The quorem(A,B,x) function computes the element-wise quotient and remainder of A and B. Each expression in A and B is interpreted as a polynomial of x.  

If the optional argument x is omitted, then x is equal to findsym(A,1) if findsym(A,1) is not empty. Otherwise, x is equal to findsym(B,1) if findsym(B,1) is not empty. Otherwise, each expression in A and B must evaluate to an integer.  In this last case, the quorem(A,B) function computes the element-wise integer quotient and remainder of A and B.

If A is a scalar, then A is divided by each element of B.

If B is a scalar, then each element of A is divided by B.

When both and A and B are non-scalar, they must be the same size.

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$A≔\mathrm{Matrix}\left(2\,3\,'\mathrm{fill}'=108xy{z}^2+y^3\right)\:$

$B≔\mathrm{Matrix}\left(2\,3\,'\mathrm{fill}'=27xy\right)\:$

$\mathrm{quorem}\left(A\,B\right)$

$\left[\begin{array}{ccc}4z^2& 4z^2& 4z^2\\ 4z^2& 4z^2& 4z^2\end{array}\right]$

$q,r≔\mathrm{quorem}\left(⟨x^3-10x^2+31x-30\,x^2-1⟩\,⟨x^3-12x^2+41x-42\,x^2+2x+1⟩\right)\:$

$q$

$\left[\begin{array}{c}1\\ 1\end{array}\right]$

$r$

$\left[\begin{array}{c}2x^2-10x+12\\ -2x-2\end{array}\right]$

$q,r≔\mathrm{quorem}\left(⟨⟨56\,23⟩|⟨45\,24⟩⟩\,⟨⟨2\,7⟩|⟨5\,0⟩⟩\right)$

$q,r≔\left[\begin{array}{cc}28& 9\\ 3& \mathrm{\infty }\end{array}\right],\left[\begin{array}{cc}0& 0\\ 2& \mathrm{undefined}\end{array}\right]$

$q$

$\left[\begin{array}{cc}28& 9\\ 3& \mathrm{\infty }\end{array}\right]$

$r$

$\left[\begin{array}{cc}0& 0\\ 2& \mathrm{undefined}\end{array}\right]$

$q,r≔\mathrm{quorem}\left(x^2+y\,y^2+x\,x\right)\:$

$q$

$-y^2+x$

$r$

$y^4+y$

$q,r≔\mathrm{quorem}\left(x^2+y\,y^2+x\,y\right)\:$

$q$

$0$

$r$

$x^2+y$