs:Hh,conditionals:this.conditionals,params:this.params}}static fromJSON(e){return new r(e.conditionals,e.params)}_toHTML(e){for(var t=e&&e.parenthesis?e.parenthesis:`keep`,r=lh(this,t,e&&e.implicit),i=this.params.map(function(n,i){var a=lh(n,t,e&&e.implicit);return t===`all`||a!==null&&a<=r?`<span class="math-parenthesis math-round-parenthesis">(</span>`+n.toHTML(e)+`<span class="math-parenthesis math-round-parenthesis">)</span>`:n.toHTML(e)}),a=i[0],o=0;o<this.conditionals.length;o++)a+=`<span class="math-operator math-binary-operator math-explicit-binary-operator">`+Zr(n[this.conditionals[o]])+`</span>`+i[o+1];return a}_toTex(e){for(var t=e&&e.parenthesis?e.parenthesis:`keep`,n=lh(this,t,e&&e.implicit),r=this.params.map(function(r,i){var a=lh(r,t,e&&e.implicit);return t===`all`||a!==null&&a<=n?`\\left(`+r.toTex(e)+`\right)`:r.toTex(e)}),i=r[0],a=0;a<this.conditionals.length;a++)i+=xh[this.conditionals[a]]+r[a+1];return i}}return $u(r,`name`,Hh),r},{isClass:!0,isNode:!0}),Wh=W(`SymbolNode`,[`math`,`?Unit`,`Node`],e=>{var{math:t,Unit:n,Node:r}=e;function i(e){return n?n.isValuelessUnit(e):!1}class o extends r{constructor(e){if(super(),typeof e!=`string`)throw TypeError(`String expected for parameter "name"`);this.name=e}get type(){return`SymbolNode`}get isSymbolNode(){return!0}_compile(e,t){var r=this.name;if(t[r]===!0)return function(e,t,n){return a(t,r)};if(r in e)return function(t,n,i){return t.has(r)?t.get(r):a(e,r)};var s=i(r);return function(e,t,i){return e.has(r)?e.get(r):s?new n(null,r):o.onUndefinedSymbol(r)}}forEach(e){}map(e){return this.clone()}static onUndefinedSymbol(e){throw Error(`Undefined symbol `+e)}clone(){return new o(this.name)}_toString(e){return this.name}_toHTML(e){var t=Zr(this.name);return t===`true`||t===`false`?`<span class="math-symbol math-boolean">`+t+`</span>`:t===`i`?`<span class="math-symbol math-imaginary-symbol">`+t+`</span>`:t===`Infinity`?`<span class="math-symbol math-infinity-symbol">`+t+`</span>`:t===`NaN`?`<span class="math-symbol math-nan-symbol">`+t+`</span>`:t===`null`?`<span class="math-symbol math-null-symbol">`+t+`</span>`:t===`undefined`?`<span class="math-symbol math-undefined-symbol">`+t+`</span>`:`<span class="math-symbol">`+t+`</span>`}toJSON(){return{mathjs:`SymbolNode`,name:this.name}}static fromJSON(e){return new o(e.name)}_toTex(e){var n=!1;t[this.name]===void 0&&i(this.name)&&(n=!0);var r=Eh(this.name,n);return r[0]===`\\`?r:` `+r}}return o},{isClass:!0,isNode:!0}),Gh=`FunctionNode`,Kh=W(Gh,[`math`,`Node`,`SymbolNode`],e=>{var t,{math:n,Node:r,SymbolNode:i}=e,o=e=>qr(e,{truncate:78});function s(e,t,n){for(var r=``,i=/\$(?:\{([a-z_][a-z_0-9]*)(?:\[([0-9]+)\])?\}|\$)/gi,a=0,o;(o=i.exec(e))!==null;)if(r+=e.substring(a,o.index),a=o.index,o[0]===`$$`)r+=`$`,a++;else{a+=o[0].length;var s=t[o[1]];if(!s)throw ReferenceError(`Template: Property `+o[1]+` does not exist.`);if(o[2]===void 0)switch(typeof s){case`string`:r+=s;break;case`object`:if(he(s))r+=s.toTex(n);else if(Array.isArray(s))r+=s.map(function(e,t){if(he(e))return e.toTex(n);throw TypeError(`Template: `+o[1]+`[`+t+`] is not a Node.`)}).join(`,`);else throw TypeError(`Template: `+o[1]+` has to be a Node, String or array of Nodes`);break;default:throw TypeError(`Template: `+o[1]+` has to be a Node, String or array of Nodes`)}else if(he(s[o[2]]&&s[o[2]]))r+=s[o[2]].toTex(n);else throw TypeError(`Template: `+o[1]+`[`+o[2]+`] is not a Node.`)}return r+=e.slice(a),r}class c extends r{constructor(e,t,n){if(super(),typeof e==`string`&&(e=new i(e)),!he(e))throw TypeError(`Node expected as parameter "fn"`);if(!Array.isArray(t)||!t.every(he))throw TypeError(`Array containing Nodes expected for parameter "args"`);var r=typeof n;if(!(r===`undefined`||r===`boolean`))throw TypeError(`optional flag, if specified, must be boolean`);this.fn=e,this.args=t||[],this.optional=!!n}get name(){return this.fn.name||``}get type(){return Gh}get isFunctionNode(){return!0}_compile(e,t){var n=this.args.map(n=>n._compile(e,t)),r=this.optional||ce(this.fn)&&this.fn.optionalChaining;if(xe(this.fn)){var i=this.fn.name;if(t[i]){var s=this.args;return function(t,c,l){var u=a(c,i);if(!(r&&u===void 0)){if(typeof u!=`function`)throw TypeError(`Argument '${i}' was not a function; received: ${o(u)}`);

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24for(var[t,n]of this.scope)if(te(n)){if(!eg(n))throw Error(`Cannot serialize external function ${t}`);e.functions[t]=`${n.syntax} = ${n.expr}`}else e.variables[t]=n;return e},r.fromJSON=function(e){var t=new r;return Object.entries(e.variables).forEach(e=>{var[n,r]=e;return t.set(n,r)}),Object.entries(e.functions).forEach(e=>{var[n,r]=e;return t.evaluate(r)}),t},r},{isClass:!0});function eg(e){return typeof e==`function`&&typeof e.syntax==`string`&&typeof e.expr==`string`}var tg=`parser`,ng=W(tg,[`typed`,`Parser`],e=>{var{typed:t,Parser:n}=e;return t(tg,{"":function(){return new n}})}),rg=`lup`,ig=W(rg,[`typed`,`matrix`,`abs`,`addScalar`,`divideScalar`,`multiplyScalar`,`subtractScalar`,`larger`,`equalScalar`,`unaryMinus`,`DenseMatrix`,`SparseMatrix`,`Spa`],e=>{var{typed:t,matrix:n,abs:r,addScalar:i,divideScalar:a,multiplyScalar:o,subtractScalar:s,larger:c,equalScalar:l,unaryMinus:u,DenseMatrix:d,SparseMatrix:f,Spa:p}=e;return t(rg,{DenseMatrix:function(e){return m(e)},SparseMatrix:function(e){return h(e)},Array:function(e){var t=m(n(e));return{L:t.L.valueOf(),U:t.U.valueOf(),p:t.p}}});function m(e){var t=e._size[0],n=e._size[1],u=Math.min(t,n),f=V(e._data),p=[],m=[t,u],h=[],g=[u,n],_,v,y,b=[];for(_=0;_<t;_++)b[_]=_;for(v=0;v<n;v++){if(v>0)for(_=0;_<t;_++){var x=Math.min(_,v),S=0;for(y=0;y<x;y++)S=i(S,o(f[_][y],f[y][v]));f[_][v]=s(f[_][v],S)}var C=v,w=0,T=0;for(_=v;_<t;_++){var E=f[_][v],D=r(E);c(D,w)&&(C=_,w=D,T=E)}if(v!==C&&(b[v]=[b[C],b[C]=b[v]][0],d._swapRows(v,C,f)),v<t)for(_=v+1;_<t;_++){var O=f[_][v];l(O,0)||(f[_][v]=a(f[_][v],T))}}for(v=0;v<n;v++)for(_=0;_<t;_++){if(v===0&&(_<n&&(h[_]=[]),p[_]=[]),_<v){_<n&&(h[_][v]=f[_][v]),v<t&&(p[_][v]=0);continue}if(_===v){_<n&&(h[_][v]=f[_][v]),v<t&&(p[_][v]=1);continue}_<n&&(h[_][v]=0),v<t&&(p[_][v]=f[_][v])}var k=new d({data:p,size:m}),A=new d({data:h,size:g}),j=[];for(_=0,u=b.length;_<u;_++)j[b[_]]=_;return{L:k,U:A,p:j,toString:function(){return`L: `+this.L.toString()+`
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26P: `+this.p}}}function h(e){var t=e._size[0],n=e._size[1],i=Math.min(t,n),s=e._values,d=e._index,m=e._ptr,h=[],g=[],_=[],v=[t,i],y=[],b=[],x=[],S=[i,n],C,w,T,E=[],D=[];for(C=0;C<t;C++)E[C]=C,D[C]=C;var O=function(e,t){var n=D[e],r=D[t];E[n]=t,E[r]=e,D[e]=r,D[t]=n},k=function(){var e=new p;w<t&&(_.push(h.length),h.push(1),g.push(w)),x.push(y.length);var n=m[w],i=m[w+1];for(T=n;T<i;T++)C=d[T],e.set(E[C],s[T]);w>0&&e.forEach(0,w-1,function(t,n){f._forEachRow(t,h,g,_,function(r,i){r>t&&e.accumulate(r,u(o(i,n)))})});var D=w,k=e.get(w),A=r(k);e.forEach(w+1,t-1,function(e,t){var n=r(t);c(n,A)&&(D=e,A=n,k=t)}),w!==D&&(f._swapRows(w,D,v[1],h,g,_),f._swapRows(w,D,S[1],y,b,x),e.swap(w,D),O(w,D)),e.forEach(0,t-1,function(e,t){e<=w?(y.push(t),b.push(e)):(t=a(t,k),l(t,0)||(h.push(t),g.push(e)))})};for(w=0;w<n;w++)k();return x.push(y.length),_.push(h.length),{L:new f({values:h,index:g,ptr:_,size:v}),U:new f({values:y,index:b,ptr:x,size:S}),p:E,toString:function(){return`L: `+this.L.toString()+`
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28P: `+this.p}}}}),ag=`qr`,og=W(ag,[`typed`,`matrix`,`zeros`,`identity`,`isZero`,`equal`,`sign`,`sqrt`,`conj`,`unaryMinus`,`addScalar`,`divideScalar`,`multiplyScalar`,`subtractScalar`,`complex`],e=>{var{typed:t,matrix:n,zeros:i,identity:a,isZero:o,equal:s,sign:c,sqrt:l,conj:u,unaryMinus:d,addScalar:f,divideScalar:p,multiplyScalar:m,subtractScalar:h,complex:g}=e;return r(t(ag,{DenseMatrix:function(e){return v(e)},SparseMatrix:function(e){return y(e)},Array:function(e){var t=v(n(e));return{Q:t.Q.valueOf(),R:t.R.valueOf()}}}),{_denseQRimpl:_});function _(e){var t=e._size[0],n=e._size[1],r=a([t],`dense`),g=r._data,_=e.clone(),v=_._data,y,b,x,S=i([t],``);for(x=0;x<Math.min(n,t);++x){var C=v[x][x],w=d(s(C,0)?1:c(C)),T=u(w),E=0;for(y=x;y<t;y++)E=f(E,m(v[y][x],u(v[y][x])));var D=m(w,l(E));if(!o(D)){var O=h(C,D);for(S[x]=1,y=x+1;y<t;y++)S[y]=p(v[y][x],O);var k=d(u(p(O,D))),A=void 0;for(b=x;b<n;b++){for(A=0,y=x;y<t;y++)A=f(A,m(u(S[y]),v[y][b]));for(A=m(A,k),y=x;y<t;y++)v[y][b]=m(h(v[y][b],m(S[y],A)),T)}for(y=0;y<t;y++){for(A=0,b=x;b<t;b++)A=f(A,m(g[y][b],S[b]));for(A=m(A,k),b=x;b<t;++b)g[y][b]=p(h(g[y][b],m(A,u(S[b]))),T)}}}return{Q:r,R:_,toString:function(){return`Q: `+this.Q.toString()+`
29R: `+this.R.toString()}}}function v(e){var t=_(e),n=t.R._data;if(e._data.length>0)for(var r=n[0][0].type===`Complex`?g(0):0,i=0;i<n.length;++i)for(var a=0;a<i&&a<(n[0]||[]).length;++a)n[i][a]=r;return t}function y(e){throw Error(`qr not implemented for sparse matrices yet`)}});function sg(e,t,n,r){for(var i=e._values,a=e._index,o=e._ptr,s=e._size,c=e._datatype,l=s[0],u=s[1],d=r&&e._values?[]:null,f=[],p=[],m=0,h=0;h<u;h++){p[h]=m;for(var g=n?n[h]:h,_=o[g],v=o[g+1],y=_;y<v;y++)f[m]=t?t[a[y]]:a[y],d&&(d[m]=i[y]),m++}return p[u]=m,e.createSparseMatrix({values:d,index:f,ptr:p,size:[l,u],datatype:c})}function cg(e,t,n,r,i,a,o){var s=0;for(n[o]=e;s>=0;){var c=n[o+s],l=n[r+c];l===-1?(s--,a[t++]=c):(n[r+c]=n[i+l],++s,n[o+s]=l)}return t}function lg(e,t){if(!e)return null;var n=0,r,i=[],a=[],o=0,s=t,c=2*t;

29for(r=0;r<t;r++)a[o+r]=-1;for(r=t-1;r>=0;r--)e[r]!==-1&&(a[s+r]=a[o+e[r]],a[o+e[r]]=r);for(r=0;r<t;r++)e[r]===-1&&(n=cg(r,n,a,o,s,i,c));return i}function ug(e,t){if(!e)return null;var n=e._index,r=e._ptr,i=e._size,a=i[0],o=i[1],s=[],c=[],l=0,u=o,d,f;if(t)for(d=0;d<a;d++)c[u+d]=-1;for(var p=0;p<o;p++){s[p]=-1,c[l+p]=-1;for(var m=r[p],h=r[p+1],g=m;g<h;g++){var _=n[g];for(d=t?c[u+_]:_;d!==-1&&d<p;d=f)f=c[l+d],c[l+d]=p,f===-1&&(s[d]=p);t&&(c[u+_]=p)}}return s}function dg(e,t,n){for(var r=e._values,i=e._index,a=e._ptr,o=e._size[1],s=0,c=0;c<o;c++){var l=a[c];for(a[c]=s;l<a[c+1];l++)t(i[l],c,r?r[l]:1,n)&&(i[s]=i[l],r&&(r[s]=r[l]),s++)}return a[o]=s,i.splice(s,i.length-s),r&&r.splice(s,r.length-s),s}function fg(e){return-e-2}var pg=W(`csAmd`,[`add`,`multiply`,`transpose`],e=>{var{add:t,multiply:n,transpose:r}=e;return function(e,t){if(!t||e<=0||e>3)return null;var n=t._size,r=n[0],l=n[1],u=0,d=Math.max(16,10*Math.sqrt(l));d=Math.min(l-2,d);var f=i(e,t,r,l,d);dg(f,c,null);for(var p=f._index,m=f._ptr,h=m[l],g=[],_=[],v=0,y=l+1,b=2*(l+1),x=3*(l+1),S=4*(l+1),C=5*(l+1),w=6*(l+1),T=7*(l+1),E=g,D=a(l,m,_,v,x,E,b,T,y,w,S,C),O=o(l,m,_,C,S,w,d,y,x,E,b),k=0,A,j,M,N,P,F,ee,te,ne,re,ie,ae,I,oe,L,se;O<l;){for(M=-1;k<l&&(M=_[x+k])===-1;k++);_[b+M]!==-1&&(E[_[b+M]]=-1),_[x+k]=_[b+M];var ce=_[S+M],R=_[y+M];O+=R;var le=0;_[y+M]=-R;var ue=m[M],z=ce===0?ue:h,B=z;for(N=1;N<=ce+1;N++){for(N>ce?(F=M,ee=ue,te=_[v+M]-ce):(F=p[ue++],ee=m[F],te=_[v+F]),P=1;P<=te;P++)A=p[ee++],!((ne=_[y+A])<=0)&&(le+=ne,_[y+A]=-ne,p[B++]=A,_[b+A]!==-1&&(E[_[b+A]]=E[A]),E[A]===-1?_[x+_[C+A]]=_[b+A]:_[b+E[A]]=_[b+A]);F!==M&&(m[F]=fg(M),_[w+F]=0)}for(ce!==0&&(h=B),_[C+M]=le,m[M]=z,_[v+M]=B-z,_[S+M]=-2,D=s(D,u,_,w,l),re=z;re<B;re++)if(A=p[re],!((ie=_[S+A])<=0)){ne=-_[y+A];var de=D-ne;for(ue=m[A],ae=m[A]+ie-1;ue<=ae;ue++)F=p[ue],_[w+F]>=D?_[w+F]-=ne:_[w+F]!==0&&(_[w+F]=_[C+F]+de)}for(re=z;re<B;re++){for(A=p[re],ae=m[A],I=ae+_[S+A]-1,oe=ae,L=0,se=0,ue=ae;ue<=I;ue++)if(F=p[ue],_[w+F]!==0){var fe=_[w+F]-D;fe>0?(se+=fe,p[oe++]=F,L+=F):(m[F]=fg(M),_[w+F]=0)}_[S+A]=oe-ae+1;var pe=oe,me=ae+_[v+A];for(ue=I+1;ue<me;ue++){j=p[ue];var he=_[y+j];he<=0||(se+=he,p[oe++]=j,L+=j)}se===0?(m[A]=fg(M),ne=-_[y+A],le-=ne,R+=ne,O+=ne,_[y+A]=0,_[S+A]=-1):(_[C+A]=Math.min(_[C+A],se),p[oe]=p[pe],p[pe]=p[ae],p[ae]=M,_[v+A]=oe-ae+1,L=(L<0?-L:L)%l,_[b+A]=_[T+L],_[T+L]=A,E[A]=L)}for(_[C+M]=le,u=Math.max(u,le),D=s(D+u,u,_,w,l),re=z;re<B;re++)if(A=p[re],!(_[y+A]>=0))for(L=E[A],A=_[T+L],_[T+L]=-1;A!==-1&&_[b+A]!==-1;A=_[b+A],D++){for(te=_[v+A],ie=_[S+A],ue=m[A]+1;ue<=m[A]+te-1;ue++)_[w+p[ue]]=D;var ge=A;for(j=_[b+A];j!==-1;){var _e=_[v+j]===te&&_[S+j]===ie;for(ue=m[j]+1;_e&&ue<=m[j]+te-1;ue++)_[w+p[ue]]!==D&&(_e=0);_e?(m[j]=fg(A),_[y+A]+=_[y+j],_[y+j]=0,_[S+j]=-1,j=_[b+j],_[b+ge]=j):(ge=j,j=_[b+j])}}for(ue=z,re=z;re<B;re++)A=p[re],!((ne=-_[y+A])<=0)&&(_[y+A]=ne,se=_[C+A]+le-ne,se=Math.min(se,l-O-ne),_[x+se]!==-1&&(E[_[x+se]]=A),_[b+A]=_[x+se],E[A]=-1,_[x+se]=A,k=Math.min(k,se),_[C+A]=se,p[ue++]=A);_[y+M]=R,(_[v+M]=ue-z)===0&&(m[M]=-1,_[w+M]=0),ce!==0&&(h=ue)}for(A=0;A<l;A++)m[A]=fg(m[A]);for(j=0;j<=l;j++)_[x+j]=-1;for(j=l;j>=0;j--)_[y+j]>0||(_[b+j]=_[x+m[j]],_[x+m[j]]=j);for(F=l;F>=0;F--)_[y+F]<=0||m[F]!==-1&&(_[b+F]=_[x+m[F]],_[x+m[F]]=F);for(M=0,A=0;A<=l;A++)m[A]===-1&&(M=cg(A,M,_,x,b,g,w));return g.splice(g.length-1,1),g};function i(e,i,a,o,s){var c=r(i);if(e===1&&o===a)return t(i,c);if(e===2){for(var l=c._index,u=c._ptr,d=0,f=0;f<a;f++){var p=u[f];if(u[f]=d,!(u[f+1]-p>s))for(var m=u[f+1];p<m;p++)l[d++]=l[p]}return u[a]=d,i=r(c),n(c,i)}return n(c,i)}function a(e,t,n,r,i,a,o,c,l,u,d,f){for(var p=0;p<e;p++)n[r+p]=t[p+1]-t[p];n[r+e]=0;for(var m=0;m<=e;m++)n[i+m]=-1,a[m]=-1,n[o+m]=-1,n[c+m]=-1,n[l+m]=1,n[u+m]=1,n[d+m]=0,n[f+m]=n[r+m];var h=s(0,0,n,u,e);return n[d+e]=-2,t[e]=-1,n[u+e]=0,h}function o(e,t,n,r,i,a,o,s,c,l,u){for(var d=0,f=0;f<e;f++){var p=n[r+f];if(p===0)n[i+f]=-2,d++,t[f]=-1,n[a+f]=0;else if(p>o)n[s+f]=0,n[i+f]=-1,d++,t[f]=fg(e),n[s+e]++;else{var m=n[c+p];m!==-1&&(l[m]=f),n[u+f]=n[c+p],n[c+p]=f}}return d}function s(e,t,n,r,i){if(e<2||e+t<0){for(var a=0;a<i;a++)n[r+a]!==0&&(n[r+a]=1);e=2}return e}function c(e,t){return e!==t}});function mg(e,t,n,r,i,a,o){var s,c,l=0,u;if(e<=t||n[r+t]<=n[i+e])return-1;n[i+e]=n[r+t];var d=n[a+e];if(n[a+e]=t,d===-1)l=1,u=e;else{for(l=2,u=d;u!==n[o+u];u=n[o+u]);for(s=d;s!==u;s=c)c=n[o+s],n[o+s]=u}return{jleaf:l,q:u}}var hg=W(`csCounts`,[`transpose`],e=>{var{transpose:t}=e;return function(e,n,r,i){if(!e||!n||!r)return null;var a=e._size,o=a[0],s=a[1],c,l,u,d,f,p,m,h=4*s+(i?s+o+1:0),g=[],_=0,v=s,y=2*s,b=3*s,x=4*s,S=5*s+1;for(u=0;

