Function: nfsubfields
Section: number_fields
C-Name: nfsubfields
Prototype: GD0,L,
Help: nfsubfields(pol,{d=0}): find all subfields of degree d of number field
defined by pol (all subfields if d is null or omitted). Result is a vector of
subfields, each being given by [g,h], where g is an absolute equation and h
expresses one of the roots of g in terms of the root x of the polynomial
defining nf.
Doc: finds all subfields of degree
$d$ of the number field defined by the (monic, integral) polynomial
\var{pol} (all subfields if $d$ is null or omitted). The result is a vector
of subfields, each being given by $[g,h]$, where $g$ is an absolute equation
and $h$ expresses one of the roots of $g$ in terms of the root $x$ of the
polynomial defining $\var{nf}$. This routine uses J.~Kl\"uners's algorithm
in the general case, and B.~Allombert's \tet{galoissubfields} when \var{nf}
is Galois (with weakly supersolvable Galois group).\sidx{Galois}\sidx{subfield}