Function: bnrstarkunit
Section: number_fields
C-Name: bnrstarkunit
Prototype: GDG
Help: bnrstarkunit(bnr,{subgroup}): bnr being as output by bnrinit, returns
 the characteristic polynomial of the (conjectural) Stark unit corresponding
 to the module in bnr and the given congruence subgroup (the trivial subgroup
 if omitted). The ground field must be totally real and all but one infinite
 place must become complex in the class field.
Doc:
 \var{bnr} being as output by \kbd{bnrinit}, returns the characteristic
 polynomial of the (conjectural) Stark unit corresponding to the modulus in
 \var{bnr} and the given congruence subgroup (as usual, omit $\var{subgroup}$
 if you want the whole ray class group).

 The ground field attached to \var{bnr} must be totally real and
 all but one infinite place must become complex in the class field, which
 must be a quadratic extension of its totally real subfield. Finally,
 the output is given as a polynomial in $x$, so the main
 variable of \var{bnr} must not be $x$. Here is an example:
 \bprog
 ? bnf = bnfinit(y^2 - 2);
 ? bnr = bnrinit(bnf, [15, [1,0]]);
 ? lift(bnrstarkunit(bnr))
 %3 = x^8 + (-9000*y - 12728)*x^7 + (57877380*y + 81850978)*x^6 + ... + 1
 @eprog