29u<h;u++)g[u]=-1;var C=[],w=t(e),T=w._index,E=w._ptr;for(u=0;u<s;u++)for(l=r[u],C[l]=+(g[b+l]===-1);l!==-1&&g[b+l]===-1;l=n[l])g[b+l]=u;if(i){for(u=0;u<s;u++)g[r[u]]=u;for(c=0;c<o;c++){for(u=s,p=E[c],m=E[c+1],f=p;f<m;f++)u=Math.min(u,g[T[f]]);g[S+c]=g[x+u],g[x+u]=c}}for(c=0;c<s;c++)g[_+c]=c;for(u=0;u<s;u++){for(l=r[u],n[l]!==-1&&C[n[l]]--,d=i?g[x+u]:l;d!==-1;d=i?g[S+d]:-1)for(f=E[d];f<E[d+1];f++){c=T[f];var D=mg(c,l,g,b,v,y,_);D.jleaf>=1&&C[l]++,D.jleaf===2&&C[D.q]--}n[l]!==-1&&(g[_+l]=n[l])}for(l=0;l<s;l++)n[l]!==-1&&(C[n[l]]+=C[l]);return C}}),gg=W(`csSqr`,[`add`,`multiply`,`transpose`],e=>{var{add:t,multiply:n,transpose:r}=e,i=pg({add:t,multiply:n,transpose:r}),a=hg({transpose:r});return function(e,t,n){var r=t._ptr,s=t._size[1],c,l={};if(l.q=i(e,t),e&&!l.q)return null;if(n){var u=e?sg(t,null,l.q,0):t;l.parent=ug(u,1);var d=lg(l.parent,s);if(l.cp=a(u,l.parent,d,1),u&&l.parent&&l.cp&&o(u,l))for(l.unz=0,c=0;c<s;c++)l.unz+=l.cp[c]}else l.unz=4*r[s]+s,l.lnz=l.unz;return l};function o(e,t){var n=e._ptr,r=e._index,i=e._size,a=i[0],o=i[1];t.pinv=[],t.leftmost=[];var s=t.parent,c=t.pinv,l=t.leftmost,u=[],d=0,f=a,p=a+o,m=a+2*o,h,g,_,v,y;for(g=0;g<o;g++)u[f+g]=-1,u[p+g]=-1,u[m+g]=0;for(h=0;h<a;h++)l[h]=-1;for(g=o-1;g>=0;g--)for(v=n[g],y=n[g+1],_=v;_<y;_++)l[r[_]]=g;for(h=a-1;h>=0;h--)c[h]=-1,g=l[h],g!==-1&&(u[m+g]++===0&&(u[p+g]=h),u[d+h]=u[f+g],u[f+g]=h);for(t.lnz=0,t.m2=a,g=0;g<o;g++)if(h=u[f+g],t.lnz++,h<0&&(h=t.m2++),c[h]=g,!(--m[g]<=0)){t.lnz+=u[m+g];var b=s[g];b!==-1&&(u[m+b]===0&&(u[p+b]=u[p+g]),u[d+u[p+g]]=u[f+b],u[f+b]=u[d+h],u[m+b]+=u[m+g])}for(h=0;h<a;h++)c[h]<0&&(c[h]=g++);return!0}});function _g(e,t){return e[t]<0}function vg(e,t){e[t]=fg(e[t])}function yg(e){return e<0?fg(e):e}function bg(e,t,n,r,i){var a=t._index,o=t._ptr,s=t._size[1],c,l,u,d=0;for(r[0]=e;d>=0;){e=r[d];var f=i?i[e]:e;_g(o,e)||(vg(o,e),r[s+d]=f<0?0:yg(o[f]));var p=1;for(l=r[s+d],u=f<0?0:yg(o[f+1]);l<u;l++)if(c=a[l],!_g(o,c)){r[s+d]=l,r[++d]=c,p=0;break}p&&(d--,r[--n]=e)}return n}function xg(e,t,n,r,i){var a=e._ptr,o=e._size,s=t._index,c=t._ptr,l=o[1],u,d,f,p=l;for(d=c[n],f=c[n+1],u=d;u<f;u++){var m=s[u];_g(a,m)||(p=bg(m,e,p,r,i))}for(u=p;u<l;u++)vg(a,r[u]);return p}var Sg=W(`csSpsolve`,[`divideScalar`,`multiply`,`subtract`],e=>{var{divideScalar:t,multiply:n,subtract:r}=e;return function(e,i,a,o,s,c,l){var u=e._values,d=e._index,f=e._ptr,p=e._size[1],m=i._values,h=i._index,g=i._ptr,_,v,y,b,x=xg(e,i,a,o,c);for(_=x;_<p;_++)s[o[_]]=0;for(v=g[a],y=g[a+1],_=v;_<y;_++)s[h[_]]=m[_];for(var S=x;

29S<p;S++){var C=o[S],w=c?c[C]:C;if(!(w<0))for(v=f[w],y=f[w+1],s[C]=t(s[C],u[l?v:y-1]),_=l?v+1:v,b=l?y:y-1;_<b;_++){var T=d[_];s[T]=r(s[T],n(u[_],s[C]))}}return x}}),Cg=W(`csLu`,[`abs`,`divideScalar`,`multiply`,`subtract`,`larger`,`largerEq`,`SparseMatrix`],e=>{var{abs:t,divideScalar:n,multiply:r,subtract:i,larger:a,largerEq:o,SparseMatrix:s}=e,c=Sg({divideScalar:n,multiply:r,subtract:i});return function(e,i,l){if(!e)return null;var u=e._size[1],d,f=100,p=100;i&&(d=i.q,f=i.lnz||f,p=i.unz||p);var m=[],h=[],g=[],_=new s({values:m,index:h,ptr:g,size:[u,u]}),v=[],y=[],b=[],x=new s({values:v,index:y,ptr:b,size:[u,u]}),S=[],C,w,T=[],E=[];for(C=0;C<u;C++)T[C]=0,S[C]=-1,g[C+1]=0;f=0,p=0;for(var D=0;D<u;D++){g[D]=f,b[D]=p;var O=d?d[D]:D,k=c(_,e,O,E,T,S,1),A=-1,j=-1;for(w=k;w<u;w++)if(C=E[w],S[C]<0){var M=t(T[C]);a(M,j)&&(j=M,A=C)}else y[p]=S[C],v[p++]=T[C];if(A===-1||j<=0)return null;S[O]<0&&o(t(T[O]),r(j,l))&&(A=O);var N=T[A];for(y[p]=D,v[p++]=N,S[A]=D,h[f]=A,m[f++]=1,w=k;w<u;w++)C=E[w],S[C]<0&&(h[f]=C,m[f++]=n(T[C],N)),T[C]=0}for(g[u]=f,b[u]=p,w=0;w<f;w++)h[w]=S[h[w]];return m.splice(f,m.length-f),h.splice(f,h.length-f),v.splice(p,v.length-p),y.splice(p,y.length-p),{L:_,U:x,pinv:S}}}),wg=`slu`,Tg=W(wg,[`typed`,`abs`,`add`,`multiply`,`transpose`,`divideScalar`,`subtract`,`larger`,`largerEq`,`SparseMatrix`],e=>{var{typed:t,abs:n,add:r,multiply:i,transpose:a,divideScalar:o,subtract:s,larger:c,largerEq:l,SparseMatrix:u}=e,d=gg({add:r,multiply:i,transpose:a}),f=Cg({abs:n,divideScalar:o,multiply:i,subtract:s,larger:c,largerEq:l,SparseMatrix:u});return t(wg,{"SparseMatrix, number, number":function(e,t,n){if(!G(t)||t<0||t>3)throw Error(`Symbolic Ordering and Analysis order must be an integer number in the interval [0, 3]`);if(n<0||n>1)throw Error(`Partial pivoting threshold must be a number from 0 to 1`);var r=d(t,e,!1),i=f(e,r,n);return{L:i.L,U:i.U,p:i.pinv,q:r.q,toString:function(){return`L: `+this.L.toString()+`
30U: `+this.U.toString()+`
31p: `+this.p.toString()+(this.q?`
32q: `+this.q.toString():``)+`
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52,coulomb:{description:`Coulomb's constant. Deprecated in favor of coulombConstant`,examples:[`coulombConstant`]},coulombConstant:{description:`Coulomb's constant`,examples:[`coulombConstant`]},elementaryCharge:{description:`Elementary charge`,examples:[`elementaryCharge`]},bohrMagneton:{description:`Bohr magneton`,examples:[`bohrMagneton`]},conductanceQuantum:{description:`Conductance quantum`,examples:[`conductanceQuantum`]},inverseConductanceQuantum:{description:`Inverse conductance quantum`,examples:[`inverseConductanceQuantum`]},magneticFluxQuantum:{description:`Magnetic flux quantum`,examples:[`magneticFluxQuantum`]},nuclearMagneton:{description:`Nuclear magneton`,examples:[`nuclearMagneton`]},klitzing:{description:`Von Klitzing constant`,examples:[`klitzing`]},bohrRadius:{description:`Bohr radius`,examples:[`bohrRadius`]},classicalElectronRadius:{description:`Classical electron radius`,examples:[`classicalElectronRadius`]},electronMass:{description:`Electron mass`,examples:[`electronMass`]},fermiCoupling:{description:`Fermi coupling constant`,examples:[`fermiCoupling`]},fineStructure:{description:`Fine-structure constant`,examples:[`fineStructure`]},hartreeEnergy:{description:`Hartree energy`,examples:[`hartreeEnergy`]},protonMass:{description:`Proton mass`,examples:[`protonMass`]},deuteronMass:{description:`Deuteron Mass`,examples:[`deuteronMass`]},neutronMass:{description:`Neutron mass`,examples:[`neutronMass`]},quantumOfCirculation:{description:`Quantum of circulation`,examples:[`quantumOfCirculation`]},rydberg:{description:`Rydberg constant`,examples:[`rydberg`]},thomsonCrossSection:{description:`Thomson cross section`,examples:[`thomsonCrossSection`]},weakMixingAngle:{description:`Weak mixing angle`,examples:[`weakMixingAngle`]},efimovFactor:{description:`Efimov factor`,examples:[`efimovFactor`]},atomicMass:{description:`Atomic mass constant`,examples:[`atomicMass`]},avogadro:{description:`Avogadro's number`,examples:[`avogadro`]},boltzmann:{description:`Boltzmann constant`,examples:[`boltzmann`]},faraday:{description:`Faraday constant`,examples:[`faraday`]},firstRadiation:{description:`First radiation constant`,examples:[`firstRadiation`]},loschmidt:{description:`Loschmidt constant at T=273.15 K and p=101.325 kPa`,examples:[`loschmidt`]},gasConstant:{description:`Gas constant`,examples:[`gasConstant`]},molarPlanckConstant:{description:`Molar Planck constant`,examples:[`molarPlanckConstant`]},molarVolume:{description:`Molar volume of an ideal gas at T=273.15 K and p=101.325 kPa`,examples:[`molarVolume`]},sackurTetrode:{description:`Sackur-Tetrode constant at T=1 K and p=101.325 kPa`,examples:[`sackurTetrode`]},secondRadiation:{description:`Second radiation constant`,examples:[`secondRadiation`]},stefanBoltzmann:{description:`Stefan-Boltzmann constant`,examples:[`stefanBoltzmann`]},wienDisplacement:{description:`Wien displacement law constant`,examples:[`wienDisplacement`]},molarMass:{description:`Molar mass constant`,examples:[`molarMass`]},molarMassC12:{description:`Molar mass constant of carbon-12`,examples:[`molarMassC12`]},gravity:{description:`Standard acceleration of gravity (standard acceleration of free-fall on Earth)`,examples:[`gravity`]},planckLength:{description:`Planck length`,examples:[`planckLength`]},planckMass:{description:`Planck mass`,examples:[`planckMass`]},planckTime:{description:`Planck time`,examples:[`planckTime`]},planckCharge:{description:`Planck charge`,examples:[`planckCharge`]},planckTemperature:{description:`Planck temperature`,examples:[`planckTemperature`]},derivative:{name:`derivative`,category:`Algebra`,syntax:[`derivative(expr, variable)`,`derivative(expr, variable, {simplify: boolean})`],description:`Takes the derivative of an expression expressed in parser Nodes. 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521], [1, 4]])`,`lup(matrix([[2, 1], [1, 4]]))`,`lup(sparse([[2, 1], [1, 4]]))`],seealso:[`lusolve`,`lsolve`,`usolve`,`matrix`,`sparse`,`slu`,`qr`]},lusolve:{name:`lusolve`,category:`Algebra`,syntax:[`x=lusolve(A, b)`,`x=lusolve(lu, b)`],description:`Solves the linear system A * x = b where A is an [n x n] matrix and b is a [n] column vector.`,examples:[`a = [-2, 3; 2, 1]`,`b = [11, 9]`,`x = lusolve(a, b)`],seealso:[`lup`,`slu`,`lsolve`,`usolve`,`matrix`,`sparse`]},leafCount:{name:`leafCount`,category:`Algebra`,syntax:[`leafCount(expr)`],description:`Computes the number of leaves in the parse tree of the given expression`,examples:[`leafCount("e^(i*pi)-1")`,`leafCount(parse("{a: 22/7, b: 10^(1/2)}"))`],seealso:[`simplify`]},polynomialRoot:{name:`polynomialRoot`,category:`Algebra`,syntax:[`x=polynomialRoot(-6, 3)`,`x=polynomialRoot(4, -4, 1)`,`x=polynomialRoot(-8, 12, -6, 1)`],description:`Finds the roots of a univariate polynomial given by its coefficients starting from constant, linear, and so on, increasing in degree.`,examples:[`a = polynomialRoot(-6, 11, -6, 1)`],seealso:[`cbrt`,`sqrt`]},resolve:{name:`resolve`,category:`Algebra`,syntax:[`resolve(node, scope)`],description:`Recursively substitute variables in an expression tree.`,examples:[`resolve(parse("1 + x"), { x: 7 })`,`resolve(parse("size(text)"), { text: "Hello World" })`,`resolve(parse("x + y"), { x: parse("3z") })`,`resolve(parse("3x"), { x: parse("y+z"), z: parse("w^y") })`],seealso:[`simplify`,`evaluate`],mayThrow:[`ReferenceError`]},simplify:{name:`simplify`,category:`Algebra`,syntax:[`simplify(expr)`,`simplify(expr, rules)`],description:`Simplify an expression tree.`,examples:[`simplify("3 + 2 / 4")`,`simplify("2x + x")`,`f = parse("x * (x + 2 + x)")`,`simplified = simplify(f)`,`simplified.evaluate({x: 2})`],seealso:[`simplifyCore`,`derivative`,`evaluate`,`parse`,`rationalize`,`resolve`]},simplifyConstant:{name:`simplifyConstant`,category:`Algebra`,syntax:[`simplifyConstant(expr)`,`simplifyConstant(expr, options)`],description:`Replace constant subexpressions of node with their values.`,examples:[`simplifyConstant("(3-3)*x")`,`simplifyConstant(parse("z-cos(tau/8)"))`],seealso:[`simplify`,`simplifyCore`,`evaluate`]},simplifyCore:{name:`simplifyCore`,category:`Algebra`,syntax:[`simplifyCore(node)`],description:`Perform simple one-pass simplifications on an expression tree.`,examples:[`simplifyCore(parse("0*x"))`,`simplifyCore(parse("(x+0)*2"))`],seealso:[`simplify`,`simplifyConstant`,`evaluate`]},symbolicEqual:{name:`symbolicEqual`,category:`Algebra`,syntax:[`symbolicEqual(expr1, expr2)`,`symbolicEqual(expr1, expr2, options)`],description:`Returns true if the difference of the expressions simplifies to 0`,examples:[`symbolicEqual("x*y","y*x")`,`symbolicEqual("abs(x^2)", "x^2")`,`symbolicEqual("abs(x)", "x", {context: {abs: {trivial: true}}})`],seealso:[`simplify`,`evaluate`]},rationalize:{name:`rationalize`,category:`Algebra`,syntax:[`rationalize(expr)`,`rationalize(expr, scope)`,`rationalize(expr, scope, detailed)`],description:`Transform a rationalizable expression in a rational fraction. If rational fraction is one variable polynomial then converts the numerator and denominator in canonical form, with decreasing exponents, returning the coefficients of numerator.`,examples:[`rationalize("2x/y - y/(x+1)")`,`rationalize("2x/y - y/(x+1)", true)`],seealso:[`simplify`]},slu:{name:`slu`,category:`Algebra`,syntax:[`slu(A, order, threshold)`],description:`Calculate the Matrix LU decomposition with full pivoting. Matrix A is decomposed in two matrices (L, U) and two permutation vectors (pinv, q) where P * A * Q = L * U`,examples:[`slu(sparse([4.5, 0, 3.2, 0; 3.1, 2.9, 0, 0.9; 0, 1.7, 3, 0; 3.5, 0.4, 0, 1]), 1, 0.001)`],seealso:[`lusolve`,`lsolve`,`usolve`,`matrix`,`sparse`,`lup`,`qr`]},usolve:{name:`usolve`,category:`Algebra`,syntax:[`x=usolve(U, b)`],description:`Finds one solution of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.`,examples:[`x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])`],seealso:[`usolveAll`,`lup`,`lusolve`,`lsolve`,`matrix`,`sparse`]},usolveAll:{name:`usolveAll`,category:`Algebra`,syntax:[`x=usolve(U, b)`],description:`Finds all solutions of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.`,examples:[`x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])`],seealso:[`usolve`,`lup`,`lusolve`,`lsolve`,`matrix`,`sparse`]},qr:{name:`qr`,category:`Algebra`,syntax:[`qr(A)`],description:"Calculates the Matrix QR decomposition. Matrix `A` is decomposed in two matrices (`Q`, `R`) where `Q` is an orthogonal matrix and `R` is an upper triangular matrix.",examples:[`qr([[1, -1,  4], [1,  4, -2], [1,  4,  2], [1,  -1, 0]])`],seealso:[`lup`,`slu`,`matrix`]},abs:{name:`abs`,category:`Arithmetic`,syntax:[`abs(x)`],description:`Compute the absolute value.`,examples:[`abs(3.5)`,`abs(-4.2)`],seealso:[`sign`]},add:{name:`add`,category:`Operators`,syntax:[`x + y`,`add(x, y)`],description:`Add two values.`,examples:[`a = 2.1 + 3.6`,`a - 3.6`,`3 + 2i`,`3 cm + 2 inch`,`"2.3" + "4"`],seealso:[`subtract`]},cbrt:{name:`cbrt`,category:`Arithmetic`,syntax:[`cbrt(x)`,`cbrt(x, allRoots)`],description:"Compute the cub

