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####
# Command translation table from GeoGebra to MPReduce
# e.g. Expand[ 2(x+3) ] is translated to ExpandBrackets( 2*(x+3) )
###
Binomial.2=<< begin scalar n!!, k!!, result1!!, result2!!; n!!:=%0; k!!:=%1; result1!!:= if numberp(n!!) and numberp(k!!) and k!!>n!! then 0 else factorial(n!!)/(factorial(k!!)*factorial(n!!-k!!)); let list(gamma(~w+1) => factorial(w)); result2!!:=result1!!; clear {gamma(~w+1) => factorial}; return result2!! end >>
BinomialDist.4=<< begin scalar n!!, p!!, k!!; n!!:=%0; p!!:=%1; k!!:=%2;return if %3='true then for i:=1:floor(k!!) sum binomial(n!!,i)*p!!^i*(1-p!!)^(n!!-i) else binomial(n!!,k!!)*p!!^k!!*(1-p!!)^(n!!-k!!) end >>
Cauchy.3=1/2+1/pi*atan(((%2)-(%1))/(%0))
CFactor.1=<<on complex$ off combinelogs$ begin scalar factorlist!!; factorlist!!:=factorize(%0); return part(!*hold((for each x in factorlist!! collect (if arglength(x)<0 or part(x,0) neq 'list then x else if part(x,2)=1 then part(x,1) else part(x,0):=**))),0):=* end >>
CFactor.2=<<on complex$ off combinelogs$ begin scalar factorlist!!; korder %1; factorlist!!:=factorize(%0); korder nil;return part(!*hold(for each x in factorlist!! collect (if arglength(x)<0 or part(x,0) neq 'list then x else if part(x,2)=1 then part(x,1) else part(x,0):=**)),0):=* end >>
ChiSquared.2=igamma((%0)/2,(%1)/2)/gamma((%0)/2)
Coefficients.1=reverse(coeff(%0,ggbcasvarx))
Coefficients.2=reverse(coeff(%0,%1))
CommonDenominator.2=lcm(den(%0),den(%1))
Covariance.2=<<begin scalar ret, tmpmean1, tmpmean2, tmplength; ret:=0$ tmpmean1:=0$ tmpmean2:=0$ tmplength:=length(%0)$ tmpmean1:=1/tmplength*for i:=1:tmplength sum part(%0,i) $ tmpmean2:=1/tmplength*for i:=1:tmplength sum part(%1,i)$ return 1/tmplength*for i:=1:tmplength sum (part(%0,i)-tmpmean1)*(part(%1,i)-tmpmean2) end>>
Covariance.1=<<begin scalar ret, tmpmean1, tmpmean2, tmplength; ret:=0$ tmpmean1:=0$ tmpmean2:=0$ tmplength:=length(%0)$ tmpmean1:=1/tmplength*for i:=1:tmplength sum part(part(%0,i),1) $ tmpmean2:=1/tmplength*for i:=1:tmplength sum part(part(%0,i),2)$ return 1/tmplength*for i:=1:tmplength sum (part(part(%0,i),1)-tmpmean1)*(part(part(%0,i),2)-tmpmean2) end>>
Cross.2=cross(%0,%1)
CSolutions.1=<<on complex$ flattenlist(for each element!! in mycsolve(%0,ggbcasvarx) collect map(rhs,element!!))>>
CSolutions.2=<<on complex$ flattenlist(for each element!! in mycsolve(%0,%1) collect map(rhs,element!!))>>
CSolve.1=<<on complex$ flattenlist(mycsolve(%0,ggbcasvarx))>>
CSolve.2=<<on complex$ flattenlist(mycsolve(%0,%1))>>
Decimal.1=<<on rounded$ (%0)>>
Degree.1=deg(%0,ggbcasvarx)
Degree.2=deg(%0,%1)
Delete.1= << clear %0; 'true>>
Denominator.1=den(%0)
Derivative.1=df(%0,ggbcasvarx)
Derivative.2=df(%0,%1)
Derivative.3=df(%0,%1,%2)
Determinant.1=<<tmpmat!!:=%0; det(tmpmat!!)>>
Dimension.1=length(%0)
Div.2=div(%0,%1)
Division.2=list(div(%0,%1),mod!!(%0,%1))
Divisors.1=<<off combinelogs$ if numberp(%0) then if (%0)=1 then 1 else for each i in map(part(~w,2)+1,factorize(%0)) product i else '?>>
