V = [1,2,3];
W = [4,5,6]~;
M = [1,2,3;4,5,6]
[1 2 3]
[4 5 6]
V*W
M*W
U = [1..10]

V[2]
W[1..2]
M[2,2]
M[1,]
M[,2]
M[1..2,1..2]
[1 2]
[4 5]

V=vector(10,i,1/i)
W=vectorv(10,i,1/i)
[1/i | i<-[1..10]]
[1/i | i<-[1..10]]~
M=matrix(4,4,i,j,i*j)
matdiagonal([1,2,3,4])

C1 = [1,2,3]~; C2=[4,5,6]~;
concat(C1,C2)
matconcat([C1,C2])
 [1,4;2,5;3,6]
matid(5)
matconcat([C1,C2])

matdet([1,2;3,4]) \\ determinant
M = [1,2,3;4,5,6];
M~ \\ transposition
matsize(M) \\ dimensions
matrank(M) \\ rank
K=matker(M) \\ kernel
M*K

V = vector(10,i,random(10^10));
M = matconcat([matid(10),V]~);
T = qflll(M)
B = qflll(M,3)
M*T==B
Q = M~*M;
U = qflllgram(Q)
T == U

E8 = matrix(8,8,i,j,if(i==1&&j==1,4, \
       i==j || (i==1 && j<8) || (j==1 && i<8),2,1));
E8==E8~ \\ symmetric
matdet(E8) \\ unimodular
qfsign(E8) \\ signature
L = qfminim(E8); L[1..2] \\ 240 minimal vectors of norm 2
V = L[3][,1] \\ one minimal vector
qfeval(E8,V) \\ the norm is 2

qfperfection(E8) \\ perfection rank
G=qfauto(E8); G[1] \\ number of isometries
A=G[2][1] \\ one isomorphim
A~*E8*A==E8

[mf,F,C]=mffromqf(E8);
mfparams(F)
mfcoefs(F,10)
mfcoef(F,100003)
L = lfunqf(E8);
lfunparams(L)
lfun(L,0)
?67 = -1;

V=concat([vector(23,i,2*i+1),51,145]);
K=matkerint(Mat(V));
M=matdiagonal(vector(25,i,if(i==25,-1,1)));
L24 = K~*M*K;