52ic root value. If x = y * y * y, then y is the cubic root of x. When `x` is a number or complex number, an optional second argument `allRoots` can be provided to return all three cubic roots. If not provided, the principal root is returned",examples:[`cbrt(64)`,`cube(4)`,`cbrt(-8)`,`cbrt(2 + 3i)`,`cbrt(8i)`,`cbrt(8i, true)`,`cbrt(27 m^3)`],seealso:[`square`,`sqrt`,`cube`,`multiply`]},ceil:{name:`ceil`,category:`Arithmetic`,syntax:[`ceil(x)`,`ceil(x, n)`,`ceil(unit, valuelessUnit)`,`ceil(unit, n, valuelessUnit)`],description:`Round a value towards plus infinity. If x is complex, both real and imaginary part are rounded towards plus infinity.`,examples:[`ceil(3.2)`,`ceil(3.8)`,`ceil(-4.2)`,`ceil(3.241cm, cm)`,`ceil(3.241cm, 2, cm)`],seealso:[`floor`,`fix`,`round`]},cube:{name:`cube`,category:`Arithmetic`,syntax:[`cube(x)`],description:`Compute the cube of a value. The cube of x is x * x * x.`,examples:[`cube(2)`,`2^3`,`2 * 2 * 2`],seealso:[`multiply`,`square`,`pow`]},divide:{name:`divide`,category:`Operators`,syntax:[`x / y`,`divide(x, y)`],description:`Divide two values.`,examples:[`a = 2 / 3`,`a * 3`,`4.5 / 2`,`3 + 4 / 2`,`(3 + 4) / 2`,`18 km / 4.5`],seealso:[`multiply`]},dotDivide:{name:`dotDivide`,category:`Operators`,syntax:[`x ./ y`,`dotDivide(x, y)`],description:`Divide two values element wise.`,examples:[`a = [1, 2, 3; 4, 5, 6]`,`b = [2, 1, 1; 3, 2, 5]`,`a ./ b`],seealso:[`multiply`,`dotMultiply`,`divide`]},dotMultiply:{name:`dotMultiply`,category:`Operators`,syntax:[`x .* y`,`dotMultiply(x, y)`],description:`Multiply two values element wise.`,examples:[`a = [1, 2, 3; 4, 5, 6]`,`b = [2, 1, 1; 3, 2, 5]`,`a .* b`],seealso:[`multiply`,`divide`,`dotDivide`]},dotPow:{name:`dotPow`,category:`Operators`,syntax:[`x .^ y`,`dotPow(x, y)`],description:`Calculates the power of x to y element wise.`,examples:[`a = [1, 2, 3; 4, 5, 6]`,`a .^ 2`],seealso:[`pow`]},exp:{name:`exp`,category:`Arithmetic`,syntax:[`exp(x)`],description:`Calculate the exponent of a value.`,examples:[`exp(1.3)`,`e ^ 1.3`,`log(exp(1.3))`,`x = 2.4`,`(exp(i*x) == cos(x) + i*sin(x))   # Euler's formula`],seealso:[`expm`,`expm1`,`pow`,`log`]},expm:{name:`expm`,category:`Arithmetic`,syntax:[`exp(x)`],description:`Compute the matrix exponential, expm(A) = e^A. The matrix must be square. Not to be confused with exp(a), which performs element-wise exponentiation.`,examples:[`expm([[0,2],[0,0]])`],seealso:[`exp`]},expm1:{name:`expm1`,category:`Arithmetic`,syntax:[`expm1(x)`],description:`Calculate the value of subtracting 1 from the exponential value.`,examples:[`expm1(2)`,`pow(e, 2) - 1`,`log(expm1(2) + 1)`],seealso:[`exp`,`pow`,`log`]},fix:{name:`fix`,category:`Arithmetic`,syntax:[`fix(x)`,`fix(x, n)`,`fix(unit, valuelessUnit)`,`fix(unit, n, valuelessUnit)`],description:`Round a value towards zero. If x is complex, both real and imaginary part are rounded towards zero.`,examples:[`fix(3.2)`,`fix(3.8)`,`fix(-4.2)`,`fix(-4.8)`,`fix(3.241cm, cm)`,`fix(3.241cm, 2, cm)`],seealso:[`ceil`,`floor`,`round`]},floor:{name:`floor`,category:`Arithmetic`,syntax:[`floor(x)`,`floor(x, n)`,`floor(unit, valuelessUnit)`,`floor(unit, n, valuelessUnit)`],description:`Round a value towards minus infinity.If x is complex, both real and imaginary part are rounded towards minus infinity.`,examples:[`floor(3.2)`,`floor(3.8)`,`floor(-4.2)`,`floor(3.241cm, cm)`,`floor(3.241cm, 2, cm)`],seealso:[`ceil`,`fix`,`round`]},gcd:{name:`gcd`,category:`Arithmetic`,syntax:[`gcd(a, b)`,`gcd(a, b, c, ...)`],description:`Compute the greatest common divisor.`,examples:[`gcd(8, 12)`,`gcd(-4, 6)`,`gcd(25, 15, -10)`],seealso:[`lcm`,`xgcd`]},hypot:{name:`hypot`,category:`Arithmetic`,syntax:[`hypot(a, b, c, ...)`,`hypot([a, b, c, ...])`],description:`Calculate the hypotenuse of a list with values.`,examples:[`hypot(3, 4)`,`sqrt(3^2 + 4^2)`,`hypot(-2)`,`hypot([3, 4, 5])`],seealso:[`abs`,`norm`]},lcm:{name:`lcm`,category:`Arithmetic`,syntax:[`lcm(x, y)`],description:`Compute the least common multiple.`,examples:[`lcm(4, 6)`,`lcm(6, 21)`,`lcm(6, 21, 5)`],seealso:[`gcd`]},log:{name:`log`,category:`Arithmetic`,syntax:[`log(x)`,`log(x, base)`],description:`Compute the logarithm of a value. If no base is provided, the natural logarithm of x is calculated. If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).`,examples:[`log(3.5)`,`a = log(2.4)`,`exp(a)`,`10 ^ 4`,`log(10000, 10)`,`log(10000) / log(10)`,`b = log(1024, 2)`,`2 ^ b`],seealso:[`exp`,`log1p`,`log2`,`log10`]},log2:{name:`log2`,category:`Arithmetic`,syntax:[`log2(x)`],description:"Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.",examples:[`log2(0.03125)`,`log2(16)`,`log2(16) / log2(2)`,`pow(2, 4)`],seealso:[`exp`,`log1p`,`log`,`log10`]},log1p:{name:`log1p`,category:`Arithmetic`,syntax:[`log1p(x)`,`log1p(x, base)`],description:"Calculate the logarithm of a `value+1`",examples:[`log1p(2.5)`,`exp(log1p(1.4))`,`pow(10, 4)`,`log1p(9999, 10)`,`log1p(9999) / log(10)`],seealso:[`exp`,`log`,`log2`,`log10`]},log10:{name:`log10`,category:`Arithmetic`,syntax:[`log10(x)`],description:`Compute the 10-base logarithm of a value.`,examples:[`log10(0.00001)`,`log10(10000)`,`10 ^ 4`,`log(10000) / log(10)`,`log(10000, 10)`],seealso:[`exp`,`log`]},mod:{name:`mod`,category:`Operators`,syntax:[`x % y`,`x mod y`,`mod(x, y)`],description:`Calculates the modulus, the remainder of an integer division.`,examples:[`7 % 3`,`11 % 2`,`10 mod 4`,`isOdd(x) = x % 2`,`isOdd(2)`,`isOdd(3)`],seealso:[`divide`]},multiply:{name:`multiply`,category:`Operators`,syntax:[`x * y`,`multiply(x, y)`],description:`multiply two values.`,examples:[`a = 2.1 * 3.4`,`a / 3.4`,`2 * 3 + 4`,`2 * (3 + 4)`,`3 * 2.1 km`],seealso:[`divide`]},norm:{name:`norm`,category:`Arithmetic`,syntax:[`norm(x)`,`norm(x, p)`],description:`Calculate the norm of a number, vector or matrix.`,examples:[`abs(-3.5)`,`norm(-3.5)`,`norm(3 - 4i)`,`norm([1, 2, -3], Infinity)`,`norm([1, 2, -3], -Infinity)`,`norm([3, 4], 2)`,`norm([[1, 2], [3, 4]], 1)`,`norm([[1, 2], [3, 4]], "inf")`,`norm([[1, 2], [3, 4]], "fro")`]}

52,nthRoot:{name:`nthRoot`,category:`Arithmetic`,syntax:[`nthRoot(a)`,`nthRoot(a, root)`],description:`Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation "x^root = A".`,examples:[`4 ^ 3`,`nthRoot(64, 3)`,`nthRoot(9, 2)`,`sqrt(9)`],seealso:[`nthRoots`,`pow`,`sqrt`]},nthRoots:{name:`nthRoots`,category:`Arithmetic`,syntax:[`nthRoots(A)`,`nthRoots(A, root)`],description:`Calculate the nth roots of a value. An nth root of a positive real number A, is a positive real solution of the equation "x^root = A". This function returns an array of complex values.`,examples:[`nthRoots(1)`,`nthRoots(1, 3)`],seealso:[`sqrt`,`pow`,`nthRoot`]},pow:{name:`pow`,category:`Operators`,syntax:[`x ^ y`,`pow(x, y)`],description:`Calculates the power of x to y, x^y.`,examples:[`2^3`,`2*2*2`,`1 + e ^ (pi * i)`,`pow([[1, 2], [4, 3]], 2)`,`pow([[1, 2], [4, 3]], -1)`],seealso:[`multiply`,`nthRoot`,`nthRoots`,`sqrt`]},round:{name:`round`,category:`Arithmetic`,syntax:[`round(x)`,`round(x, n)`,`round(unit, valuelessUnit)`,`round(unit, n, valuelessUnit)`],description:`round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.`,examples:[`round(3.2)`,`round(3.8)`,`round(-4.2)`,`round(-4.8)`,`round(pi, 3)`,`round(123.45678, 2)`,`round(3.241cm, 2, cm)`,`round([3.2, 3.8, -4.7])`],seealso:[`ceil`,`floor`,`fix`]},sign:{name:`sign`,category:`Arithmetic`,syntax:[`sign(x)`],description:`Compute the sign of a value. The sign of a value x is 1 when x>0, -1 when x<0, and 0 when x=0.`,examples:[`sign(3.5)`,`sign(-4.2)`,`sign(0)`],seealso:[`abs`]},sqrt:{name:`sqrt`,category:`Arithmetic`,syntax:[`sqrt(x)`],description:`Compute the square root value. If x = y * y, then y is the square root of x.`,examples:[`sqrt(25)`,`5 * 5`,`sqrt(-1)`],seealso:[`square`,`sqrtm`,`multiply`,`nthRoot`,`nthRoots`,`pow`]},sqrtm:{name:`sqrtm`,category:`Arithmetic`,syntax:[`sqrtm(x)`],description:"Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.",examples:[`sqrtm([[33, 24], [48, 57]])`],seealso:[`sqrt`,`abs`,`square`,`multiply`]},square:{name:`square`,category:`Arithmetic`,syntax:[`square(x)`],description:`Compute the square of a value. The square of x is x * x.`,examples:[`square(3)`,`sqrt(9)`,`3^2`,`3 * 3`],seealso:[`multiply`,`pow`,`sqrt`,`cube`]},subtract:{name:`subtract`,category:`Operators`,syntax:[`x - y`,`subtract(x, y)`],description:`subtract two values.`,examples:[`a = 5.3 - 2`,`a + 2`,`2/3 - 1/6`,`2 * 3 - 3`,`2.1 km - 500m`],seealso:[`add`]},unaryMinus:{name:`unaryMinus`,category:`Operators`,syntax:[`-x`,`unaryMinus(x)`],description:`Inverse the sign of a value. Converts booleans and strings to numbers.`,examples:[`-4.5`,`-(-5.6)`,`-"22"`],seealso:[`add`,`subtract`,`unaryPlus`]},unaryPlus:{name:`unaryPlus`,category:`Operators`,syntax:[`+x`,`unaryPlus(x)`],description:`Converts booleans and strings to numbers.`,examples:[`+true`,`+"2"`],seealso:[`add`,`subtract`,`unaryMinus`]},xgcd:{name:`xgcd`,category:`Arithmetic`,syntax:[`xgcd(a, b)`],description:`Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.`,examples:[`xgcd(8, 12)`,`gcd(8, 12)`,`xgcd(36163, 21199)`],seealso:[`gcd`,`lcm`]}

