Function: algdivl
Section: algebras
C-Name: algdivl
Prototype: DGGG
Help: algdivl({al},x,y): element x\y in al (Hamilton quaternions if omitted).
Doc: Given two elements $x$ and $y$ in \var{al} (Hamilton quaternions if
 omitted), computes their left quotient $x\backslash y$ in the algebra \var{al}:
 an element $z$ such that $xz=y$ (such an element is not unique when $x$ is a
 zerodivisor). If~$x$ is invertible, this is the same as $x^{-1}y$. Assumes that
 $y$ is left divisible by $x$ (i.e. that $z$ exists). Also accepts square
 matrices with coefficients in~\var{al}.

 \bprog
 ? A = alginit(nfinit(y),[-1,1]);
 ? x = [1,1]~; algisinv(A,x)
 % = 0
 ? z = algmul(A,x,algrandom(A,2))
 % = [0, 0, 0, 8]~
 ? algdivl(A,x,z)
 % = [4, 4, 0, 0]~
 @eprog
