chargalois

Function: chargalois
Section: number_theoretical
C-Name: chargalois
Prototype: GDG
Help: chargalois(cyc,{ORD}): let cyc represent a finite abelian group G
 by its elementary divisors cyc, return a list of representatives for the
 Galois orbits of characters of G. If ORD is present, select characters
 depending on their orders: if ORD is a t_INT, restrict to orders less than
 this bound; if ORD is a t_VEC or t_VECSMALL, restrict to orders in the list.
Doc: Let \var{cyc} represent a finite abelian group by its elementary divisors
 (any object which has a \kbd{.cyc} method is also allowed, i.e. the output of
 \kbd{znstar} or \kbd{bnrinit}). Return a list of representatives for the
 Galois orbits of complex characters of $G$.
 If \kbd{ORD} is present, select characters depending on their orders:

 \item if \kbd{ORD} is a \typ{INT}, restrict to orders less than this
 bound;

 \item if \kbd{ORD} is a \typ{VEC} or \typ{VECSMALL}, restrict to orders in
 the list.

 \bprog
 ? G = znstar(96);
 ? #chargalois(G) \\ 16 orbits of characters mod 96
 %2 = 16
 ? #chargalois(G,4) \\ order less than 4
 %3 = 12
 ? chargalois(G,[1,4]) \\ order 1 or 4; 5 orbits
 %4 = [[0, 0, 0], [2, 0, 0], [2, 1, 0], [2, 0, 1], [2, 1, 1]]
 @eprog\noindent
 Given a character $\chi$, of order $n$ (\kbd{charorder(G,chi)}), the
 elements in its orbit are the $\phi(n)$ characters $\chi^i$, $(i,n)=1$.