Function: idealaddtoone
Section: number_fields
C-Name: idealaddtoone0
Prototype: GGDG
Help: idealaddtoone(nf,x,{y}): if y is omitted, when the sum of the ideals
 in the number field K defined by nf and given in the vector x is equal to
 Z_K, gives a vector of elements of the corresponding ideals who sum to 1.
 Otherwise, x and y are ideals, and if they sum up to 1, find one element in
 each of them such that the sum is 1.
Doc: $x$ and $y$ being two co-prime
 integral ideals (given in any form), this gives a two-component row vector
 $[a,b]$ such that $a\in x$, $b\in y$ and $a+b=1$.

 The alternative syntax $\kbd{idealaddtoone}(\var{nf},v)$, is supported, where
 $v$ is a $k$-component vector of ideals (given in any form) which sum to
 $\Z_{K}$. This outputs a $k$-component vector $e$ such that $e[i]\in x[i]$ for
 $1\le i\le k$ and $\sum_{1\le i\le k}e[i]=1$.