52,invmod:{name:`invmod`,category:`Arithmetic`,syntax:[`invmod(a, b)`],description:`Calculate the (modular) multiplicative inverse of a modulo b. Solution to the equation ax â£ 1 (mod b)`,examples:[`invmod(8, 12)`,`invmod(7, 13)`,`invmod(15151, 15122)`],seealso:[`gcd`,`xgcd`]},num:{name:`num`,category:`Fraction`,syntax:[`num(x)`],description:`Get the numerator of a fraction.`,examples:[`num(fraction(2, 3))`,`num(fraction(5, 8))`],seealso:[`den`,`fraction`]},den:{name:`den`,category:`Fraction`,syntax:[`den(x)`],description:`Get the denominator of a fraction.`,examples:[`den(fraction(2, 3))`,`den(fraction(5, 8))`],seealso:[`num`,`fraction`]},bitAnd:{name:`bitAnd`,category:`Bitwise`,syntax:[`x & y`,`bitAnd(x, y)`],description:`Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0`,examples:[`5 & 3`,`bitAnd(53, 131)`,`[1, 12, 31] & 42`],seealso:[`bitNot`,`bitOr`,`bitXor`,`leftShift`,`rightArithShift`,`rightLogShift`]},bitNot:{name:`bitNot`,category:`Bitwise`,syntax:[`~x`,`bitNot(x)`],description:`Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.`,examples:[`~1`,`~2`,`bitNot([2, -3, 4])`],seealso:[`bitAnd`,`bitOr`,`bitXor`,`leftShift`,`rightArithShift`,`rightLogShift`]},bitOr:{name:`bitOr`,category:`Bitwise`,syntax:[`x | y`,`bitOr(x, y)`],description:`Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.`,examples:[`5 | 3`,`bitOr([1, 2, 3], 4)`],seealso:[`bitAnd`,`bitNot`,`bitXor`,`leftShift`,`rightArithShift`,`rightLogShift`]},bitXor:{name:`bitXor`,category:`Bitwise`,syntax:[`bitXor(x, y)`],description:`Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.`,examples:[`bitOr(1, 2)`,`bitXor([2, 3, 4], 4)`],seealso:[`bitAnd`,`bitNot`,`bitOr`,`leftShift`,`rightArithShift`,`rightLogShift`]},leftShift:{name:`leftShift`,category:`Bitwise`,syntax:[`x << y`,`leftShift(x, y)`],description:`Bitwise left logical shift of a value x by y number of bits.`,examples:[`4 << 1`,`8 >> 1`],seealso:[`bitAnd`,`bitNot`,`bitOr`,`bitXor`,`rightArithShift`,`rightLogShift`]},rightArithShift:{name:`rightArithShift`,category:`Bitwise`,syntax:[`x >> y`,`rightArithShift(x, y)`],description:`Bitwise right arithmetic shift of a value x by y number of bits.`,examples:[`8 >> 1`,`4 << 1`,`-12 >> 2`],seealso:[`bitAnd`,`bitNot`,`bitOr`,`bitXor`,`leftShift`,`rightLogShift`]},rightLogShift:{name:`rightLogShift`,category:`Bitwise`,syntax:[`x >>> y`,`rightLogShift(x, y)`],description:`Bitwise right logical shift of a value x by y number of bits.`,examples:[`8 >>> 1`,`4 << 1`,`-12 >>> 2`],seealso:[`bitAnd`,`bitNot`,`bitOr`,`bitXor`,`leftShift`,`rightArithShift`]},bellNumbers:{name:`bellNumbers`,category:`Combinatorics`,syntax:[`bellNumbers(n)`],description:"The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.",examples:[`bellNumbers(3)`,`bellNumbers(8)`],seealso:[`stirlingS2`]},catalan:{name:`catalan`,category:`Combinatorics`,syntax:[`catalan(n)`],description:`The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.`,examples:[`catalan(3)`,`catalan(8)`],seealso:[`bellNumbers`]},composition:{name:`composition`,category:`Combinatorics`,syntax:[`composition(n, k)`],description:`The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.`,examples:[`composition(5, 3)`],seealso:[`combinations`]},stirlingS2:{name:`stirlingS2`,category:`Combinatorics`,syntax:[`stirlingS2

52(n, k)`],description:"The Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.",examples:[`stirlingS2(5, 3)`],seealso:[`bellNumbers`,`bernoulli`]},config:{name:`config`,category:`Core`,syntax:[`config()`,`config(options)`],description:`Get configuration or change configuration.`,examples:[`config()`,`1/3 + 1/4`,`config({number: "Fraction"})`,`1/3 + 1/4`],seealso:[]},import:{name:`import`,category:`Core`,syntax:[`import(functions)`,`import(functions, options)`],description:`Import functions or constants from an object.`,examples:[`import({myFn: f(x)=x^2, myConstant: 32 })`,`myFn(2)`,`myConstant`],seealso:[]},typed:{name:`typed`,category:`Core`,syntax:[`typed(signatures)`,`typed(name, signatures)`],description:`Create a typed function.`,examples:[`double = typed({ "number": f(x)=x+x, "string": f(x)=concat(x,x) })`,`double(2)`,`double("hello")`],seealso:[]},arg:{name:`arg`,category:`Complex`,syntax:[`arg(x)`],description:`Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).`,examples:[`arg(2 + 2i)`,`atan2(3, 2)`,`arg(2 + 3i)`],seealso:[`re`,`im`,`conj`,`abs`]},conj:{name:`conj`,category:`Complex`,syntax:[`conj(x)`],description:`Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.`,examples:[`conj(2 + 3i)`,`conj(2 - 3i)`,`conj(-5.2i)`],seealso:[`re`,`im`,`abs`,`arg`]},re:{name:`re`,category:`Complex`,syntax:[`re(x)`],description:`Get the real part of a complex number.`,examples:[`re(2 + 3i)`,`im(2 + 3i)`,`re(-5.2i)`,`re(2.4)`],seealso:[`im`,`conj`,`abs`,`arg`]},im:{name:`im`,category:`Complex`,syntax:[`im(x)`],description:`Get the imaginary part of a complex number.`,examples:[`im(2 + 3i)`,`re(2 + 3i)`,`im(-5.2i)`,`im(2.4)`],seealso:[`re`,`conj`,`abs`,`arg`]},evaluate:{name:`evaluate`,category:`Expression`,syntax:[`evaluate(expression)`,`evaluate(expression, scope)`,`evaluate([expr1, expr2, expr3, ...])`,`evaluate([expr1, expr2, expr3, ...], scope)`],description:`Evaluate an expression or an array with expressions.`,examples:[`evaluate("2 + 3")`,`evaluate("sqrt(16)")`,`evaluate("2 inch to cm")`,`evaluate("sin(x * pi)", { "x": 1/2 })`,`evaluate(["width=2", "height=4","width*height"])`],seealso:[`parser`,`parse`,`compile`]},help:{name:`help`,category:`Expression`,syntax:[`help(object)`,`help(string)`],description:`Display documentation on a function or data type.`,examples:[`help(sqrt)`,`help("complex")`],seealso:[]},parse:{name:`parse`,category:`Expression`,syntax:[`parse(expr)`,`parse(expr, options)`,`parse([expr1, expr2, expr3, ...])`,`parse([expr1, expr2, expr3, ...], options)`],description:`Parse an expression. Returns a node tree, which can be evaluated by invoking node.evaluate() or transformed into a functional object via node.compile().`,examples:[`node1 = parse("sqrt(3^2 + 4^2)")`,`node1.evaluate()`,`code1 = node1.compile()`,`code1.evaluate()`,`scope = {a: 3, b: 4}`,`node2 = parse("a * b")`,`node2.evaluate(scope)`,`code2 = node2.compile()`,`code2.evaluate(scope)`],seealso:[`parser`,`evaluate`,`compile`]},parser:{name:`parser`,category:`Expression`,syntax:[`parser()`],description:`Create a parser object that keeps a context of variables and their values, allowing the evaluation of expressions in that context.`,examples:[`myParser = parser()`,`myParser.evaluate("sqrt(3^2 + 4^2)")`,`myParser.set("x", 3)`,`myParser.evaluate("y = x + 3")`,`myParser.evaluate(["y = x + 3", "y = y + 1"])`,`myParser.get("y")`],seealso:[`evaluate`,`parse`,`compile`]},compile:{name:`compile`,category:`Expression`,syntax:[`compile(expr) `,`compile([expr1, expr2, expr3, ...])`],description:`Parse and compile an expression. Returns a an object with a function evaluate([scope]) to evaluate the compiled expression.`,examples:[`code1 = compile("sqrt(3^2 + 4^2)")`,`code1.evaluate() `,`code2 = compile("a * b")`,`code2.evaluate({a: 3, b: 4})`],seealso:[`parser`,`parse`,`evaluate`]},distance:{name:`distance`,category:`Geometry`,syntax:[`distance([x1, y1], [x2, y2])`,`distance([[x1, y1], [x2, y2]])`],description:`Calculates the Euclidean distance between two points.`,examples:[`distance([0,0], [4,4])`,`distance([[0,0], [4,4]])`],seealso:[]},intersect:{name:`intersect`,category:`Geometry`,syntax:[`intersect(expr1, expr2, expr3, expr4)`,`intersect(expr1, expr2, expr3)`],description:`Computes the intersection point of lines and/or planes.`,examples:[`intersect([0, 0], [10, 10], [10, 0], [0, 10])`,`intersect([1, 0, 1],  [4, -2, 2], [1, 1, 1, 6])`],seealso:[]},and:{name:`and`,category:`Logical`,syntax:[`x and y`,`and(x, y)`],description:`Logical and. Test whether two values are both defined with a nonzero/nonempty value.`,examples:[`true and false`,`true and true`,`2 and 4`],seealso:[`not`,`or`,`xor`]}

52,not:{name:`not`,category:`Logical`,syntax:[`not x`,`not(x)`],description:`Logical not. Flips the boolean value of given argument.`,examples:[`not true`,`not false`,`not 2`,`not 0`],seealso:[`and`,`or`,`xor`]},nullish:{name:`nullish`,category:`Logical`,syntax:[`x ?? y`,`nullish(x, y)`],description:`Nullish coalescing operator. Returns the right-hand operand when the left-hand operand is null or undefined, and otherwise returns the left-hand operand.`,examples:[`null ?? 42`,`undefined ?? 42`,`0 ?? 42`,`false ?? 42`,`null ?? undefined ?? 42`],seealso:[`and`,`or`,`not`]},or:{name:`or`,category:`Logical`,syntax:[`x or y`,`or(x, y)`],description:`Logical or. Test if at least one value is defined with a nonzero/nonempty value.`,examples:[`true or false`,`false or false`,`0 or 4`],seealso:[`not`,`and`,`xor`]},xor:{name:`xor`,category:`Logical`,syntax:[`x xor y`,`xor(x, y)`],description:`Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.`,examples:[`true xor false`,`false xor false`,`true xor true`,`0 xor 4`],seealso:[`not`,`and`,`or`]},mapSlices:{name:`mapSlices`,category:`Matrix`,syntax:[`mapSlices(A, dim, callback)`],description:`Generate a matrix one dimension less than A by applying callback to each slice of A along dimension dim.`,examples:[`A = [[1, 2], [3, 4]]`,`mapSlices(A, 1, sum)`,`mapSlices(A, 2, prod)`],seealso:[`map`,`forEach`]},concat:{name:`concat`,category:`Matrix`,syntax:[`concat(A, B, C, ...)`,`concat(A, B, C, ..., dim)`],description:`Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.`,examples:[`A = [1, 2; 5, 6]`,`B = [3, 4; 7, 8]`,`concat(A, B)`,`concat(A, B, 1)`,`concat(A, B, 2)`],seealso:[`det`,`diag`,`identity`,`inv`,`ones`,`range`,`size`,`squeeze`,`subset`,`trace`,`transpose`,`zeros`]},count:{name:`count`,category:`Matrix`,syntax:[`count(x)`],description:`Count the number of elements of a matrix, array or string.`,examples:[`a = [1, 2; 3, 4; 5, 6]`,`count(a)`,`size(a)`,`count("hello world")`],seealso:[`size`]},cross:{name:`cross`,category:`Matrix`,syntax:[`cross(A, B)`],description:`Calculate the cross product for two vectors in three dimensional space.`,examples:[`cross([1, 1, 0],  [0, 1, 1])`,`cross([3, -3, 1], [4, 9, 2])`,`cross([2, 3, 4],  [5, 6, 7])`],seealso:[`multiply`,`dot`]},column:{name:`column`,category:`Matrix`,syntax:[`column(x, index)`],description:`Return a column from a matrix or array.`,examples:[`A = [[1, 2], [3, 4]]`,`column(A, 1)`,`column(A, 2)`],seealso:[`row`,`matrixFromColumns`]},ctranspose:{name:`ctranspose`,category:`Matrix`,syntax:[`x'`,`ctranspose(x)`],description:`Complex Conjugate and Transpose a matrix`,examples:[`a = [1, 2, 3; 4, 5, 6]`,`a'`,`ctranspose(a)`],seealso:[`concat`,`det`,`diag`,`identity`,`inv`,`ones`,`range`,`size`,`squeeze`,`subset`,`trace`,`zeros`]},det:{name:`det`,category:`Matrix`,syntax:[`det(x)`],description:`Calculate the determinant of a matrix`,examples:[`det([1, 2; 3, 4])`,`det([-2, 2, 3; -1, 1, 3; 2, 0, -1])`],seealso:[`concat`,`diag`,`identity`,`inv`,`ones`,`range`,`size`,`squeeze`,`subset`,`trace`,`transpose`,`zeros`]},diag:{name:`diag`,category:`Matrix`,syntax:[`diag(x)`,`diag(x, k)`],description:`Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.`,examples:[`diag(1:3)`,`diag(1:3, 1)`,`a = [1, 2, 3; 4, 5, 6; 7, 8, 9]`,`diag(a)`],seealso:[`concat`,`det`,`identity`,`inv`,`ones`,`range`,`size`,`squeeze`,`subset`,`trace`,`transpose`,`zeros`]},diff:{name:`diff`,category:`Matrix`,syntax:[`diff(arr)`,`diff(arr, dim)`],description:[`Create a new matrix or array with the difference of the passed matrix or array.`,`Dim parameter is optional and used to indicate the dimension of the array/matrix to apply the difference`,`If no dimension parameter is passed it is assumed as dimension 0`,`Dimension is zero-based in javascript and one-based in the parser`,`Arrays must be 'rectangular' meaning arrays like [1, 2]`,`If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays`],examples:[`A = [1, 2, 4, 7, 0]`,`diff(A)`,`diff(A, 1)`,`B = [[1, 2], [3, 4]]`,`diff(B)`,`diff(B, 1)`,`diff(B, 2)`,`diff(B, bignumber(2))`,`diff([[1, 2], matrix([3, 4])], 2)`],seealso:[`subtract`,`partitionSelect`]},dot:{name:`dot`,category:`Matrix`,syntax:[`dot(A, B)`,`A * B`],description:`Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn`,examples:[`dot([2, 4, 1], [2, 2, 3])`,`[2, 4, 1] * [2, 2, 3]`],seealso:[`multiply`,`

52cross`]},getMatrixDataType:{name:`getMatrixDataType`,category:`Matrix`,syntax:[`getMatrixDataType(x)`],description:`Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. If a matrix contains more than one data type, it will return "mixed".`,examples:[`getMatrixDataType([1, 2, 3])`,`getMatrixDataType([[5 cm], [2 inch]])`,`getMatrixDataType([1, "text"])`,`getMatrixDataType([1, bignumber(4)])`],seealso:[`matrix`,`sparse`,`typeOf`]},identity:{name:`identity`,category:`Matrix`,syntax:[`identity(n)`,`identity(m, n)`,`identity([m, n])`],description:`Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.`,examples:[`identity(3)`,`identity(3, 5)`,`a = [1, 2, 3; 4, 5, 6]`,`identity(size(a))`],seealso:[`concat`,`det`,`diag`,`inv`,`ones`,`range`,`size`,`squeeze`,`subset`,`trace`,`transpose`,`zeros`]},filter:{name:`filter`,category:`Matrix`,syntax:[`filter(x, test)`],description:`Filter items in a matrix.`,examples:[`isPositive(x) = x > 0`,`filter([6, -2, -1, 4, 3], isPositive)`,`filter([6, -2, 0, 1, 0], x != 0)`],seealso:[`sort`,`map`,`forEach`]},flatten:{name:`flatten`,category:`Matrix`,syntax:[`flatten(x)`],description:`Flatten a multi dimensional matrix into a single dimensional matrix.`,examples:[`a = [1, 2, 3; 4, 5, 6]`,`size(a)`,`b = flatten(a)`,`size(b)`],seealso:[`concat`,`resize`,`size`,`squeeze`]},forEach:{name:`forEach`,category:`Matrix`,syntax:[`forEach(x, callback)`],description:`Iterates over all elements of a matrix/array, and executes the given callback function.`,examples:[`numberOfPets = {}`,`addPet(n) = numberOfPets[n] = (numberOfPets[n] ? numberOfPets[n]:0 ) + 1;`,`forEach(["Dog","Cat","Cat"], addPet)`,`numberOfPets`],seealso:[`map`,`sort`,`filter`]},inv:{name:`inv`,category:`Matrix`,syntax:[`inv(x)`],description:`Calculate the inverse of a matrix`,examples:[`inv([1, 2; 3, 4])`,`inv(4)`,`1 / 4`],seealso:[`concat`,`det`,`diag`,`identity`,`ones`,`range`,`size`,`squeeze`,`subset`,`trace`,`transpose`,`zeros`]},pinv:{name:`pinv`,category:`Matrix`,syntax:[`pinv(x)`],description:`Calculate the MooreâPenrose inverse of a matrix`,examples:[`pinv([1, 2; 3, 4])`,`pinv([[1, 0], [0, 1], [0, 1]])`,`pinv(4)`],seealso:[`inv`]},eigs:{name:`eigs`,category:`Matrix`,syntax:[`eigs(x)`],description:`Calculate the eigenvalues and optionally eigenvectors of a square matrix`,examples:[`eigs([[5, 2.3], [2.3, 1]])`,`eigs([[1, 2, 3], [4, 5, 6], [7, 8, 9]], { precision: 1e-6, eigenvectors: false })`],seealso:[`inv`]},kron:{name:`kron`,category:`Matrix`,syntax:[`kron(x, y)`],description:`Calculates the Kronecker product of 2 matrices or vectors.`,examples:[`kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])`,`kron([1,1], [2,3,4])`],seealso:[`multiply`,`dot`,`cross`]},matrixFromFunction:{name:`matrixFromFunction`,category:`Matrix`,syntax:[`matrixFromFunction(size, fn)`,`matrixFromFunction(size, fn, format)`,`matrixFromFunction(size, fn, format, datatype)`,`matrixFromFunction(size, format, fn)`,`matrixFromFunction(size, format, datatype, fn