DivisorsList.1=<<off combinelogs$ if numberp(%0) then if %0=1 then list(1) else <<begin scalar divlist!!, return!!; divlist!!:=for each x in factorize(%0) collect for i:=0:part(x,2) collect part(x,1)^i; return!!:=part(divlist!!,1); for i:=2:length(divlist!!) do return!!:=for each x in part(divlist!!,i) join for each y in return!! collect x*y; return mysort(return!!) end>> else '? >>
DivisorsSum.1=<<off combinelogs$ if numberp(%0) then if %0=1 then 1 else for each x in factorize(%0) product (part(x,1)^(part(x,2)+1)-1)/(part(x,1)-1) else '? >>
Dot.2=dot(%0,%1)
Element.2=part(%0,%1)
Element.3=<<clear input!!; input!!:=%0; if arglength(input!!)>-1 and part(input!!,0)='mat then input!!(%1,%2) else for i:=%1:%2 collect part(input!!,i)>>
Expand.1=<<clear tmp!!; off factor, pri, combinelogs$ on div, expandlogs$ tmp!!:=%0; off factor, pri, combinelogs$ on div, expandlogs$ tmp!!>>
ExpandComplex.1=<<clear tmp!!; off factor, pri, combinelogs$ on div, complex, expandlogs$ tmp!!:=%0; off factor, pri, combinelogs$ on div, expandlogs$ tmp!!>>
Exponential.2=1-exp(-(%0)*(%1))
Factor.1=<<off combinelogs$ begin scalar factorlist!!, tmpexp!!; if numberp(den(%0)) then <<factorlist!!:=factorize(%0); return part(!*hold((for each x in factorlist!! collect (if arglength(x)<0 or part(x,0) neq \\'list then x else if part(x,2)=1 then part(x,1) else part(x,0):=**))),0):=*>> else <<on factor; tmpexp!!:=(%0); on factor; return tmpexp!! >> end >>
Factor.2=<<off combinelogs$ begin scalar factorlist!!; korder append(list(%1),varorder!!); factorlist!!:=factorize(%0); korder varorder!!;return part(!*hold(for each x in factorlist!! collect (if arglength(x)<0 or part(x,0) neq \\'list then x else if part(x,2)=1 then part(x,1) else part(x,0):=**)),0):=* end >>
Factors.1=<<off combinelogs$ off complex, rounded; for each x in factorize(%0) collect if arglength(x)<0 or part(x,0) neq \\'list then x:=list(x,1) else x >>
FDistribution.3=betaRegularized((%0)/2,(%1)/2,(%0)*(%2)/((%0)*(%2)+%1))
First.1=list(first(%0))
First.2=<<begin scalar list!!; list!!:=%0; return if length(list!!)<=%1 then list!! else for i:=1:%1 collect part(list!!,i) end>>
FractionalPart.1=if (%0)>0 then %0-floor(%0) else %0-ceiling(%0)
#These implementations follow the one in GeoGebra
FitExp.1=<<on rounded, roundall, numval; begin scalar p1!!, p2!!, input!!, sigmax!!, sigmay!!, sigmaxy!!, sigmax2!!, length!!, denominator!!, xlist!!, ylist!!; input!!:=mattolistoflists(%0); xlist!!:=map(part(~w!!,1), input!!); ylist!!:=map(log,map(part(~w!!,2), input!!)); length!!:=length(ylist!!); sigmax!!:=for each i in xlist!! sum i; sigmay!!:= for each i in ylist!! sum i; sigmax2!!:= for each i in xlist!! sum i^2; sigmaxy!!:=for i:=1:length!! sum part(xlist!!,i)*part(ylist!!,i);denominator!!:= length!!*sigmax2!!-sigmax!!**2; p2!!:=(length!!*sigmaxy!!-sigmax!!*sigmay!!)/denominator!!; p1!!:= exp((sigmay!!*sigmax2!!-sigmax!!*sigmaxy!!)/denominator!!); return p1!!*exp(x*p2!!) end>>
