1Function: ideallistarch
2Section: number_fields
3C-Name: ideallistarch
4Prototype: GGG
5Help: ideallistarch(nf,list,arch): list is a vector of vectors of bid's as
6 output by ideallist. Return a vector of vectors with the same number of
7 components as the original list. The leaves give information about
8 moduli whose finite part is as in original list, in the same order, and
9 Archimedean part is now arch. The information contained is of the same kind
10 as was present in the input.
11Doc:
12 \var{list} is a vector of vectors of bid's, as output by \tet{ideallist} with
13 flag $0$ to $3$. Return a vector of vectors with the same number of
14 components as the original \var{list}. The leaves give information about
15 moduli whose finite part is as in original list, in the same order, and
16 Archimedean part is now \var{arch} (it was originally trivial). The
17 information contained is of the same kind as was present in the input; see
18 \tet{ideallist}, in particular the meaning of \fl.
19
20 \bprog
21 ? bnf = bnfinit(x^2-2);
22 ? bnf.sign
23 %2 = [2, 0]                         \\@com two places at infinity
24 ? L = ideallist(bnf, 100, 0);
25 ? l = L[98]; vector(#l, i, l[i].clgp)
26 %4 = [[42, [42]], [36, [6, 6]], [42, [42]]]
27 ? La = ideallistarch(bnf, L, [1,1]); \\@com add them to the modulus
28 ? l = La[98]; vector(#l, i, l[i].clgp)
29 %6 = [[168, [42, 2, 2]], [144, [6, 6, 2, 2]], [168, [42, 2, 2]]]
30 @eprog
31 Of course, the results above are obvious: adding $t$ places at infinity will
32 add $t$ copies of $\Z/2\Z$ to $(\Z_K/f)^*$. The following application
33 is more typical:
34 \bprog
35 ? L = ideallist(bnf, 100, 2);        \\@com units are required now
36 ? La = ideallistarch(bnf, L, [1,1]);
37 ? H = bnrclassnolist(bnf, La);
38 ? H[98];
39 %4 = [2, 12, 2]
40 @eprog
41