52)`],description:`Create a matrix by evaluating a generating function at each index.`,examples:[`f(I) = I[1] - I[2]`,`matrixFromFunction([3,3], f)`,`g(I) = I[1] - I[2] == 1 ? 4 : 0`,`matrixFromFunction([100, 100], "sparse", g)`,`matrixFromFunction([5], random)`],seealso:[`matrix`,`matrixFromRows`,`matrixFromColumns`,`zeros`]},matrixFromRows:{name:`matrixFromRows`,category:`Matrix`,syntax:[`matrixFromRows(...arr)`,`matrixFromRows(row1, row2)`,`matrixFromRows(row1, row2, row3)`],description:`Create a dense matrix from vectors as individual rows.`,examples:[`matrixFromRows([1, 2, 3], [[4],[5],[6]])`],seealso:[`matrix`,`matrixFromColumns`,`matrixFromFunction`,`zeros`]},matrixFromColumns:{name:`matrixFromColumns`,category:`Matrix`,syntax:[`matrixFromColumns(...arr)`,`matrixFromColumns(row1, row2)`,`matrixFromColumns(row1, row2, row3)`],description:`Create a dense matrix from vectors as individual columns.`,examples:[`matrixFromColumns([1, 2, 3], [[4],[5],[6]])`],seealso:[`matrix`,`matrixFromRows`,`matrixFromFunction`,`zeros`]},map:{name:`map`,category:`Matrix`,syntax:[`map(x, callback)`,`map(x, y, ..., callback)`],description:`Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array or the matrices/arrays.`,examples:[`map([1, 2, 3], square)`,`map([1, 2], [3, 4], f(a,b) = a + b)`],seealso:[`filter`,`forEach`]},ones:{name:`ones`,category:`Matrix`,syntax:[`ones(m)`,`ones(m, n)`,`ones(m, n, p, ...)`,`ones([m])`,`ones([m, n])`,`ones([m, n, p, ...])`],description:`Create a matrix containing ones.`,examples:[`ones(3)`,`ones(3, 5)`,`ones([2,3]) * 4.5`,`a = [1, 2, 3; 4, 5, 6]`,`ones(size(a))`],seealso:[`concat`,`det`,`diag`,`identity`,`inv`,`range`,`size`,`squeeze`,`subset`,`trace`,`transpose`,`zeros`]},partitionSelect:{name:`partitionSelect`,category:`Matrix`,syntax:[`partitionSelect(x, k)`,`partitionSelect(x, k, compare)`],description:`Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.`,examples:[`partitionSelect([5, 10, 1], 2)`,`partitionSelect(["C", "B", "A", "D"], 1, compareText)`,`arr = [5, 2, 1]`,`partitionSelect(arr, 0) # returns 1, arr is now: [1, 2, 5]`,`arr`,`partitionSelect(arr, 1, 'desc') # returns 2, arr is now: [5, 2, 1]`,`arr`],seealso:[`sort`]},range:{name:`range`,category:`Type`,syntax:[`start:end`,`start:step:end`,`range(start, end)`,`range(start, end, step)`,`range(string)`],description:`Create a range. Lower bound of the range is included, upper bound is excluded.`,examples:[`1:5`,`3:-1:-3`,`range(3, 7)`,`range(0, 12, 2)`,`range("4:10")`,`range(1m, 1m, 3m)`,`a = [1, 2, 3, 4; 5, 6, 7, 8]`,`a[1:2, 1:2]`],seealso:[`concat`,`det`,`diag`,`identity`,`inv`,`ones`,`size`,`squeeze`,`subset`,`trace`,`transpose`,`zeros`]},resize:{name:`resize`,category:`Matrix`,syntax:[`resize(x, size)`,`resize(x, size, defaultValue)`],description:`Resize a matrix.`,examples:[`resize([1,2,3,4,5], [3])`,`resize([1,2,3], [5])`,`resize([1,2,3], [5], -1)`,`resize(2, [2, 3])`,`resize("hello", [8], "!")`],seealso:[`size`,`subset`,`squeeze`,`reshape`]},reshape:{name:`reshape`,category:`Matrix`,syntax:[`reshape(x, sizes)`],description:`Reshape a multi dimensional array to fit the specified dimensions.`,examples:[`reshape([1, 2, 3, 4, 5, 6], [2, 3])`,`reshape([[1, 2], [3, 4]], [1, 4])`,`reshape([[1, 2], [3, 4]], [4])`,`reshape([1, 2, 3, 4], [-1, 2])`],seealso:[`size`,`squeeze`,`resize`]},rotate:{name:`rotate`,category:`Matrix`,syntax:[`rotate(w, theta)`,`rotate(w, theta, v)`],description:`Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.`,examples:[`rotate([1, 0], pi / 2)`,`rotate(matrix([1, 0]), unit("35deg"))`,`rotate([1, 0, 0], unit("90deg"), [0, 0, 1])`,`rotate(matrix([1, 0, 0]), unit("90deg"), matrix([0, 0, 1]))`],seealso:[`matrix`,`rotationMatrix`]},rotationMatrix:{name:`rotationMatrix`,category:`Matrix`,syntax:[`rotationMatrix(theta)`,`rotationMatrix(theta, v)`,`rotationMatrix(theta, v, format)`],description:`Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.`,examples:[`rotationMatrix(pi / 2)`,`rotationMatrix(unit("45deg"), [0, 0, 1])`,`rotationMatrix(1, matrix([0, 0, 1]), "sparse")`],seealso:[`cos`,`sin`]},row:{name:`row`,category:`Matrix`,syntax:[`row(x, index)`],description:`Return a row from a matrix or array.`,examples:[`A = [[1, 2], [3, 4]]`,`row(A, 1)`,`row(A, 2)`],seealso:[`column`,`matrixFromRows`]},size:{name:`size`,category:`Matrix`,syntax:[`size(x)`],description:`Calculate the size of a matrix.`,examples:[`size(2.3)`,`size("hello world")`,`a = [1, 2; 3, 4; 5, 6]`,`size(a)`,`size(1:6)`],seealso:[`concat`,`count`,`det`,`diag`,`identity`,`inv`,`ones`,`range`,`squeeze`,`subset`,`trace`,`transpose`,`zeros`]},sort:{name:`sort`,category:`Matrix`,syntax:[`sort(x)`,`sort(x, compare)`],description:`Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.`,examples:[`sort([5, 10, 1])`,`sort(["C", "B", "A", "D"], "natural")`,`sortByLength(a, b) = size(a)[1] - size(b)[1]`,`sort(["Langdon", "Tom", "Sara"], sortByLength)`,`sort(["10", "1", "2"], "natural")`],seealso:[`map`,`filter`,`forEach`]}

52,squeeze:{name:`squeeze`,category:`Matrix`,syntax:[`squeeze(x)`],description:`Remove inner and outer singleton dimensions from a matrix.`,examples:[`a = zeros(3,2,1)`,`size(squeeze(a))`,`b = zeros(1,1,3)`,`size(squeeze(b))`],seealso:[`concat`,`det`,`diag`,`identity`,`inv`,`ones`,`range`,`size`,`subset`,`trace`,`transpose`,`zeros`]},subset:{name:`subset`,category:`Matrix`,syntax:[`value(index)`,`value(index) = replacement`,`subset(value, [index])`,`subset(value, [index], replacement)`],description:"Get or set a subset of the entries of a matrix or characters of a string. Indexes are one-based. There should be one index specification for each dimension of the target. Each specification can be a single index, a list of indices, or a range in colon notation `l:u`. In a range, both the lower bound l and upper bound u are included; and if a bound is omitted it defaults to the most extreme valid value. The cartesian product of the indices specified in each dimension determines the target of the operation.",examples:[`d = [1, 2; 3, 4]`,`e = []`,`e[1, 1:2] = [5, 6]`,`e[2, :] = [7, 8]`,`f = d * e`,`f[2, 1]`,`f[:, 1]`,`f[[1,2], [1,3]] = [9, 10; 11, 12]`,`f`],seealso:[`concat`,`det`,`diag`,`identity`,`inv`,`ones`,`range`,`size`,`squeeze`,`trace`,`transpose`,`zeros`]},trace:{name:`trace`,category:`Matrix`,syntax:[`trace(A)`],description:`Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.`,examples:[`A = [1, 2, 3; -1, 2, 3; 2, 0, 3]`,`trace(A)`],seealso:[`concat`,`det`,`diag`,`identity`,`inv`,`ones`,`range`,`size`,`squeeze`,`subset`,`transpose`,`zeros`]},transpose:{name:`transpose`,category:`Matrix`,syntax:[`x'`,`transpose(x)`],description:`Transpose a matrix`,examples:[`a = [1, 2, 3; 4, 5, 6]`,`a'`,`transpose(a)`],seealso:[`concat`,`det`,`diag`,`identity`,`inv`,`ones`,`range`,`size`,`squeeze`,`subset`,`trace`,`zeros`]},zeros:{name:`zeros`,category:`Matrix`,syntax:[`zeros(m)`,`zeros(m, n)`,`zeros(m, n, p, ...)`,`zeros([m])`,`zeros([m, n])`,`zeros([m, n, p, ...])`],description:`Create a matrix containing zeros.`,examples:[`zeros(3)`,`zeros(3, 5)`,`a = [1, 2, 3; 4, 5, 6]`,`zeros(size(a))`],seealso:[`concat`,`det`,`diag`,`identity`,`inv`,`ones`,`range`,`size`,`squeeze`,`subset`,`trace`,`transpose`]},fft:{name:`fft`,category:`Matrix`,syntax:[`fft(x)`],description:`Calculate N-dimensional Fourier transform`,examples:[`fft([[1, 0], [1, 0]])`],seealso:[`ifft`]},ifft:{name:`ifft`,category:`Matrix`,syntax:[`ifft(x)`],description:`Calculate N-dimensional inverse Fourier transform`,examples:[`ifft([[2, 2], [0, 0]])`],seealso:[`fft`]},sylvester:{name:`sylvester`,category:`Algebra`,syntax:[`sylvester(A,B,C)`],description:`Solves the real-valued Sylvester equation AX+XB=C for X`,examples:[`sylvester([[-1, -2], [1, 1]], [[-2, 1], [-1, 2]], [[-3, 2], [3, 0]])`,`A = [[-1, -2], [1, 1]]; B = [[2, -1], [1, -2]]; C = [[-3, 2], [3, 0]]`,`sylvester(A, B, C)`],seealso:[`schur`,`lyap`]},schur:{name:`schur`,category:`Algebra`,syntax:[`schur(A)`],description:`Performs a real Schur decomposition of the real matrix A = UTU'`,examples:[`schur([[1, 0], [-4, 3]])`,`A = [[1, 0], [-4, 3]]`,`schur(A)`],seealso:[`lyap`,`sylvester`]},lyap:{name:`lyap`,category:`Algebra`,syntax:[`lyap(A,Q)`],description:`Solves the Continuous-time Lyapunov equation AP+PA'+Q=0 for P`,examples:[`lyap([[-2, 0], [1, -4]], [[3, 1], [1, 3]])`,`A = [[-2, 0], [1, -4]]`,`Q = [[3, 1], [1, 3]]`,`lyap(A,Q)`],seealso:[`schur`,`sylvester`]},solveODE:{name:`solveODE`,category:`Numeric`,syntax:[`solveODE(func, tspan, y0)`,`solveODE(func, tspan, y0, options)`],description:`Numerical Integration of Ordinary Differential Equations.`,examples:[`f(t,y) = y`,`tspan = [0, 4]`,`solveODE(f, tspan, 1)`,`solveODE(f, tspan, [1, 2])`,`solveODE(f, tspan, 1, { method:"RK23", maxStep:0.1 })`],seealso:[`derivative`,`simplifyCore`]},bernoulli:{name:`bernoulli`,category:`Probability`,syntax:[`bernoulli(n)`],description:`The nth Bernoulli number`,examples:[`bernoulli(4)`,`bernoulli(fraction(12))`],seealso:[`combinations`,`gamma`,`stirlingS2`]},combinations:{name:`combinations`,category:`Probability`,syntax:[`combinations(n, k)`],description:`Compute the number of combinations of n items taken k at a time`,examples:[`combinations(7, 5)`],seealso:[`combinationsWithRep`,`permutations`,`factorial`]},combinationsWithRep:{name:`combinationsWithRep`,category:`Probability`,syntax:[`combinationsWithRep(n, k)`],description:`Compute the number of combinations of n items taken k at a time with replacements.`,examples:[`combinationsWithRep(7, 5)`],seealso:[`combinations`,`permutations`,`factorial`]},factorial:{name:`factorial`,category:`Probability`,syntax:[`n!`,`factorial(n)`],description:`Compute the factorial of a value`,examples:[`5!`,`5 * 4 * 3 * 2 * 1`,`3!`],seealso:[`combinations`,`combinationsWithRep`,`permutations`,`gamma`]},gamma:{name:`gamma`,category:`Probability`,syntax:[`gamma(n)`],description:`Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.`,examples:[`gamma(4)`,`3!`,`gamma(1/2)`,`sqrt(pi)`],seealso:[`factorial`]},kldivergence:{name:`kldivergence`,category:`Probability`,syntax:[`kldivergence(x, y)`],description:`Calculate the Kullback-Leibler

52(KL) divergence  between two distributions.`,examples:[`kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])`],seealso:[]},lgamma:{name:`lgamma`,category:`Probability`,syntax:[`lgamma(n)`],description:`Logarithm of the gamma function for real, positive numbers and complex numbers, using Lanczos approximation for numbers and Stirling series for complex numbers.`,examples:[`lgamma(4)`,`lgamma(1/2)`,`lgamma(i)`,`lgamma(complex(1.1, 2))`],seealso:[`gamma`]},multinomial:{name:`multinomial`,category:`Probability`,syntax:[`multinomial(A)`],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:[`multinomial([1, 2, 1])`],seealso:[`combinations`,`factorial`]},permutations:{name:`permutations`,category:`Probability`,syntax:[`permutations(n)`,`permutations(n, k)`],description:`Compute the number of permutations of n items taken k at a time`,examples:[`permutations(5)`,`permutations(5, 3)`],seealso:[`combinations`,`combinationsWithRep`,`factorial`]},pickRandom:{name:`pickRandom`,category:`Probability`,syntax:[`pickRandom(array)`,`pickRandom(array, number)`,`pickRandom(array, weights)`,`pickRandom(array, number, weights)`,`pickRandom(array, weights, number)`],description:`Pick a random entry from a given array.`,examples:[`pickRandom(0:10)`,`pickRandom([1, 3, 1, 6])`,`pickRandom([1, 3, 1, 6], 2)`,`pickRandom([1, 3, 1, 6], [2, 3, 2, 1])`,`pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])`,`pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)`],seealso:[`random`,`randomInt`]},random:{name:`random`,category:`Probability`,syntax:[`random()`,`random(max)`,`random(min, max)`,`random(size)`,`random(size, max)`,`random(size, min, max)`],description:`Return a random number.`,examples:[`random()`,`random(10, 20)`,`random([2, 3])`],seealso:[`pickRandom`,`randomInt`]},randomInt:{name:`randomInt`,category:`Probability`,syntax:[`randomInt(max)`,`randomInt(min, max)`,`randomInt(size)`,`randomInt(size, max)`,`randomInt(size, min, max)`],description:`Return a random integer number`,examples:[`randomInt(10, 20)`,`randomInt([2, 3], 10)`],seealso:[`pickRandom`,`random`]},compare:{name:`compare`,category:`Relational`,syntax:[`compare(x, y)`],description:`Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.`,examples:[`compare(2, 3)`,`compare(3, 2)`,`compare(2, 2)`,`compare(5cm, 40mm)`,`compare(2, [1, 2, 3])`],seealso:[`equal`,`unequal`,`smaller`,`smallerEq`,`largerEq`,`compareNatural`,`compareText`]},compareNatural:{name:`compareNatural`,category:`Relational`,syntax:[`compareNatural(x, y)`],description:`Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.`,examples:[`compareNatural(2, 3)`,`compareNatural(3, 2)`,`compareNatural(2, 2)`,`compareNatural(5cm, 40mm)`,`compareNatural("2", "10")`,`compareNatural(2 + 3i, 2 + 4i)`,`compareNatural([1, 2, 4], [1, 2, 3])`,`compareNatural([1, 5], [1, 2, 3])`,`compareNatural([1, 2], [1, 2])`,`compareNatural({a: 2}, {a: 4})`],seealso:[`equal`,`unequal`,`smaller`,`smallerEq`,`largerEq`,`compare`,`compareText`]},compareText:{name:`compareText`,category:`Relational`,syntax:[`compareText(x, y)`],description:`Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.`,examples:[`compareText("B", "A")`,`compareText("A", "B")`,`compareText("A", "A")`,`compareText("2", "10")`,`compare("2", "10")`,`compare(2, 10)`,`compareNatural("2", "10")`,`compareText("B", ["A", "B", "C"])`],seealso:[`compare`,`compareNatural`]},deepEqual:{name:`deepEqual`,category:`Relational`,syntax:[`deepEqual(x, y)`],description:`Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.`,examples:[`deepEqual([1,3,4], [1,3,4])`,`deepEqual([1,3,4], [1,3])`],seealso:[`equal`,`unequal`,`smaller`,`larger`,`smallerEq`,`largerEq`,`compare`]},equal:{name:`equal`,category:`Relational`,syntax:[`x == y`,`equal(x, y)`],description:`Check equality of two values. Returns true if the values are equal, and false if not.`,examples:[`2+2 == 3`,`2+2 == 4`,`a = 3.2`,`b = 6-2.8`,`a == b`,`50cm == 0.5m`],seealso:[`unequal`,`smaller`,`larger`,`smallerEq`,`largerEq`,`compare`,`deepEqual`,`equalText`]},equalText:{name:`equalText`,category:`Relational`,syntax:[`equalText(x, y)`],description:`Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.`,examples:[`equalText("Hello", "Hello")`,`equalText("a", "A")`,`equal("2e3", "2000")`,`equalText("2e3", "2000")`,`equalText("B", ["A", "B", "C"])`],seealso:[`compare`,`compareNatural`,`compareText`,`equal`]},larger:{name:`larger`,category:`Relational`,syntax:[`x > y`,`larger(x, y)`],description:`Check if value x is larger than y. Returns true if x is larger than y, and false if not. Comparing a value with NaN returns false.`,examples:[`2 > 3`,`5 > 2*2`,`a = 3.3`,`b = 6-2.8`,`(a > b)`,`(b < a)`,`5 cm > 2 inch`],seealso:[`equal`,`unequal`,`smaller`,`smallerEq`,`largerEq`,`compare`]}