FitLog.1=<<on rounded, roundall, numval; begin scalar p1!!, p2!!, input!!, sigmax!!, sigmay!!, sigmaxy!!, sigmax2!!, length!!, denominator!!, xlist!!, ylist!!; input!!:=mattolistoflists(%0); xlist!!:=map(log,map(part(~w!!,1), input!!)); ylist!!:=map(part(~w!!,2), input!!); length!!:=length(ylist!!); sigmax!!:=for each i in xlist!! sum i; sigmay!!:= for each i in ylist!! sum i; sigmax2!!:= for each i in xlist!! sum i^2; sigmaxy!!:=for i:=1:length!! sum part(xlist!!,i)*part(ylist!!,i);denominator!!:= length!!*sigmax2!!-sigmax!!**2; p2!!:=(length!!*sigmaxy!!-sigmax!!*sigmay!!)/denominator!!; p1!!:= (sigmay!!*sigmax2!!-sigmax!!*sigmaxy!!)/denominator!!; return p1!!+log(x)*p2!! end >>
FitPoly.2=<< clear tmpx!!, tmpy!!; on rounded, roundall, numval; begin scalar xvec!!, yvec!!, input!!; input!!:= mattolistoflists(%0); xvec!!:=map(part(~w!!,1), input!!); yvec!!:= map(part(~w!!,2), input!!); tmpx!!:=vandermonde(xvec!!); tmpx!!:=sub\\_matrix(tmpx!!,for i:=1:length(input!!) collect i, for i:=1:(%1+1) collect i); tmpy!!:=listtocolumnvector(yvec!!);tmpx!!:=(1/(tp(tmpx!!)*tmpx!!))*tp(tmpx!!); tmpy!!:=tmpx!!*tmpy!!; return for i:=1:part(length(tmpy!!),1) sum tmpy!!(i,1)*x^(i-1) end>>
FitPow.1=<<on rounded, roundall, numval; begin scalar p1!!, p2!!, input!!, sigmax!!, sigmay!!, sigmaxy!!, sigmax2!!, length!!, denominator!!, xlist!!, ylist!!; input!!:=mattolistoflists(%0); xlist!!:=map(log,map(part(~w!!,1), input!!)); ylist!!:=map(log,map(part(~w!!,2), input!!)); length!!:=length(ylist!!); sigmax!!:=for each i in xlist!! sum i; sigmay!!:= for each i in ylist!! sum i; sigmax2!!:= for each i in xlist!! sum i^2; sigmaxy!!:=for i:=1:length!! sum part(xlist!!,i)*part(ylist!!,i);denominator!!:= length!!*sigmax2!!-sigmax!!**2; p2!!:=(length!!*sigmaxy!!-sigmax!!*sigmay!!)/denominator!!; p1!!:= exp((sigmay!!*sigmax2!!-sigmax!!*sigmaxy!!)/denominator!!); return p1!!*x^p2!! end >>
#FitSin
Gamma.3=(((%1)*(%2))^(%0))/(%0)*kummerm(%0,%0+1,-(%1)*(%2))/beta(%0)
GCD.2=<<begin scalar gcd!!; off rounded, roundall, numval; gcd!!:=gcd(%0,%1); if numeric!!=0 then off rounded, roundall, numval; return gcd!! end>>
GCD.1=<<begin scalar gcd!!; off rounded, roundall, numval; gcd!!:=0; for each term in (%0) do gcd!!:=gcd(gcd!!,term); if numeric!!=0 then off rounded, roundall, numval; return gcd!! end >>
#GetPrecision.1
HyperGeometric.5=<<begin scalar m,kk,ng,n; m:=%1$ ng:=%0$ n:=%2$ kk:=%3$ return if %4=true then sum(binomial(m,k)*binomial((ng-m),(n-k))/binomial(ng,n),k,0,kk) else binomial(m,kk)*binomial((ng-m),(n-kk))/binomial(ng,n) end>>
Identity.1=<<make\\_identity(%0)>>
Imaginary.1=impart(%0)
ImplicitDerivative.3=-df(%0,%1)/df(%0,%2)
Integral.1=<<begin scalar integral!!; let intrules!!; integral!!:=int(%0,ggbcasvarx); clearrules intrules!!; return if freeof(integral!!,\\'int) then part(list(integral!!,newarbconst()),0):=+ else \\'? end>>
Integral.2=<<begin scalar integral!!; let intrules!!; integral!!:=int(%0,%1); clearrules intrules!!; return if freeof(integral!!,\\'int) then part(list(integral!!,newarbconst()),0):=+ else \\'? end>>
Integral.3=<<begin scalar integral!!; let intrules!!; integral!!:=int(%0,ggbcasvarx,%1,%2); clearrules intrules!!; return if freeof(integral!!,\\'int) then integral!! else \\'? end>>
Integral.4=<<begin scalar integral!!; let intrules!!; integral!!:=int(%0,%1,%2,%3); clearrules intrules!!; return if freeof(integral!!,\\'int) then integral!! else \\'? end>>
