1Function: algmultable
2Section: algebras
3C-Name: algmultable
4Prototype: mG
5Help: algmultable(al): multiplication table of al over its prime subfield.
6Doc:
7 returns a multiplication table of \var{al} over its
8 prime subfield ($\Q$ or $\F_p$), as a \typ{VEC} of \typ{MAT}: the left
9 multiplication tables of basis elements. If \var{al} was output by
10 \tet{algtableinit}, returns the multiplication table used to define \var{al}.
11 If \var{al} was output by \tet{alginit}, returns the multiplication table of
12 the order~${\cal O}_0$ stored in \var{al}.
13 \bprog
14 ? A = alginit(nfinit(y), [-1,-1]);
15 ? M = algmultable(A);
16 ? #M
17 %3 = 4
18 ? M[1]  \\ multiplication by e_1 = 1
19 %4 =
20 [1 0 0 0]
21
22 [0 1 0 0]
23
24 [0 0 1 0]
25
26 [0 0 0 1]
27
28 ? M[2]
29 %5 =
30 [0 -1  1  0]
31
32 [1  0  1  1]
33
34 [0  0  1  1]
35
36 [0  0 -2 -1]
37 @eprog
38