52,largerEq:{name:`largerEq`,category:`Relational`,syntax:[`x >= y`,`largerEq(x, y)`],description:`Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.`,examples:[`2 >= 1+1`,`2 > 1+1`,`a = 3.2`,`b = 6-2.8`,`(a >= b)`],seealso:[`equal`,`unequal`,`smallerEq`,`smaller`,`compare`]},smaller:{name:`smaller`,category:`Relational`,syntax:[`x < y`,`smaller(x, y)`],description:`Check if value x is smaller than value y. Returns true if x is smaller than y, and false if not. Comparing a value with NaN returns false.`,examples:[`2 < 3`,`5 < 2*2`,`a = 3.3`,`b = 6-2.8`,`(a < b)`,`5 cm < 2 inch`],seealso:[`equal`,`unequal`,`larger`,`smallerEq`,`largerEq`,`compare`]},smallerEq:{name:`smallerEq`,category:`Relational`,syntax:[`x <= y`,`smallerEq(x, y)`],description:`Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.`,examples:[`2 <= 1+1`,`2 < 1+1`,`a = 3.2`,`b = 6-2.8`,`(a <= b)`],seealso:[`equal`,`unequal`,`larger`,`smaller`,`largerEq`,`compare`]},unequal:{name:`unequal`,category:`Relational`,syntax:[`x != y`,`unequal(x, y)`],description:`Check unequality of two values. Returns true if the values are unequal, and false if they are equal.`,examples:[`2+2 != 3`,`2+2 != 4`,`a = 3.2`,`b = 6-2.8`,`a != b`,`50cm != 0.5m`,`5 cm != 2 inch`],seealso:[`equal`,`smaller`,`larger`,`smallerEq`,`largerEq`,`compare`,`deepEqual`]},setCartesian:{name:`setCartesian`,category:`Set`,syntax:[`setCartesian(set1, set2)`],description:`Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays and the values will be sorted in ascending order before the operation.`,examples:[`setCartesian([1, 2], [3, 4])`],seealso:[`setUnion`,`setIntersect`,`setDifference`,`setPowerset`]},setDifference:{name:`setDifference`,category:`Set`,syntax:[`setDifference(set1, set2)`],description:`Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.`,examples:[`setDifference([1, 2, 3, 4], [3, 4, 5, 6])`,`setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])`],seealso:[`setUnion`,`setIntersect`,`setSymDifference`]},setDistinct:{name:`setDistinct`,category:`Set`,syntax:[`setDistinct(set)`],description:`Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.`,examples:[`setDistinct([1, 1, 1, 2, 2, 3])`],seealso:[`setMultiplicity`]},setIntersect:{name:`setIntersect`,category:`Set`,syntax:[`setIntersect(set1, set2)`],description:`Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.`,examples:[`setIntersect([1, 2, 3, 4], [3, 4, 5, 6])`,`setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])`],seealso:[`setUnion`,`setDifference`]},setIsSubset:{name:`setIsSubset`,category:`Set`,syntax:[`setIsSubset(set1, set2)`],description:`Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.`,examples:[`setIsSubset([1, 2], [3, 4, 5, 6])`,`setIsSubset([3, 4], [3, 4, 5, 6])`],seealso:[`setUnion`,`setIntersect`,`setDifference`]},setMultiplicity:{name:`setMultiplicity`,category:`Set`,syntax:[`setMultiplicity(element, set)`],description:`Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.`,examples:[`setMultiplicity(1, [1, 2, 2, 4])`,`setMultiplicity(2, [1, 2, 2, 4])`],seealso:[`setDistinct`,`setSize`]},setPowerset:{name:`setPowerset`,category:`Set`,syntax:[`setPowerset(set)`],description:`Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.`,examples:[`setPowerset([1, 2, 3])`],seealso:[`setCartesian`]},setSize:{name:`setSize`,category:`Set`,syntax:[`setSize(set)`,`setSize(set, unique)`],description:`Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.`,examples:[`setSize([1, 2, 2, 4])`,`setSize([1, 2, 2, 4], true)`],seealso:[`setUnion`,`setIntersect`,`setDifference`]},setSymDifference:{name:`setSymDifference`,category:`Set`,syntax:[`setSymDifference(set1, set2)`],description:`Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.`,examples:[`setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])`,`setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])`],seealso:[`setUnion`,`setIntersect`,`setDifference`]},setUnion:{name:`setUnion`,category:`Set`,syntax:[`setUnion(set1, set2)`],description:`Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.`,examples:[`setUnion([1, 2, 3, 4], [3, 4, 5, 6])`,`setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])`],seealso:[`setIntersect`,`setDifference`]},zpk2tf:{name:`zpk2tf`,category:`Signal`,syntax:[`zpk2tf(z, p, k)`],description:`Compute the transfer function of a zero-pole-gain model.`,examples:[`zpk2tf([1, 2], [-1, -2], 1)`,`zpk2tf([1, 2], [-1, -2])`,`zpk2tf([1 - 3i, 2 + 2i], [-1, -2])`],seealso:[]},freqz:{name:`freqz`,category:`Signal`,syntax:[`freqz(b, a)`,`freqz(b, a, w)`],description:`Calculates the frequency response of a filter given its numerator and denominator coefficients.`,examples:[`freqz([1, 2], [1, 2, 3])`,`freqz([1, 2], [1, 2, 3], [0, 1])`,`freqz([1, 2], [1, 2, 3], 512)`],seealso:[]},erf:{name:`erf`,category:`Special`,syntax:[`erf(x)`],description:`Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x`,examples:[`erf(0.2)`,`erf(-0.5)`,`erf(4)`],seealso:[]},zeta:{name:`zeta`,category:`Special`,syntax:[`zeta(s)`],description:`Compute the Riemann Zeta Function using an infinite series and Riemann's Functional Equation for the entire complex plane`,examples:[`zeta(0.2)`,`zeta(-0.5)`,`zeta(4)`],seealso:[]},cumsum:{name:`cumsum`,category:`Statistics`,syntax:[`cumsum(a, b, c, ...)`,`cumsum(A)`],description:`Compute the cumulative sum of all values.`,examples:[`cumsum(2, 3, 4, 1)`,`cumsum([2, 3, 4, 1])`,`cumsum([1, 2; 3, 4])`,`cumsum([1, 2;

52 3, 4], 1)`,`cumsum([1, 2; 3, 4], 2)`],seealso:[`max`,`mean`,`median`,`min`,`prod`,`std`,`sum`,`variance`]},mad:{name:`mad`,category:`Statistics`,syntax:[`mad(a, b, c, ...)`,`mad(A)`],description:`Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.`,examples:[`mad(10, 20, 30)`,`mad([1, 2, 3])`],seealso:[`mean`,`median`,`std`,`abs`]},max:{name:`max`,category:`Statistics`,syntax:[`max(a, b, c, ...)`,`max(A)`,`max(A, dimension)`],description:`Compute the maximum value of a list of values. If any NaN values are found, the function yields the last NaN in the input.`,examples:[`max(2, 3, 4, 1)`,`max([2, 3, 4, 1])`,`max([2, 5; 4, 3])`,`max([2, 5; 4, 3], 1)`,`max([2, 5; 4, 3], 2)`,`max(2.7, 7.1, -4.5, 2.0, 4.1)`,`min(2.7, 7.1, -4.5, 2.0, 4.1)`],seealso:[`mean`,`median`,`min`,`prod`,`std`,`sum`,`variance`]},mean:{name:`mean`,category:`Statistics`,syntax:[`mean(a, b, c, ...)`,`mean(A)`,`mean(A, dimension)`],description:`Compute the arithmetic mean of a list of values.`,examples:[`mean(2, 3, 4, 1)`,`mean([2, 3, 4, 1])`,`mean([2, 5; 4, 3])`,`mean([2, 5; 4, 3], 1)`,`mean([2, 5; 4, 3], 2)`,`mean([1.0, 2.7, 3.2, 4.0])`],seealso:[`max`,`median`,`min`,`prod`,`std`,`sum`,`variance`]},median:{name:`median`,category:`Statistics`,syntax:[`median(a, b, c, ...)`,`median(A)`],description:`Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.`,examples:[`median(5, 2, 7)`,`median([3, -1, 5, 7])`],seealso:[`max`,`mean`,`min`,`prod`,`std`,`sum`,`variance`,`quantileSeq`]},min:{name:`min`,category:`Statistics`,syntax:[`min(a, b, c, ...)`,`min(A)`,`min(A, dimension)`],description:`Compute the minimum value of a list of values. If any NaN values are found, the function yields the last NaN in the input.`,examples:[`min(2, 3, 4, 1)`,`min([2, 3, 4, 1])`,`min([2, 5; 4, 3])`,`min([2, 5; 4, 3], 1)`,`min([2, 5; 4, 3], 2)`,`min(2.7, 7.1, -4.5, 2.0, 4.1)`,`max(2.7, 7.1, -4.5, 2.0, 4.1)`],seealso:[`max`,`mean`,`median`,`prod`,`std`,`sum`,`variance`]},mode:{name:`mode`,category:`Statistics`,syntax:[`mode(a, b, c, ...)`,`mode(A)`,`mode(A, a, b, B, c, ...)`],description:`Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.`,examples:[`mode(2, 1, 4, 3, 1)`,`mode([1, 2.7, 3.2, 4, 2.7])`,`mode(1, 4, 6, 1, 6)`],seealso:[`max`,`mean`,`min`,`median`,`prod`,`std`,`sum`,`variance`]},prod:{name:`prod`,category:`Statistics`,syntax:[`prod(a, b, c, ...)`,`prod(A)`],description:`Compute the product of all values.`,examples:[`prod(2, 3, 4)`,`prod([2, 3, 4])`,`prod([2, 5; 4, 3])`],seealso:[`max`,`mean`,`min`,`median`,`min`,`std`,`sum`,`variance`]},quantileSeq:{name:`quantileSeq`,category:`Statistics`,syntax:[`quantileSeq(A, prob[, sorted])`,`quantileSeq(A, [prob1, prob2, ...][, sorted])`,`quantileSeq(A, N[, sorted])`],description:`Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probability are: Number, BigNumber. 
53
54In case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.`,examples:[`quantileSeq([3, -1, 5, 7], 0.5)`,`quantileSeq([3, -1, 5, 7], [1/3, 2/3])`,`quantileSeq([3, -1, 5, 7], 2)`,`quantileSeq([-1, 3, 5, 7], 0.5, true)`],seealso:[`mean`,`median`,`min`,`max`,`prod`,`std`,`sum`,`variance`]},std:{name:`std`,category:`Statistics`,syntax:[`std(a, b, c, ...)`,`std(A)`,`std(A, dimension)`,`std(A, normalization)`,`std(A, dimension, normalization)`],description:`Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".`,examples:[`std(2, 4, 6)`,`std([2, 4, 6, 8])`,`std([2, 4, 6, 8], "uncorrected")`,`std([2, 4, 6, 8], "biased")`,`std([1, 2, 3; 4, 5, 6])`],seealso:[`max`,`mean`,`min`,`median`,`prod`,`sum`,`variance`]},sum:{name:`sum`,category:`Statistics`,syntax:[`sum(a, b, c, ...)`,`sum(A)`,`sum(A, dimension)`],description:`Compute the sum of all values.`,examples:[`sum(2, 3, 4, 1)`,`sum([2, 3, 4, 1])`,`sum([2, 5; 4, 3])`],seealso:[`max`,`mean`,`median`,`min`,`prod`,`std`,`variance`]},variance:{name:`variance`,category:`Statistics`,syntax:[`variance(a, b, c, ...)`,`variance(A)`,`variance(A, dimension)`,`variance(A, normalization)`,`variance(A, dimension, normalization)`],description:`Compute the variance of all values. Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".`,examples:[`variance(2, 4, 6)`,`variance([2, 4, 6, 8])`,`variance([2, 4, 6, 8], "uncorrected")`,`variance([2, 4, 6, 8], "biased")`,`variance([1, 2, 3; 4, 5, 6])`],seealso:[`max`,`mean`,`min`,`median`,`min`,`prod`,`std`,`sum`]}

54,corr:{name:`corr`,category:`Statistics`,syntax:[`corr(A,B)`],description:`Compute the correlation coefficient of a two list with values, For matrices, the matrix correlation coefficient is calculated.`,examples:[`corr([2, 4, 6, 8],[1, 2, 3, 6])`,`corr(matrix([[1, 2.2, 3, 4.8, 5], [1, 2, 3, 4, 5]]), matrix([[4, 5.3, 6.6, 7, 8], [1, 2, 3, 4, 5]]))`],seealso:[`max`,`mean`,`min`,`median`,`min`,`prod`,`std`,`sum`]},acos:{name:`acos`,category:`Trigonometry`,syntax:[`acos(x)`],description:`Compute the inverse cosine of a value in radians.`,examples:[`acos(0.5)`,`acos(cos(2.3))`],seealso:[`cos`,`atan`,`asin`]},acosh:{name:`acosh`,category:`Trigonometry`,syntax:[`acosh(x)`],description:"Calculate the hyperbolic arccos of a value, defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.",examples:[`acosh(1.5)`],seealso:[`cosh`,`asinh`,`atanh`]},acot:{name:`acot`,category:`Trigonometry`,syntax:[`acot(x)`],description:`Calculate the inverse cotangent of a value.`,examples:[`acot(0.5)`,`acot(cot(0.5))`,`acot(2)`],seealso:[`cot`,`atan`]},acoth:{name:`acoth`,category:`Trigonometry`,syntax:[`acoth(x)`],description:"Calculate the inverse hyperbolic tangent of a value, defined as `acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.",examples:[`acoth(2)`,`acoth(0.5)`],seealso:[`acsch`,`asech`]},acsc:{name:`acsc`,category:`Trigonometry`,syntax:[`acsc(x)`],description:`Calculate the inverse cotangent of a value.`,examples:[`acsc(2)`,`acsc(csc(0.5))`,`acsc(0.5)`],seealso:[`csc`,`asin`,`asec`]},acsch:{name:`acsch`,category:`Trigonometry`,syntax:[`acsch(x)`],description:"Calculate the inverse hyperbolic cosecant of a value, defined as `acsch(x) = ln(1/x + sqrt(1/x^2 + 1))`.",examples:[`acsch(0.5)`],seealso:[`asech`,`acoth`]},asec:{name:`asec`,category:`Trigonometry`,syntax:[`asec(x)`],description:`Calculate the inverse secant of a value.`,examples:[`asec(0.5)`,`asec(sec(0.5))`,`asec(2)`],seealso:[`acos`,`acot`,`acsc`]},asech:{name:`asech`,category:`Trigonometry`,syntax:[`asech(x)`],description:`Calculate the inverse secant of a value.`,examples:[`asech(0.5)`],seealso:[`acsch`,`acoth`]},asin:{name:`asin`,category:`Trigonometry`,syntax:[`asin(x)`],description:`Compute the inverse sine of a value in radians.`,examples:[`asin(0.5)`,`asin(sin(0.5))`],seealso:[`sin`,`acos`,`atan`]},asinh:{name:`asinh`,category:`Trigonometry`,syntax:[`asinh(x)`],description:"Calculate the hyperbolic arcsine of a value, defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.",examples:[`asinh(0.5)`],seealso:[`acosh`,`atanh`]},atan:{name:`atan`,category:`Trigonometry`,syntax:[`atan(x)`],description:`Compute the inverse tangent of a value in radians.`,examples:[`atan(0.5)`,`atan(tan(0.5))`],seealso:[`tan`,`acos`,`asin`]},atanh:{name:`atanh`,category:`Trigonometry`,syntax:[`atanh(x)`],description:"Calculate the hyperbolic arctangent of a value, defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.",examples:[`atanh(0.5)`],seealso:[`acosh`,`asinh`]},atan2:{name:`atan2`,category:`Trigonometry`,syntax:[`atan2(y, x)`],description:`Computes the principal value of the arc tangent of y/x in radians.`,examples:[`atan2(2, 2) / pi`,`angle = 60 deg in rad`,`x = cos(angle)`,`y = sin(angle)`,`atan2(y, x)`],seealso:[`sin`,`cos`,`tan`]},cos:{name:`cos`,category:`Trigonometry`,syntax:[`cos(x)`],description:`Compute the cosine of x in radians.`,examples:[`cos(2)`,`cos(pi / 4) ^ 2`,`cos(180 deg)`,`cos(60 deg)`,`sin(0.2)^2 + cos(0.2)^2`],seealso:[`acos`,`sin`,`tan`]},cosh:{name:`cosh`,category:`Trigonometry`,syntax:[`cosh(x)`],description:`Compute the hyperbolic cosine of x in radians.`,examples:[`cosh(0.5)`],seealso:[`sinh`,`tanh`,`coth`]},cot:{name:`cot`,category:`Trigonometry`,syntax:[`cot(x)`],description:`Compute the cotangent of x in radians. Defined as 1/tan(x)`,examples:[`cot(2)`,`1 / tan(2)`],seealso:[`sec`,`csc`,`tan`]},coth:{name:`coth`,category:`Trigonometry`,syntax:[`coth(x)`],description:`Compute the hyperbolic cotangent of x in radians.`,examples:[`coth(2)`,`1 / tanh(2)`],seealso:[`sech`,`csch`,`tanh`]},csc:{name:`csc`,category:`Trigonometry`,syntax:[`csc(x)`],description:`Compute the cosecant of x in radians. Defined as 1/sin(x)`,examples:[`csc(2)`,`1 / sin(2)`],seealso:[`sec`,`cot`,`sin`]},csch:{name:`csch`,category:`Trigonometry`,syntax:[`csch(x)`],description:`Compute the hyperbolic cosecant of x in radians. Defined as 1/sinh(x)`,examples:[`csch(2)`,`1 / sinh(2)`],seealso:[`sech`,`coth`,`sinh`]}