IntegralBetween.4=<< begin scalar integral!!; let intrules!!; integral!!:=int(%0-(%1),ggbcasvarx,%2,%3); clearrules intrules!!; return if freeof(integral!!,\\'int) then integral!! else \\'? end >>
IntegralBetween.5=<< begin scalar integral!!; let intrules!!; integral!!:=int(%0-(%1),%2,%3,%4); clearrules intrules!!; return if freeof(integral!!,\\'int) then integral!! else \\'? end >>
Intersect.2=<<begin scalar eqn1!!, eqn2!!; eqn1!!:=%0; eqn2!!:=%1; if freeof(eqn1!!,=) then eqn1!!:= eqn1!!=ggbcasvary; if freeof(eqn2!!,=) then eqn2!!:= eqn2!!=ggbcasvary; return flattenlist(for each element!! in mysolve(list(eqn1!!,eqn2!!),list(ggbcasvarx, ggbcasvary)) collect map(rhs,element!!)) end>>
Invert.1=1/(%0)
IntegerPart.1=if %0>0 then floor(%0) else ceiling(%0)
IsPrime.1=if primep(%0) and (%0)>1 then true else false
#IsBound.1=if << symbolic; p!!:=isbound!!('%0); algebraic; p!!>>=1 then 'true else 'false
Last.1=<<begin scalar list!!; list!!:=%0; return list(part(list!!,length(list!!))) end >>
Last.2=<<begin scalar list!!; list!!:=%0; return if length(list!!)<=%1 then list!! else for i:=1:%1 collect part(list!!,length(list!!)-%1+i) end >>
LCM.1=<<begin scalar lcm!!; off rounded, roundall, numval; lcm!!:=1; for each term in (%0) do lcm!!:=lcm(lcm!!,term); if numeric!!=0 then off rounded, roundall, numval; return lcm!! end >>
LCM.2=<<begin scalar lcm!!; off rounded, roundall, numval; lcm!!:=lcm(%0,%1); if numeric!!=0 then off rounded, roundall, numval; return lcm!! end>>
LeftSide.1=<<begin scalar input!!; input!!:=%0; return if arglength(input!!) and part(%0,0)='list then map(lhs,input!!) else lhs(input!!) end>>
Length.3=int(sqrt(1+df(%0,ggbcasvarx)^2),ggbcasvarx,%1,%2)
Length.4=int(sqrt(1+df(%0,%1)^2),%1,%2,%3)
Limit.2=<<begin scalar input!!,limitabove!!, limitbelow!!; input!!:=(%0); return if (%1)=infinity or (%1)=-infinity then limit(input!!, ggbcasvarx, %1) else <<limitabove!!:=limit!+(input!!,ggbcasvarx,%1); limitbelow!!:=limit!-(input!!,ggbcasvarx,%1); if limitabove!!=limitbelow!! then limitabove!! else \\'?>> end>>
Limit.3=<<begin scalar input!!,limitabove!!, limitbelow!!; input!!:=(%0); return if (%2)=infinity or (%2)=-infinity then limit(input!!, %1, %2) else <<limitabove!!:=limit!+(input!!,%1,%2); limitbelow!!:=limit!-(input!!,%1,%2); if limitabove!!=limitbelow!! then limitabove!! else \\'?>> end>>
LimitAbove.2=limit!+(%0,ggbcasvarx,%1)
LimitAbove.3=limit!+(%0,%1,%2)
LimitBelow.2=limit!-(%0,ggbcasvarx,%1)
LimitBelow.3=limit!-(%0,%1,%2)
Max.N=max(%)
MatrixRank.1=rank(%0)
Mean.1=<<begin scalar list!!; list!!:=%0$ return 1/length(list!!)*for i:=1:length(list!!) sum part(list!!,i) end>>
Median.1=<<begin scalar list!!; list!!:=%0$ list!!:= mysort list!!$ return if remainder(length(list!!),2)=0 then (part(list!!,length(list!!)/2)+part(list!!,1+length(list!!)/2))/2 else part(list!!,(length(list!!)+1)/2) end>>
Min.N=min(%)
Mod.2=mod!!(%0,%1)
NextPrime.1=if %0<2 then 2 else nextprime(%0)
NIntegral.3=<<on numval, roundall$ num\\_int(%0,ggbcasvarx=((%1) .. (%2))) >>
