divrem

Function: divrem
Section: operators
C-Name: divrem
Prototype: GGDn
Help: divrem(x,y,{v}): euclidean division of x by y giving as a
 2-dimensional column vector the quotient and the remainder, with respect to
 v (to main variable if v is omitted).
Doc: creates a column vector with two components, the first being the Euclidean
 quotient (\kbd{$x$ \bs\ $y$}), the second the Euclidean remainder
 (\kbd{$x$ - ($x$\bs$y$)*$y$}), of the division of $x$ by $y$. This avoids the
 need to do two divisions if one needs both the quotient and the remainder.
 If $v$ is present, and $x$, $y$ are multivariate
 polynomials, divide with respect to the variable $v$.

 Beware that \kbd{divrem($x$,$y$)[2]} is in general not the same as
 \kbd{$x$ \% $y$}; no GP operator corresponds to it:
 \bprog
 ? divrem(1/2, 3)[2]
 %1 = 1/2
 ? (1/2) % 3
 %2 = 2
 ? divrem(Mod(2,9), 3)[2]
  ***   at top-level: divrem(Mod(2,9),3)[2
  ***                 ^--------------------
  ***   forbidden division t_INTMOD \ t_INT.
 ? Mod(2,9) % 6
 %3 = Mod(2,3)
 @eprog
Variant: Also available is \fun{GEN}{gdiventres}{GEN x, GEN y} when $v$ is
 not needed.