Function: polred
Section: number_fields
C-Name: polred0
Prototype: GD0,L,DG
Obsolete: 2013-03-27
Help: polred(T,{flag=0}): deprecated, use polredbest. Reduction of the
 polynomial T (gives minimal polynomials only). The following binary digits of
 (optional) flag are significant 1: partial reduction, 2: gives also elements.
Doc: This function is \emph{deprecated}, use \tet{polredbest} instead.
 Finds polynomials with reasonably small coefficients defining subfields of
 the number field defined by $T$. One of the polynomials always defines $\Q$
 (hence has degree $1$), and another always defines the same number field
 as $T$ if $T$ is irreducible.

 All $T$ accepted by \tet{nfinit} are also allowed here;
 in particular, the format \kbd{[T, listP]} is recommended, e.g. with
 $\kbd{listP} = 10^5$ or a vector containing all ramified primes. Otherwise,
 the maximal order of $\Q[x]/(T)$ must be computed.

 The following binary digits of $\fl$ are significant:

 1: Possibly use a suborder of the maximal order. The
 primes dividing the index of the order chosen are larger than
 \tet{primelimit} or divide integers stored in the \tet{addprimes} table.
 This flag is \emph{deprecated}, the \kbd{[T, listP]} format is more
 flexible.

 2: gives also elements. The result is a two-column matrix, the first column
 giving primitive elements defining these subfields, the second giving the
 corresponding minimal polynomials.
 \bprog
 ? M = polred(x^4 + 8, 2)
 %1 =
 [           1         x - 1]

 [ 1/2*x^2 + 1 x^2 - 2*x + 3]

 [-1/2*x^2 + 1 x^2 - 2*x + 3]

 [     1/2*x^2       x^2 + 2]

 [     1/4*x^3       x^4 + 2]
 ? minpoly(Mod(M[2,1], x^4+8))
 %2 = x^2 + 2
 @eprog

 \synt{polred}{GEN T} ($\fl = 0$). Also available is
 \fun{GEN}{polred2}{GEN T} ($\fl = 2$). The function \kbd{polred0} is
 deprecated, provided for backward compatibility.