NIntegral.4=<<on numval, roundall$ num\\_int(%0,%1=((%2) .. (%3))) >>
Normal.3=1/2*(1+erf((%2-(%0))/sqrt(2*(%1)^2)))
nPr.2=factorial(%0)/factorial(%0-%1)
NRoot.2=(%0)^(1/(%1))
NSolve.1=<<on rounded, numval, roundall$ num\\_solve(%0,ggbcasvarx, iterations=10000) >>
NSolve.2=<<on rounded, numval, roundall$ num\\_solve(%0,%1, iterations=10000) >>
NSolutions.1=<<on rounded, numval, roundall$ map(rhs,num\\_solve(%0,ggbcasvarx, iterations=10000)) >>
NSolutions.2=<<on rounded, numval, roundall$ map(rhs,num\\_solve(%0,%1, iterations=10000)) >>
Numerator.1=num(%0)
Numeric.1=<<numeric!!:=1; on rounded, roundall, numval$ if printprecision!!<=16 then <<print\\_precision(printprecision!!)$ %0>> else <<precision(printprecision!!)$ print\\_precision(printprecision!!)$ %0 >> >>
Numeric.2=<<numeric!!:=1; on rounded, roundall, numval$ if %1<=16 then <<print\\_precision(%1)$ %0>> else <<precision(%1)$ print\\_precision(%1)$ %0 >> >>
OrthogonalVector.1=if arglength(%0)>-1 and part(%0,0)='list then list(-part(%0,2),part(%0,1)) else if arglength(%0)>-1 and part(%0,0)='mat then part mat((0,-1),(1,0))*(%0)
PartialFractions.1=part(pf(%0,ggbcasvarx),0):=+
PartialFractions.2=part(pf(%0,%1),0):=+
Pascal.4=if %3=true then betaRegularized(%0,1+floor(%2),%1) else (1-(%1))^(%2)*(%1)^(%0)*binomial(%0+%2-1,%0-1)
Poisson.3=if %2=true then exp(-(%0))*for i:=0:(%1) sum (%0)^i/factorial(floor(i)) else (%0)^(%1)/factorial(floor(%1))*exp(-%0)
PreviousPrime.1=<<begin scalar tmp!!;return if (%0)>2 then <<tmp!!:=%0-1; while not(primep(tmp!!)) do tmp!!:=tmp!!-1; tmp!!>> else '? end>>
PrimeFactors.1=<<off combinelogs, rounded; if (%0)=1 then {} else begin scalar factorlist!!; factorlist!!:=factorize(%0); factorlist!!:= for each x!! in factorlist!! collect for i:=1:part(x!!,2) collect part(x!!,1); return mkdepthone(factorlist!!) end>>
Product.1=<< begin scalar input!!; input!!:=%0; return for i:=1:length(input!!) product part(input!!,i) end >>
Product.4=prod(%0,%1,%2,%3)
#Prog.1=<<%0>>
#Prog.2=<<begin scalar %0; return %1 end>>
MixedNumber.1=<<begin scalar result!!, input!!; off pri; input!!:=%0; if part(input!!,0) neq quotient then result!!:=list(input!!,0) else <<arguments!!:=(part(abs(input!!),0):=list); result!!:=list(sign(input!!)*div(first(arguments!!), second(arguments!!)), mod!!(first(arguments!!), second(arguments!!))/second(arguments!!))>>; return if part(result!!,2)=0 then part(result!!,1) else if part(result!!,1)=0 then sign(input!!)*part(result!!,2) else if input!!<0 then part(result!!,0):=- else part(result!!,0):=+ end>>
Random.2=random(%1-%0+1)+%0
RandomBinomial.2=<<on rounded, roundall, numval; for each x in for i:=1:%0 collect random(10000000)/10000000 sum if (x<%1) then 1 else 0 >>
RandomElement.1=part(%0,random(length(%0))+1)
RandomPoisson.1=<<on rounded, roundall, numval; begin scalar L!!, k!!, p!!; L!!:=exp(-%0); k!!:=0; p!!:=1; repeat <<k!!:=k!!+1; p!!:=p!!*(random(10000000)/10000000)>> until p!!<=L!!; return k!!-1 end>>
RandomNormal.2=<<on rounded, roundall, numval; %0+(%1)*cos(2*pi*random(10000000)/10000000)*sqrt(-2*log(random(10000000)/10000000)) >>
