Function: bnfsunit
Section: number_fields
C-Name: bnfsunit
Prototype: GGp
Help: bnfsunit(bnf,S): compute the fundamental S-units of the number field
 bnf output by bnfinit, S being a list of prime ideals. res[1] contains the
 S-units, res[5] the S-classgroup. See manual for details.
Doc: computes the fundamental $S$-units of the
 number field $\var{bnf}$ (output by \kbd{bnfinit}), where $S$ is a list of
 prime ideals (output by \kbd{idealprimedec}). The output is a vector $v$ with
 6 components.

 $v[1]$ gives a minimal system of (integral) generators of the $S$-unit group
 modulo the unit group.

 $v[2]$ contains technical data needed by \kbd{bnfissunit}.

 $v[3]$ is an empty vector (used to give the logarithmic embeddings of the
 generators in $v[1]$ in version 2.0.16).

 $v[4]$ is the $S$-regulator (this is the product of the regulator, the
 determinant of $v[2]$ and the natural logarithms of the norms of the ideals
 in $S$).

 $v[5]$ gives the $S$-class group structure, in the usual format
 (a row vector whose three components give in order the $S$-class number,
 the cyclic components and the generators).

 $v[6]$ is a copy of $S$.