54,sec:{name:`sec`,category:`Trigonometry`,syntax:[`sec(x)`],description:`Compute the secant of x in radians. Defined as 1/cos(x)`,examples:[`sec(2)`,`1 / cos(2)`],seealso:[`cot`,`csc`,`cos`]},sech:{name:`sech`,category:`Trigonometry`,syntax:[`sech(x)`],description:`Compute the hyperbolic secant of x in radians. Defined as 1/cosh(x)`,examples:[`sech(2)`,`1 / cosh(2)`],seealso:[`coth`,`csch`,`cosh`]},sin:{name:`sin`,category:`Trigonometry`,syntax:[`sin(x)`],description:`Compute the sine of x in radians.`,examples:[`sin(2)`,`sin(pi / 4) ^ 2`,`sin(90 deg)`,`sin(30 deg)`,`sin(0.2)^2 + cos(0.2)^2`],seealso:[`asin`,`cos`,`tan`]},sinh:{name:`sinh`,category:`Trigonometry`,syntax:[`sinh(x)`],description:`Compute the hyperbolic sine of x in radians.`,examples:[`sinh(0.5)`],seealso:[`cosh`,`tanh`]},tan:{name:`tan`,category:`Trigonometry`,syntax:[`tan(x)`],description:`Compute the tangent of x in radians.`,examples:[`tan(0.5)`,`sin(0.5) / cos(0.5)`,`tan(pi / 4)`,`tan(45 deg)`],seealso:[`atan`,`sin`,`cos`]},tanh:{name:`tanh`,category:`Trigonometry`,syntax:[`tanh(x)`],description:`Compute the hyperbolic tangent of x in radians.`,examples:[`tanh(0.5)`,`sinh(0.5) / cosh(0.5)`],seealso:[`sinh`,`cosh`]},to:{name:`to`,category:`Units`,syntax:[`x to unit`,`to(x, unit)`],description:`Change the unit of a value.`,examples:[`5 inch to cm`,`3.2kg to g`,`16 bytes in bits`],seealso:[]},toBest:{name:`toBest`,category:`Units`,syntax:[`toBest(x)`,`toBest(x, unitList)`,`toBest(x, unitList, options)`],description:`Converts to the most appropriate display unit.`,examples:[`toBest(unit(5000, "m"))`,`toBest(unit(3500000, "W"))`,`toBest(unit(0.000000123, "A"))`,`toBest(unit(10, "m"), "cm")`,`toBest(unit(10, "m"), "mm,km", {offset: 1.5})`],seealso:[]},clone:{name:`clone`,category:`Utils`,syntax:[`clone(x)`],description:`Clone a variable. Creates a copy of primitive variables, and a deep copy of matrices`,examples:[`clone(3.5)`,`clone(2 - 4i)`,`clone(45 deg)`,`clone([1, 2; 3, 4])`,`clone("hello world")`],seealso:[]},format:{name:`format`,category:`Utils`,syntax:[`format(value)`,`format(value, precision)`],description:`Format a value of any type as string.`,examples:[`format(2.3)`,`format(3 - 4i)`,`format([])`,`format(pi, 3)`],seealso:[`print`]},bin:{name:`bin`,category:`Utils`,syntax:[`bin(value)`],description:`Format a number as binary`,examples:[`bin(2)`],seealso:[`oct`,`hex`]},oct:{name:`oct`,category:`Utils`,syntax:[`oct(value)`],description:`Format a number as octal`,examples:[`oct(56)`],seealso:[`bin`,`hex`]},hex:{name:`hex`,category:`Utils`,syntax:[`hex(value)`],description:`Format a number as hexadecimal`,examples:[`hex(240)`],seealso:[`bin`,`oct`]},isNaN:{name:`isNaN`,category:`Utils`,syntax:[`isNaN(x)`],description:`Test whether a value is NaN (not a number)`,examples:[`isNaN(2)`,`isNaN(0 / 0)`,`isNaN(NaN)`,`isNaN(Infinity)`],seealso:[`isNegative`,`isNumeric`,`isPositive`,`isZero`,`isFinite`,`isBounded`]},isBounded:{name:`isBounded`,category:`Utils`,syntax:[`isBounded(x)`],description:`Test whether a value or its entries are bounded.`,examples:[`isBounded(Infinity)`,`isBounded(bigint(3))`,`isBounded([3, -Infinity, -3])`],seealso:[`isFinite`,`isNumeric`,`isNaN`,`isNegative`,`isPositive`]},isFinite:{name:`isFinite`,category:`Utils`,syntax:[`isFinite(x)`],description:`Test whether a value is finite, elementwise on collections.`,examples:[`isFinite(Infinity)`,`isFinite(bigint(3))`,`isFinite([3, -Infinity, -3])`],seealso:[`isBounded`,`isNumeric`,`isNaN`,`isNegative`,`isPositive`]},isInteger:{name:`isInteger`,category:`Utils`,syntax:[`isInteger(x)`],description:`Test whether a value is an integer number.`,examples:[`isInteger(2)`,`isInteger(3.5)`,`isInteger([3, 0.5, -2])`],seealso:[`isNegative`,`isNumeric`,`isPositive`,`isZero`]},isNegative:{name:`isNegative`,category:`Utils`,syntax:[`isNegative(x)`],description:`Test whether a value is negative: smaller than zero.`,examples:[`isNegative(2)`,`isNegative(0)`,`isNegative(-4)`,`isNegative([3, 0.5, -2])`],seealso:[`isInteger`,`isNumeric`,`isPositive`,`isZero`]},isNumeric:{name:`isNumeric`,category:`Utils`,syntax:[`isNumeric(x)`],description:`Test whether a value is a numeric value. Returns true when the input is a number, BigNumber, Fraction, or boolean.`,examples:[`isNumeric(2)`,`isNumeric("2")`,`hasNumericValue("2")`,`isNumeric(0)`,`isNumeric(bignumber(500))`,`isNumeric(fraction(0.125))`,`isNumeric(2 + 3i)`,`isNumeric([2.3, "foo", false])`],seealso:[`isInteger`,`isZero`,`isNegative`,`isPositive`,`isNaN`,`hasNumericValue`,`isFinite`,`isBounded`]},hasNumericValue:{name:`hasNumericValue`,category:`Utils`,syntax:[`hasNumericValue(x)`],description:`Test whether a value is an numeric value. In case of a string, true is returned if the string contains a numeric value.`,examples:[`hasNumericValue(2)`,`hasNumericValue("2")`,`isNumeric("2")`,`hasNumericValue(0)`,`hasNumericValue(bignumber(500))`,`hasNumericValue(fraction(0.125))`,`hasNumericValue(2 + 3i)`,`hasNumericValue([2.3, "foo", false])`],seealso:[`isInteger`,`isZero`,`isNegative`,`isPositive`,`isNaN`,`isNumeric`]},isPositive:{name:`isPositive`,category:`Utils`,syntax:[`isPositive(x)`],description:`Test whether a value is positive: larger than zero.`,examples:[`isPositive(2)`,`isPositive(0)`,`isPositive(-4)`,`isPositive([3, 0.5, -2])`],seealso:[`isInteger`,`isNumeric`,`isNegative`,`isZero`]}

54,isPrime:{name:`isPrime`,category:`Utils`,syntax:[`isPrime(x)`],description:`Test whether a value is prime: has no divisors other than itself and one.`,examples:[`isPrime(3)`,`isPrime(-2)`,`isPrime([2, 17, 100])`],seealso:[`isInteger`,`isNumeric`,`isNegative`,`isZero`]},isZero:{name:`isZero`,category:`Utils`,syntax:[`isZero(x)`],description:`Test whether a value is zero.`,examples:[`isZero(2)`,`isZero(0)`,`isZero(-4)`,`isZero([3, 0, -2, 0])`],seealso:[`isInteger`,`isNumeric`,`isNegative`,`isPositive`]},print:{name:`print`,category:`Utils`,syntax:[`print(template, values)`,`print(template, values, precision)`],description:`Interpolate values into a string template.`,examples:[`print("Lucy is $age years old", {age: 5})`,`print("The value of pi is $pi", {pi: pi}, 3)`,`print("Hello, $user.name!", {user: {name: "John"}})`,`print("Values: $1, $2, $3", [6, 9, 4])`],seealso:[`format`]},typeOf:{name:`typeOf`,category:`Utils`,syntax:[`typeOf(x)`],description:`Get the type of a variable.`,examples:[`typeOf(3.5)`,`typeOf(2 - 4i)`,`typeOf(45 deg)`,`typeOf("hello world")`],seealso:[`getMatrixDataType`]},numeric:{name:`numeric`,category:`Utils`,syntax:[`numeric(x)`],description:`Convert a numeric input to a specific numeric type: number, BigNumber, bigint, or Fraction.`,examples:[`numeric("4")`,`numeric("4", "number")`,`numeric("4", "bigint")`,`numeric("4", "BigNumber")`,`numeric("4", "Fraction")`,`numeric(4, "Fraction")`,`numeric(fraction(2, 5), "number")`],seealso:[`number`,`bigint`,`fraction`,`bignumber`,`string`,`format`]}},Kg=`help`,qg=W(Kg,[`typed`,`mathWithTransform`,`Help`],e=>{var{typed:t,mathWithTransform:n,Help:r}=e;return t(Kg,{any:function(e){var t,i=e;if(typeof e!=`string`){for(t in n)if(H(n,t)&&e===n[t]){i=t;break}}var o=a(Gg,i);if(!o){var s=typeof i==`function`?i.name:i;throw Error(`No documentation found on "`+s+`"`)}return new r(o)}})}),Jg=`chain`,Yg=W(Jg,[`typed`,`Chain`],e=>{var{typed:t,Chain:n}=e;return t(Jg,{"":function(){return new n},any:function(e){return new n(e)}})}),Xg=`det`,Zg=W(Xg,[`typed`,`matrix`,`subtractScalar`,`multiply`,`divideScalar`,`isZero`,`unaryMinus`],e=>{var{typed:t,matrix:n,subtractScalar:r,multiply:i,divideScalar:a,isZero:o,unaryMinus:s}=e;return t(Xg,{any:function(e){return V(e)},"Array | Matrix":function(e){var t;switch(O(e)?t=e.size():Array.isArray(e)?(e=n(e),t=e.size()):t=[],t.length){case 0:return V(e);case 1:if(t[0]===1)return V(e.valueOf()[0]);if(t[0]===0)return 1;throw RangeError(`Matrix must be square (size: `+qr(t)+`)`);case 2:var r=t[0],i=t[1];if(r===i)return c(e.clone().valueOf(),r,i);if(i===0)return 1;throw RangeError(`Matrix must be square (size: `+qr(t)+`)`);default:throw RangeError(`Matrix must be two dimensional (size: `+qr(t)+`)`)}}});function c(e,t,n){if(t===1)return V(e[0][0]);if(t===2)return r(i(e[0][0],e[1][1]),i(e[1][0],e[0][1]));for(var c=!1,l=Array(t).fill(0).map((e,t)=>t),u=0;u<t;u++){var d=l[u];if(o(e[d][u])){var f=void 0;for(f=u+1;f<t;f++)if(!o(e[l[f]][u])){d=l[f],l[f]=l[u],l[u]=d,c=!c;break}if(f===t)return e[d][u]}for(var p=e[d][u],m=u===0?1:e[l[u-1]][u-1],h=u+1;h<t;h++)for(var g=l[h],_=u+1;_<t;_++)e[g][_]=a(r(i(e[g][_],p),i(e[g][u],e[d][_])),m)}var v=e[l[t-1]][t-1];return c?s(v):v}}),Qg=`inv`,$g=W(Qg,[`typed`,`matrix`,`divideScalar`,`addScalar`,`multiply`,`unaryMinus`,`det`,`identity`,`abs`],e=>{var{typed:t,matrix:n,divideScalar:r,addScalar:i,multiply:a,unaryMinus:o,det:s,identity:c,abs:l}=e;return t(Qg,{"Array | Matrix":function(e){var t=O(e)?e.size():ri(e);switch(t.length){case 1:if(t[0]===1)return O(e)?n([r(1,e.valueOf()[0])]):[r(1,e[0])];throw RangeError(`Matrix must be square (size: `+qr(t)+`)`);case 2:var i=t[0],a=t[1];if(i===a)return O(e)?n(u(e.valueOf(),i,a),e.storage()):u(e,i,a);throw RangeError(`Matrix must be square (size: `+qr(t)+`)`);default:throw RangeError(`Matrix must be two dimensional (size: `+qr(t)+`)`)}},any:function(e){return r(1,e)}});function u(e,t,n){var u,d,f,p,m;if(t===1){if(p=e[0][0],p===0)throw Error(`Cannot calculate inverse, determinant is zero`);return[[r(1,p)]]}else if(t===2){var h=s(e);if(h===0)throw Error(`Cannot calculate inverse, determinant is zero`);return[[r(e[1][1],h),r(o(e[0][1]),h)],[r(o(e[1][0]),h),r(e[0][0],h)]]}else{var g=e.concat();for(u=0;

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v([e.pointOneX,e.pointOneY],[t.pointTwoX,t.pointTwoY]);throw TypeError(`Key names do not match`)}else if(Object.keys(e).length===3&&Object.keys(t).length===3){if(!d(e))throw TypeError(`Values of pointOneX, pointOneY and pointOneZ should be numbers or BigNumbers`);if(!d(t))throw TypeError(`Values of pointTwoX, pointTwoY and pointTwoZ should be numbers or BigNumbers`);if(`pointOneX`in e&&`pointOneY`in e&&`pointOneZ`in e&&`pointTwoX`in t&&`pointTwoY`in t&&`pointTwoZ`in t)return v([e.pointOneX,e.pointOneY,e.pointOneZ],[t.pointTwoX,t.pointTwoY,t.pointTwoZ]);throw TypeError(`Key names do not match`)}else throw TypeError(`Invalid Arguments: Try again`)},Array:function(e){if(!h(e))throw TypeError(`Incorrect array format entered for pairwise distance calculation`);return y(e)}});function l(e){return typeof e==`number`||x(e)}function u(e){return e.constructor!==Array&&(e=m(e)),l(e[0])&&l(e[1])}function d(e){return e.constructor!==Array&&(e=m(e)),l(e[0])&&l(e[1])&&l(e[2])}function f(e){return 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a=i+1;a<e.length;a++)e[0].length===2?(n=[e[i][0],e[i][1]],r=[e[a][0],e[a][1]]):e[0].length===3&&(n=[e[i][0],e[i][1],e[i][2]],r=[e[a][0],e[a][1],e[a][2]]),t.push(v(n,r));return t}}),v_=W(`intersect`,[`typed`,`config`,`abs`,`add`,`addScalar`,`matrix`,`multiply`,`multiplyScalar`,`divideScalar`,`subtract`,`smaller`,`equalScalar`,`flatten`,`isZero`,`isNumeric`],e=>{var{typed:t,config:n,abs:r,add:i,addScalar:a,matrix:o,multiply:s,multiplyScalar:c,divideScalar:l,subtract:u,smaller:d,equalScalar:f,flatten:p,isZero:m,isNumeric:h}=e;return t(`intersect`,{"Array, Array, Array":g,"Array, Array, Array, Array":_,"Matrix, Matrix, Matrix":function(e,t,n){var r=g(e.valueOf(),t.valueOf(),n.valueOf());return r===null?null:o(r)},"Matrix, Matrix, Matrix, Matrix":function(e,t,n,r){var i=_(e.valueOf(),t.valueOf(),n.valueOf(),r.valueOf());return i===null?null:o(i)}});function g(e,t,n){if(e=v(e),t=v(t),n=v(n),!b(e))throw TypeError(`Array with 3 numbers or BigNumbers expected for first argument`);if(!b(t))throw 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v=C(e,s,h,s,t,d,g,d,n,p,_,p),y=C(h,s,r,e,g,d,i,t,_,p,o,n),b=C(e,s,r,e,t,d,i,t,n,p,o,n),x=C(h,s,h,s,g,d,g,d,_,p,_,p),S=C(r,e,r,e,i,t,i,t,o,n,o,n),w=u(c(v,y),c(b,x)),T=u(c(S,x),c(y,y));if(m(T))return null;