RandomPolynomial.3=<<begin scalar a, b, min!!, max!!; min!!:=myround(%1); max!!:=myround(%2); a:=for i:=0:%0-1 sum (random(max!!-(min!!)+1)+(min!!))*ggbcasvarx^i; return a+ggbcasvarx^(%0)*if min!!<=0 and max!!>0 then <<b:=random(max!!-(min!!))+(min!!); if b>=0 then b+1 else b>> else random(max!!-(min!!)+1)+min!! end>>
RandomPolynomial.4=<<begin scalar a, b, min!!, max!!; min!!:=myround(%2); max!!:=myround(%3); a:=for i:=0:%1-1 sum (random(max!!-min!!+1)+min!!)*(%0)^i; return a+(%0)^(%1)*if min!!<=0 and max!!>0 then <<b:=random(max!!-min!!)+min!!; if b>=0 then b+1 else b>> else random(max!!-min!!+1)+min!! end>>
Rationalize.1=<<off rounded; %0 >>
Real.1=repart(%0)
RightSide.1=<<begin scalar input!!; input!!:=%0; return if arglength(input!!) and part(%0,0)='list then map(rhs,input!!) else rhs(input!!) end>>
Root.1=flattenlist(mysolve(%0,ggbcasvarx))
ReducedRowEchelonForm.1=<<begin scalar tmpcolumn!!; clear tmpmatrix!!; tmpmatrix!!:=%0$ tmpcolumn!!:=1$ for i:=1:row\\_dim(tmpmatrix!!) do <<if tmpcolumn!!<column\\_dim(tmpmatrix!!) and tmpmatrix!!(i,tmpcolumn!!)=0 then while (tmpcolumn!!<=column\\_dim(tmpmatrix!!) and tmpmatrix!!(i,tmpcolumn!!)=0 and i<=row\\_dim(tmpmatrix!!)) do << for j:=i+1:row\\_dim(tmpmatrix!!) do if (j<=column\\_dim(tmpmatrix!!) and tmpmatrix!!(i,j) neq 0) then tmpmatrix!!:=swap\\_rows(tmpmatrix!!,tmpcolumn!!, j)$ if (tmpmatrix!!(i,tmpcolumn!!)=0) then tmpcolumn!!:=tmpcolumn!!+1 >>$ if tmpcolumn!!<=column\\_dim(tmpmatrix!!) then if tmpmatrix!!(i, tmpcolumn!!) neq 0 then << tmpmatrix!!:=pivot(tmpmatrix!!,i,tmpcolumn!!); tmpmatrix!!:=mult\\_rows(tmpmatrix!!,i,1/tmpmatrix!!(i,tmpcolumn!!))$ tmpcolumn!!:=tmpcolumn!!+1 >>; >>$ return tmpmatrix!! end>>
Sample.2=<< begin scalar list!!; list!!:=%0; return for i:=1:%1 collect part(list!!,1+random(length(list!!))) end >>
Sample.3=<< begin scalar list!!; list!!:=%0; return if %2=true then for i:=1:%1 collect part(list!!,1+random(length(list!!))) else <<list!!:=shuffle(list!!); for i:=1:%1 collect part(list!!,i)>> end >>
SampleVariance.1=<< begin scalar n!!, list!!; list!!:=%0; n!!:=length(list!!); return 1/(n!!-1)*(for each i in list!! sum i^2)-1/(n!!^2-n!!)*(for each i in list!! sum i)^2 end >>
SampleSD.1=<< begin scalar n!!, list!!; list!!:=%0; n!!:=length(list!!); return sqrt(1/(n!!-1)*(for each i in list!! sum i^2)-1/(n!!^2-n!!)*(for each i in list!! sum i)^2) end >>
Sequence.1=<<listofliststomat(for i:=1:(%0) collect i)>>
Sequence.4=<<listofliststomat(<<begin scalar %1; return for %1:=(%2):(%3) collect (%0) end>>)>>
Sequence.5=<<listofliststomat(<<begin scalar %1; return for %1:=(%2) step (%4) until (%3) collect (%0) end>>)>>
SetSignificantNumbersNumeric.1=printprecision!!:=%0
SD.1=<<begin scalar tmpmean, tmplist; tmplist:=%0$ tmpmean:=0$ tmpmean:= (1/length(tmplist))*for i:=1:length(tmplist) sum part(tmplist,i)$ return sqrt((1/length(tmplist))*for i:=1:length(tmplist) sum (part(tmplist,i)^2-tmpmean^2)) end>>
Shuffle.1=shuffle(%0)
Simplify.1=<<on combinelogs; trigsimp(%0, combine)>>
#SimplifyFull.1=trigsimp(%0, combine)
Solutions.1=flattenlist(for each element!! in mysolve(%0,ggbcasvarx) collect map(rhs,element!!))
