Function: rnfsteinitz
Section: number_fields
C-Name: rnfsteinitz
Prototype: GG
Help: rnfsteinitz(nf,x): given an order x as output by rnfpseudobasis,
 gives [A,I,D,d] where (A,I) is a pseudo basis where all the ideals except
 perhaps the last are trivial.
Doc: given a number field $\var{nf}$ as
 output by \kbd{nfinit} and either a polynomial $x$ with coefficients in
 $\var{nf}$ defining a relative extension $L$ of $\var{nf}$, or a pseudo-basis
 $x$ of such an extension as output for example by \kbd{rnfpseudobasis},
 computes another pseudo-basis $(A,I)$ (not in HNF in general) such that all
 the ideals of $I$ except perhaps the last one are equal to the ring of
 integers of $\var{nf}$, and outputs the four-component row vector $[A,I,D,d]$
 as in \kbd{rnfpseudobasis}. The name of this function comes from the fact
 that the ideal class of the last ideal of $I$, which is well defined, is the
 \idx{Steinitz class} of the $\Z_K$-module $\Z_L$ (its image in $SK_0(\Z_K)$).
