Function: rnfpolredabs
Section: number_fields
C-Name: rnfpolredabs
Prototype: GGD0,L,
Help: rnfpolredabs(nf,pol,{flag=0}): given a pol with coefficients in nf,
 finds a relative simpler polynomial defining the same field. Binary digits
 of flag mean: 1: return also the element whose characteristic polynomial is
 the given polynomial, 2: return an absolute polynomial, 16: partial
 reduction.
Doc: relative version of
 \kbd{polredabs}. Given a monic polynomial \var{pol} with coefficients in
 $\var{nf}$, finds a simpler relative polynomial defining the same field. The
 binary digits of $\fl$ mean

 1: returns $[P,a]$ where $P$ is the default output and $a$ is an
 element expressed on a root of $P$ whose characteristic polynomial is
 \var{pol}

 2: returns an absolute polynomial (same as
 {\tt rnfequation(\var{nf},rnfpolredabs(\var{nf},\var{pol}))}
 but faster).

 16: possibly use a suborder of the maximal order. This is slower than the
 default when the relative discriminant is smooth, and much faster otherwise.
 See \secref{se:polredabs}.

 \misctitle{Remark} In the present implementation, this is both faster and
 much more efficient than \kbd{rnfpolred}, the difference being more
 dramatic than in the absolute case. This is because the implementation of
 \kbd{rnfpolred} is based on (a partial implementation of) an incomplete
 reduction theory of lattices over number fields, the function
 \kbd{rnflllgram}, which deserves to be improved.