Solutions.2=flattenlist(for each element!! in mysolve(%0,%1) collect map(rhs,element!!))
Solve.1=flattenlist(mysolve(aeval(%0),ggbcasvarx))
Solve.2=<< begin scalar equations!!; equations!!:=%0; if arglength(equations!!)>-1 and part(equations!!,0)='list then equations!!:=mkdepthone(equations!!); return flattenlist(mysolve(aeval(equations!!),%1)) end >>
SolveODE.1=<<begin scalar tmpret, tmpeqn; tmpeqn:=%0$ if freeof(tmpeqn,=) then tmpret:=odesolve(df(ggbcasvary,ggbcasvarx)=tmpeqn,ggbcasvary,ggbcasvarx) else tmpret:=odesolve(tmpeqn,ggbcasvary,ggbcasvarx)$ return if length(tmpret)=1 then first(tmpret) else tmpret end>>
SolveODE.3=<<begin scalar tmpret, tmpeqn; tmpeqn:=%0$ if freeof(tmpeqn,=) then tmpret:=odesolve(df(%1,%2)=tmpeqn,%1,%2) else tmpret:=odesolve(tmpeqn,%1,%2)$ return if length(tmpret)=1 then first(tmpret) else tmpret end>>
Substitute.2=<<if keepinput!!=1 then <<keepinput!!:=2; sub(%1, !*hold(%0)) >> else begin scalar rulelist!!, replacements!!; replacements!!:=%1; if arglength(replacements!!)>-1 and part(replacements!!,0)='list then 0 else replacements!!:=list(replacements!!); rulelist!!:= for each element in replacements!! collect part(element,0):=replaceby; return %0 where rulelist!! end>>
#Substitute.3=if hold!!=0 then sub(%1=%2,%0) else sub(%1=%2,!*hold(%0))
Substitute.3=<<if keepinput!!=1 then <<keepinput!!:=2; sub(%1=%2, !*hold(%0)) >> else begin scalar rulelist!!; rulelist!!:=list(%1,%2); rulelist!!:=list(part(rulelist!!,0):=replaceby); return %0 where rulelist!! end>>
#SubstituteParallel.2=if hold!!=0 then sub(%1,%0) else sub(%1,!*hold(%0))
Sum.1=<<begin scalar input!!; input!!:=%0;return for i:=1:length(input!!) sum part(input!!,i) end>>
Sum.4=<<begin scalar sm!!; sm!!:=if %2=-infinity and %3=infinity then limit(limit(sum(%0,%1,k!!,m!!),k!!,-infinity),m!!,infinity) else if %2=-infinity then limit(sum(%0,%1,k!!,%3),k!!,-infinity) else if %3=infinity then limit(sum(%0,%1,%2,k!!),k!!,infinity) else sum(%0,%1,%2,%3); return if freeof(sm!!,'sum) then sm!! else '? end>>
Take.3=<<begin scalar tmpret, list!!; list!!:=%0; tmpret:=list()$ for i:=%1:%2 do tmpret:=part(list!!,i).tmpret$ return reverse(tmpret) end>>
TaylorSeries.3=<<on div$ off pri$ taylortostandard(taylor(%0,ggbcasvarx,%1,%2))>>
TaylorSeries.4=<<on div$ off pri$ taylortostandard(taylor(%0,%1,%2,%3))>>
TDistribution.2=<<begin scalar t!!,n!!; n!!:=%0; t!!:=%1 ;beta!Regularized(((t!!+sqrt(t!!^2+n!!)/(2*sqrt(t!!^2+n!!)),n!!/2,n!!/2)
ToComplex.1=<<begin scalar list!!; list!!:=%0; return part(list!!,1)+i*part(list!!,2) end >>
ToExponential.1=<< begin scalar real!!, imag!!, input!!, mag!!, phi!!; input!!:=%0; if arglength(input!!)>-1 and part(input!!,0)='list then <<real!!:= part(input!!,1); imag!!:=part(input!!,2)>> else <<real!!:= repart(input!!); imag!!:=impart(input!!)>>;mag!!:=sqrt(real!!^2+imag!!^2); phi!!:=myatan2(imag!!,real!!); return if mag!!=0 then 0 else if phi!!=0 then mag!! else if mag!!=1 then part(list(i*phi!!),0):=exp else part(list(mag!!,part(list(i*phi!!),0):=exp),0):=* end>>