54var E=l(w,T),D=l(a(v,c(E,y)),x),O=a(e,c(E,u(r,e))),k=a(t,c(E,u(i,t))),A=a(n,c(E,u(o,n))),j=a(s,c(D,u(h,s))),M=a(d,c(D,u(g,d))),N=a(p,c(D,u(_,p)));return f(O,j)&&f(k,M)&&f(A,N)?[O,k,A]:null}function T(e,t,n,r,i,o,s,d,f,p){var m=c(e,s),h=c(r,s),g=c(t,d),_=c(i,d),v=c(n,f),y=c(o,f),b=l(u(u(u(p,m),g),v),u(u(u(a(a(h,_),y),m),g),v));return[a(e,c(b,u(r,e))),a(t,c(b,u(i,t))),a(n,c(b,u(o,n)))]}}),y_=`sum`,b_=W(y_,[`typed`,`config`,`add`,`numeric`],e=>{var{typed:t,config:n,add:r,numeric:i}=e;return t(y_,{"Array | Matrix":a,"Array | Matrix, number | BigNumber":o,"...":function(e){if(Ji(e))throw TypeError(`Scalar values expected in function sum`);return a(e)}});function a(e){var t;return Yi(e,function(e){try{t=t===void 0?e:r(t,e)}catch(t){throw pd(t,`sum`,e)}}),t===void 0&&(t=i(0,n.number)),typeof t==`string`&&(t=i(t,He(t,n))),t}function o(e,t){try{return Zi(e,t,r)}catch(e){throw pd(e,`sum`)}}}),x_=`cumsum`,S_=W(x_,[`typed`,`add`,`unaryPlus`],e=>{var{typed:t,add:n,unaryPlus:r}=e;return t(x_,{Array:i,Matrix:function(e){return e.create(i(e.valueOf(),e.datatype()))},"Array, number | BigNumber":o,"Matrix, number | BigNumber":function(e,t){return e.create(o(e.valueOf(),t),e.datatype())},"...":function(e){if(Ji(e))throw TypeError(`All values expected to be scalar in function cumsum`);return i(e)}});function i(e){try{return a(e)}catch(e){throw pd(e,x_)}}function a(e){if(e.length===0)return[];for(var t=[r(e[0])],i=1;i<e.length;++i)t.push(n(t[i-1],e[i]));return t}function o(e,t){var n=ri(e);if(t<0||t>=n.length)throw new ni(t,n.length);try{return s(e,t)}catch(e){throw pd(e,x_)}}function s(e,t){var n,r,i;if(t<=0){var o=e[0][0];if(Array.isArray(o)){for(i=qi(e),r=[],n=0;n<i.length;n++)r[n]=s(i[n],t-1);return r}else return a(e)}else{for(r=[],n=0;n<e.length;n++)r[n]=s(e[n],t-1);return r}}}),C_=`mean`,w_=W(C_,[`typed`,`add`,`divide`],e=>{var{typed:t,add:n,divide:r}=e;return t(C_,{"Array | Matrix":a,"Array | Matrix, number | BigNumber":i,"...":function(e){if(Ji(e))throw TypeError(`Scalar values expected in function mean`);return a(e)}});function i(e,t){try{return r(Zi(e,t,n),(Array.isArray(e)?ri(e):e.size())[t])}catch(e){throw pd(e,`mean`)}}function a(e){var t,i=0;if(Yi(e,function(e){try{t=t===void 0?e:n(t,e),i++}catch(t){throw pd(t,`mean`,e)}}),i===0)throw Error(`Cannot calculate the mean of an empty array`);return r(t,i)}}),T_=`median`,E_=W(T_,[`typed`,`add`,`divide`,`compare`,`partitionSelect`],e=>{var{typed:t,add:n,divide:r,compare:i,partitionSelect:a}=e;function o(e){try{e=yi(e.valueOf());var t=e.length;if(t===0)throw Error(`Cannot calculate median of an empty array`);if(t%2==0){for(var n=t/2-1,r=a(e,n+1),o=e[n],l=0;l<n;++l)i(e[l],o)>0&&(o=e[l]);return c(o,r)}else return s(a(e,(t-1)/2))}catch(e){throw pd(e,`median`)}}var s=t({"number | BigNumber | Complex | Unit":function(e){return e}}),c=t({"number | BigNumber | Complex | Unit, number | BigNumber | Complex | Unit":function(e,t){return r(n(e,t),2)}});return t(T_,{"Array | Matrix":o,"Array | Matrix, number | BigNumber":function(e,t){throw Error(`median(A, dim) is not yet supported`)},"...":function(e){if(Ji(e))throw TypeError(`Scalar values expected in function median`);return o(e)}})}),D_=`mad`,O_=W(D_,[`typed`,`abs`,`map`,`median`,`subtract`],e=>{var{typed:t,abs:n,map:r,median:i,subtract:a}=e;return t(D_,{"Array | Matrix":o,"...":function(e){return o(e)}});function o(e){if(e=yi(e.valueOf()),e.length===0)throw Error(`Cannot calculate median absolute deviation (mad) of an empty array`);try{var t=i(e);return i(r(e,function(e){return n(a(e,t))}))}catch(e){throw e instanceof TypeError&&e.message.includes(`median`)?TypeError(e.message.replace(`median`,`mad`)):pd(e,`mad`)}}}),k_=`unbiased`,A_=`variance`,j_=W(A_,[`typed`,`add`,`subtract`,`multiply`,`divide`,`mapSlices`,`isNaN`],e=>{var{typed:t,add:n,subtract:r,multiply:i,divide:a,mapSlices:o,isNaN:s}=e;return t(A_,{"Array | Matrix":function(e){return c(e,k_)},"Array | Matrix, string":c,"Array | Matrix, number | BigNumber":function(e,t){return l(e,t,k_)},"Array | Matrix, number | BigNumber, string":l,"...":function(e){return c(e,k_)}});function c(e,t){var o,c=0;if(e.length===0)throw SyntaxError(`Function variance requires one or more parameters (0 provided)`);if(Yi(e,function(e){try{o=o===void 0?e:n(o,e),c++}catch(t){throw pd(t,`variance`,e)}}),c===0)throw Error(`Cannot calculate variance of an empty array`);var l=a(o,c);if(o=void 0,Yi(e,function(e){var t=r(e,l);o=o===void 0?i(t,t):n(o,i(t,t))}),s(o))return o;switch(t){case`uncorrected`:return a(o,c);case`biased`:return a(o,c+1);case`unbiased`:var u=x(o)?o.mul(0):0;return c===1?u:a(o,c-1);

54default:throw Error(`Unknown normalization "`+t+`". Choose "unbiased" (default), "uncorrected", or "biased".`)}}function l(e,t,n){try{if(e.length===0)throw SyntaxError(`Function variance requires one or more parameters (0 provided)`);return o(e,t,e=>c(e,n))}catch(e){throw pd(e,`variance`)}}}),M_=`quantileSeq`,N_=W(M_,[`typed`,`?bignumber`,`add`,`subtract`,`divide`,`multiply`,`partitionSelect`,`compare`,`isInteger`,`smaller`,`smallerEq`,`larger`,`mapSlices`],e=>{var{typed:t,bignumber:n,add:r,subtract:i,divide:a,multiply:o,partitionSelect:s,compare:c,isInteger:l,smaller:u,smallerEq:d,larger:f,mapSlices:p}=e;return t(M_,{"Array | Matrix, number | BigNumber":(e,t)=>h(e,t,!1),"Array | Matrix, number | BigNumber, number":(e,t,n)=>m(e,t,!1,n,h),"Array | Matrix, number | BigNumber, boolean":h,"Array | Matrix, number | BigNumber, boolean, number":(e,t,n,r)=>m(e,t,n,r,h),"Array | Matrix, Array | Matrix":(e,t)=>g(e,t,!1),"Array | Matrix, Array | Matrix, number":(e,t,n)=>m(e,t,!1,n,g),"Array | Matrix, Array | Matrix, boolean":g,"Array | Matrix, Array | Matrix, boolean, number":(e,t,n,r)=>m(e,t,n,r,g)});function m(e,t,n,r,i){return p(e,r,e=>i(e,t,n))}function h(e,t,i){var o,s=e.valueOf();if(u(t,0))throw Error(`N/prob must be non-negative`);if(d(t,1))return b(t)?_(s,t,i):n(_(s,t,i));if(f(t,1)){if(!l(t))throw Error(`N must be a positive integer`);if(f(t,4294967295))throw Error(`N must be less than or equal to 2^32-1, as that is the maximum length of an Array`);var c=r(t,1);o=[];for(var p=0;u(p,t);p++){var m=a(p+1,c);o.push(_(s,m,i))}return b(t)?o:n(o)}}function g(e,t,n){for(var r=e.valueOf(),i=t.valueOf(),a=[],o=0;o<i.length;++o)a.push(_(r,i[o],n));return a}function _(e,t,n){var a=yi(e),u=a.length;if(u===0)throw Error(`Cannot calculate quantile of an empty sequence`);var d=b(t)?t*(u-1):t.times(u-1),f=b(t)?Math.floor(d):d.floor().toNumber(),p=b(t)?d%1:d.minus(f);if(l(d))return n?a[d]:s(a,b(t)?d:d.valueOf());var m,h;if(n)m=a[f],h=a[f+1];else{h=s(a,f+1),m=a[f];for(var g=0;g<f;++g)c(a[g],m)>0&&(m=a[g])}return r(o(m,i(1,p)),o(h,p))}}),P_=`std`,F_=W(P_,[`typed`,`map`,`sqrt`,`variance`],e=>{var{typed:t,map:n,sqrt:r,variance:i}=e;return t(P_,{"Array | Matrix":a,"Array | Matrix, string":a,"Array | Matrix, number | BigNumber":a,"Array | Matrix, number | BigNumber, string":a,"...":function(e){return a(e)}});function a(e,t){if(e.length===0)throw SyntaxError(`Function std requires one or more parameters (0 provided)`);try{var a=i.apply(null,arguments);return k(a)?n(a,r):r(a)}catch(e){throw e instanceof TypeError&&e.message.includes(` variance`)?TypeError(e.message.replace(` variance`,` std`)):e}}}),I_=`corr`,L_=W(I_,[`typed`,`matrix`,`mean`,`sqrt`,`sum`,`add`,`subtract`,`multiply`,`pow`,`divide`],e=>{var{typed:t,matrix:n,sqrt:r,sum:i,add:a,subtract:o,multiply:s,pow:c,divide:l}=e;return t(I_,{"Array, Array":function(e,t){return u(e,t)},"Matrix, Matrix":function(e,t){var r=u(e.toArray(),t.toArray());return Array.isArray(r)?n(r):r}});function u(e,t){var n=[];if(Array.isArray(e[0])&&Array.isArray(t[0])){if(e.length!==t.length)throw SyntaxError(`Dimension mismatch. 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u&&e.name!==t.name)return[];if(t.args.length===1&&e.args.length===1||!x(t,n)&&t.args.length===e.args.length||i){for(var o=[],s=0;s<e.args.length;s++){var c=L(e.args[s],t.args[s],n);if(c.length===0)break;o.push(c)}if(o.length!==e.args.length){if(!b(t,n)||e.args.length===1)return[];if(e.args.length>2)throw Error(`permuting >2 commutative non-associative rule arguments not yet implemented`);var d=L(e.args[0],t.args[1],n);if(d.length===0)return[];var f=L(e.args[1],t.args[0],n);if(f.length===0)return[];o=[d,f]}a=oe(o)}else if(t.args.length>=2&&e.args.length===2){for(var m=ie(t,n),g=[],_=0;_<m.length;_++){var v=L(e,m[_],n,!0);g=g.concat(v)}return g}else if(e.args.length>2)throw Error(`Unexpected non-binary associative function: `+e.toString());else return[]}

54else if(e instanceof h){if(e.name.length===0)throw Error(`Symbol in rule has 0 length...!?`);if(M[e.name]){if(e.name!==t.name)return[]}else switch(e.name[1]>=`a`&&e.name[1]<=`z`?e.name.substring(0,2):e.name[0]){case`n`:case`_p`:a[0].placeholders[e.name]=t;break;case`c`:case`cl`:if(B(t))a[0].placeholders[e.name]=t;else return[];break;case`v`:if(!B(t))a[0].placeholders[e.name]=t;else return[];break;case`vl`:if(xe(t))a[0].placeholders[e.name]=t;else return[];break;case`cd`:if(Pv(t))a[0].placeholders[e.name]=t;else return[];break;case`vd`:if(!Pv(t))a[0].placeholders[e.name]=t;else return[];break;case`ce`:if(Fv(t))a[0].placeholders[e.name]=t;else return[];break;case`ve`:if(!Fv(t))a[0].placeholders[e.name]=t;else return[];break;default:throw Error(`Invalid symbol in rule: `+e.name)}}else if(e instanceof l){if(!r(e.value,t.value))return[]}else return[];return a}function se(e,t){if(e instanceof l&&t instanceof l){if(!r(e.value,t.value))return!1}else if(e instanceof h&&t instanceof h){if(e.name!==t.name)return!1}else if(e instanceof p&&t instanceof p||e instanceof u&&t instanceof u){if(e instanceof p){if(e.op!==t.op||e.fn!==t.fn)return!1}else if(e instanceof u&&e.name!==t.name)return!1;if(e.args.length!==t.args.length)return!1;for(var n=0;n<e.args.length;n++)if(!se(e.args[n],t.args[n]))return!1}else return!1;return!0}return A}),Bv=W(`simplifyConstant`,[`typed`,`config`,`mathWithTransform`,`matrix`,`isBounded`,`?fraction`,`?bignumber`,`AccessorNode`,`ArrayNode`,`ConstantNode`,`FunctionNode`,`IndexNode`,`ObjectNode`,`OperatorNode`,`SymbolNode`],e=>{var{typed:t,config:n,mathWithTransform:r,matrix:i,isBounded:a,fraction:o,bignumber:s,AccessorNode:c,ArrayNode:l,ConstantNode:u,FunctionNode:d,IndexNode:f,ObjectNode:p,OperatorNode:m,SymbolNode:h}=e,{isCommutative:g,isAssociative:_,allChildren:v,createMakeNodeFunction:y}=Rv({FunctionNode:d,OperatorNode:m,SymbolNode:h}),b=t(`simplifyConstant`,{Node:e=>T(N(e,{})),"Node, Object":function(e,t){return T(N(e,t))}});function x(e){return w(e)?e.valueOf():e instanceof Array?e.map(x):O(e)?i(x(e.valueOf())):e}function S(e,t,n){try{return r[e].apply(null,t)}catch{return t=t.map(x),D(r[e].apply(null,t),n)}}var C=t({Fraction:A,number:function(e){return e<0?k(new u(-e)):new u(e)},BigNumber:function(e){return e<0?k(new u(-e)):new u(e)},bigint:function(e){return e<0n?k(new u(-e)):new u(e)},Complex:function(e){throw Error(`Cannot convert Complex number to Node`)},string:function(e){return new u(e)},Matrix:function(e){return new l(e.valueOf().map(e=>C(e)))}});function T(e){return he(e)?e:C(e)}function E(e,t){if(t&&t.exactFractions!==!1&&a(e)&&o){var n=o(e),r=t&&typeof t.fractionsLimit==`number`?t.fractionsLimit:1/0;if(n.valueOf()===e&&n.n<r&&n.d<r)return n}return e}var D=t({"string, Object":function(e,t){var r=He(e,n);return r===`BigNumber`?(s===void 0&&gu(),s(e)):r===`bigint`?BigInt(e):r===`Fraction`?(o===void 0&&_u(),o(e)):E(parseFloat(e),t)},"Fraction, Object":function(e,t){return e},"BigNumber, Object":function(e,t){return e},"number, Object":function(e,t){return E(e,t)},"bigint, Object":function(e,t){return e},"Complex, Object":function(e,t){return e.im===0?E(e.re,t):e},"Matrix, Object":function(e,t){return i(E(e.valueOf()))},"Array, Object":function(e,t){return e.map(E)}});function k(e){return new m(`-`,`unaryMinus`,[e])}function A(e){var t=e=>n.number===`BigNumber`&&s?s(e):Number(e),r=e.s*e.n,i=r<0n?new m(`-`,`unaryMinus`,[new u(-t(r))]):new u(t(r));return e.d===1n?i:new m(`/`,`divide`,[i,new u(t(e.d))])}function j(e,t,n){if(!me(t))return new c(T(e),T(t));if(R(e)||O(e)){for(var r=Array.from(t.dimensions);r.length>0;)if(B(r[0])&&typeof r[0].value!=`string`){var a=D(r.shift().value,n);R(e)?e=e.items[a-1]:(e=e.valueOf()[a-1],e instanceof Array&&(e=i(e)))}else if(r.length>1&&B(r[1])&&typeof r[1].value!=`string`){var o=D(r[1].value,n),s=[],d=R(e)?e.items:e.valueOf();for(var p of d)if(R(p))s.push(p.items[o-1]);else if(O(e))s.push(p[o-1]);else break;if(s.length===d.length)e=R(e)?new l(s):i(s),r.splice(1,1);else break}else break;return r.length===t.dimensions.length?new c(T(e),t):r.length>0?(t=new f(r),new c(T(e),t)):e}if(ge(e)&&t.dimensions.length===1&&B(t.dimensions[0])){var m=t.dimensions[0].value;return m in e.properties?e.properties[m]:new u}return new c(T(e),t)}function M(e,t,n,r){var i=t.shift(),a=t.reduce((t,i)=>{if(!he(i)){var a=t.pop();if(he(a))return[a,i];try{return t.push(S(e,[a,i],r)),t}catch{t.push(a)}}

54return t.push(T(t.pop())),[n([t.length===1?t[0]:n(t),T(i)])]},[i]);return a.length===1?a[0]:n([a[0],C(a[1])])}function N(e,t){switch(e.type){case`SymbolNode`:return e;case`ConstantNode`:switch(typeof e.value){case`number`:return D(e.value,t);case`bigint`:return D(e.value,t);case`string`:return e.value;default:if(!isNaN(e.value))return D(e.value,t)}return e;case`FunctionNode`:if(r[e.name]&&r[e.name].rawArgs)return e;if(![`add`,`multiply`].includes(e.name)){var n=e.args.map(e=>N(e,t));if(!n.some(he))try{return S(e.name,n,t)}catch{}if(e.name===`size`&&n.length===1&&R(n[0])){for(var a=[],o=n[0];R(o);)a.push(o.items.length),o=o.items[0];return i(a)}return new d(e.name,n.map(T))}case`OperatorNode`:var s=e.fn.toString(),c,u,m=y(e);if(_e(e)&&e.isUnary())c=[N(e.args[0],t)],u=he(c[0])?m(c):S(s,c,t);else if(_(e,t.context))if(c=v(e,t.context),c=c.map(e=>N(e,t)),g(s,t.context)){for(var h=[],x=[],C=0;C<c.length;C++)he(c[C])?x.push(c[C]):h.push(c[C]);h.length>1?(u=M(s,h,m,t),x.unshift(u),u=M(s,x,m,t)):u=M(s,c,m,t)}else u=M(s,c,m,t);else c=e.args.map(e=>N(e,t)),u=M(s,c,m,t);return u;case`ParenthesisNode`:return N(e.content,t);case`AccessorNode`:return j(N(e.object,t),N(e.index,t),t);case`ArrayNode`:var w=e.items.map(e=>N(e,t));return w.some(he)?new l(w.map(T)):i(w);case`IndexNode`:return new f(e.dimensions.map(e=>b(e,t)));case`ObjectNode`:var E={};for(var O in e.properties)E[O]=b(e.properties[O],t);return new p(E);default:throw Error(`Unimplemented node type in simplifyConstant: ${e.type}`)}}return b}),Vv=`simplifyCore`,Hv=W(Vv,[`typed`,`parse`,`equal`,`isZero`,`add`,`subtract`,`multiply`,`divide`,`pow`,`AccessorNode`,`ArrayNode`,`ConstantNode`,`FunctionNode`,`IndexNode`,`ObjectNode`,`OperatorNode`,`ParenthesisNode`,`SymbolNode`],e=>{var{typed:t,parse:n,equal:r,isZero:i,add:a,subtract:o,multiply:s,divide:c,pow:l,AccessorNode:u,ArrayNode:d,ConstantNode:f,FunctionNode:p,IndexNode:m,ObjectNode:h,OperatorNode:g,ParenthesisNode:_,SymbolNode:v}=e,y=new f(0),b=new f(1),x=new f(!0),S=new f(!1);function C(e){return _e(e)&&[`and`,`not`,`or`].includes(e.op)}var{hasProperty:w,isCommutative:T}=Rv({FunctionNode:p,OperatorNode:g,SymbolNode:v});function E(e){var t=arguments.length>1&&arguments[1]!==void 0?arguments[1]:{},n=t?t.context:void 0;if(w(e,`trivial`,n)){if(pe(e)&&e.args.length===1)return E(e.args[0],t);var a=!1,o=0;if(e.forEach(e=>{++o,o===1&&(a=E(e,t))}),o===1)return a}var s=e;if(pe(s)){var c=fh(s.name);if(c){if(s.args.length>2&&w(s,`associative`,n))for(;s.args.length>2;){var l=s.args.pop(),f=s.args.pop();s.args.push(new g(c,s.name,[l,f]))}s=new g(c,s.name,s.args)}else return new p(E(s.fn),s.args.map(e=>E(e,t)))}if(_e(s)&&s.isUnary()){var _=E(s.args[0],t);

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