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