ToPolar.1=<< begin scalar input!!; input!!:=%0; return if arglength(input!!)>-1 and part(input!!,0)='list then if length(input!!)=2 then part(list(sqrt(part(input!!,1)^2+part(input!!,2)^2),myatan2(part(input!!,2),part(input!!,1))),0):=polartopoint!\u00a7 else '? else part(list(sqrt(repart(input!!)^2+impart(input!!)^2),myatan2(impart(input!!),repart(input!!))),0):=polartopoint!\u00a7 end >>
ToPoint.1=<< begin scalar input!!; input!!:=%0; return part(if arglength(input!!)>-1 and part(input!!,0)='list then input!! else list(repart(input!!),impart(input!!)),0):=point!\u00a7 end >>
Transpose.1=tp(<<listofliststomat(%0)>>)
#http://reduce-algebra.com/docs/trigsimp.pdf
TrigExpand.1=sub(list(x=ggbcasvarx),trigsimp(sub(list(ggbcasvarx=x),%0)))
TrigExpand.2=sub(list(x=ggbcasvarx),trigsimp(sub(list(ggbcasvarx=x),%0), part(%1,0)))
TrigExpand.3=<< begin scalar input1!!; input1!!:=sub(list(ggbcasvarx=x),%2); return sub(list(x=ggbcasvarx),trigsimp(sub(list(ggbcasvarx=x),%0), input1!!, part(%1,0))) end >>
TrigExpand.4=<< begin scalar input1!!, input2!!; input1!!:=sub(list(ggbcasvarx=x),%2); input2!!:=sub(list(ggbcasvarx=x),%3); return sub(list(x=ggbcasvarx),trigsimp(sub(list(ggbcasvarx=x),%0), input1!!, input2!!, part(%1,0))) end >>
TrigSimplify.1=sub(list(x=ggbcasvarx),trigsimp(sub(list(ggbcasvarx=x),%0),compact))
TrigCombine.1=sub(list(x=ggbcasvarx),trigsimp(sub(list(ggbcasvarx=x),%0),combine))
TrigCombine.2=sub(list(x=ggbcasvarx),trigsimp(sub(list(ggbcasvarx=x),%0),part(%1,0),combine))
Unique.1=mkset(%0)
UnitOrthogonalVector.1=<<begin; clear mat!!,norm!!; input!!:=%0;return if arglength(input!!)>-1 and part(input!!,0)='list then if length(input!!) neq 2 then '? else <<norm!!:=sqrt(<<for each i in input!! sum i^2>>); list(-part(input!!,2)/norm!!,part(input!!,1)/norm!!) >> else if length(input!!)=list(2,1) then <<norm!!:=sqrt(<<for i:=1:row\\_dim(input!!) sum input!!(i,1)^2>>); norm!!*mat((0,-1),(1,0))*input!! >> else if length(input!!)=list(1,2) then <<norm!!:=sqrt(<<for i:=1:column\\_dim(input!!) sum input!!(1,i)^2>>); norm!!*input!!*mat((0,-1),(1,0)) >> else '? end >>
UnitVector.1=<<begin; clear input!!; input!!:=%0; return if arglength(input!!)>-1 and part(input!!,0)='list then map(~w/sqrt(<<for each i in input!! sum i^2>>),input!!) else input!!/sqrt(<<for i:=1:row\\_dim(input!!) sum input!!(i,1)^2>>) end>>
Variance.1=<<begin scalar x!!,n!!,xd!!; x!!:=%0$ n!!:=length(x!!)$ xd!!:=1/n!!*for each i in x!! sum i; return 1/n!!* for each i in x!! sum (i-xd!!)**2 end>>
Weibull.3=1-exp(-(%0)*(%2)^(%1))
Zipf.4=<<begin scalar s; s:= %1; return if %3=true then harmonic(%2,s)/harmonic(%0,s) else 1/((%2)^s*harmonic(%0,s)) end>>
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