\p 38
\e
algdep(2*cos(2*Pi/13),6)
algdep(2*cos(2*Pi/13),6,15)
charpoly([1,2;3,4],z)
charpoly(Mod(x^2+x+1,x^3+5*x+1),z)
charpoly([1,2;3,4],z,1)
charpoly(Mod(1,8191)*[1,2;3,4],z,2)
lindep(Mod(1,7)*[2,-1;1,3],-2)
lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
matadjoint([1,2;3,4])
matcompanion(x^5-12*x^3+0.0005)
matdet([1,2,3;1,5,6;9,8,7])
matdet([1,2,3;1,5,6;9,8,7],1)
matdetint([1,2,3;4,5,6])
matdiagonal([2,4,6])
mateigen([1,2,3;4,5,6;7,8,9])
mathess(mathilbert(7))
mathilbert(5)
amat=1/mathilbert(7)
mathnf(amat)
mathnf(amat,1)
mathnf(amat,4)
mathnf(amat,3)
mathnfmod(amat,matdetint(amat))
mathnfmodid(amat,123456789*10^100)
matid(5)
matimage([1,3,5;2,4,6;3,5,7])
matimage([1,3,5;2,4,6;3,5,7],1)
matimage(Pi*[1,3,5;2,4,6;3,5,7])
matimagecompl([1,3,5;2,4,6;3,5,7])
matimagecompl(Pi*[1,3,5;2,4,6;3,5,7])
matindexrank([1,1,1;1,1,1;1,1,2])
matintersect([1,2;3,4;5,6],[2,3;7,8;8,9])
matinverseimage([1,1;2,3;5,7],[2,2,6]~)
matisdiagonal([1,0,0;0,5,0;0,0,0])
matker(matrix(4,4,x,y,x/y))
matker(matrix(4,4,x,y,sin(x+y)))
matker(matrix(4,4,x,y,x+y),1)
matkerint(matrix(4,4,x,y,x*y))
matkerint(matrix(4,4,x,y,x*y),1)
matkerint(matrix(4,6,x,y,2520/(x+y)))
matmuldiagonal(amat,[1,2,3,4,5,6,7])
matmultodiagonal(amat^-1,%)
matpascal(8)
matrank(matrix(5,5,x,y,x+y))
matrix(5,5,x,y,gcd(x,y))
matrixqz([1,3;3,5;5,7],0)
matrixqz([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0],-1)
matrixqz([1,3;3,5;5,7],-2)
matsize([1,2;3,4;5,6])
matsnf(matrix(5,5,j,k,random))
matsnf(1/mathilbert(6))
matsnf(x*matid(5)-matrix(5,5,j,k,1),2)
matsolve(mathilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
matsolvemod([2,3;5,4],[7,11],[1,4]~)
matsolvemod([2,3;5,4],[7,11],[1,4]~,1)
matsupplement([1,3;2,4;3,6])
mattranspose(vector(2,x,x))
%*%~
norml2(vector(10,x,x))
qfgaussred(mathilbert(5))
qfjacobi(mathilbert(6))
m=1/mathilbert(7)
mp=concat(m,matid(7))
qflll(m)
qflll(m,7)
qflllgram(m)
qflllgram(m,7)
qflllgram(m,1)
qflllgram(mp~*mp,4)
qflll(m,1)
qflll(m,2)
qflll(mp,4)
qfminim([2,1;1,2],4,6)
qfperfection([2,0,1;0,2,1;1,1,2])
qfsign(mathilbert(5)-0.11*matid(5))
aset=Set([5,-2,7,3,5,1])
bset=Set([7,5,-5,7,2])
setintersect(aset,bset)
setisset([-3,5,7,7])
setminus(aset,bset)
setsearch(aset,3)
setsearch(bset,3)
setunion(aset,bset)
trace(1+I)
trace(Mod(x+5,x^3+x+1))
Vec(sin(x))
vecmax([-3,7,-2,11])
vecmin([-3,7,-2,11])
concat([1,2],[3,4])
concat(Mat(vector(4,x,x)~),vector(4,x,10+x)~)
vecextract([1,2,3,4,5,6,7,8,9,10],1000)
vecextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
(1.*mathilbert(7))^(-1)
vecsort([8,7,6,5],,1)
vecsort([[1,5],[2,4],[1,5,1],[1,4,2]],,2)
vecsort(vector(17,x,5*x%17))
vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],2)
vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],[2,1])
vector(10,x,1/x)
setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8))
setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8))
getheap
print("Total time spent: ",gettime);
\q