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The numer := numden(M) calling sequence computes the numerator of the expression M.

The (numer,denom) := numden(M) calling sequence computes both the numerator of M, which is stored in the variable numer, and the denominator of M, which is stored in the variable denom.

The numden(M) function computes element-wise numerator and denominator of M. The results, R1 and R2, are formed as R1[i,j] = numer(M[i,j]) and R2[i,j] = denom(M[i,j]).

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

$M≔\mathrm{Matrix}\left(2\,3\,'\mathrm{fill}'=\frac{x}{y}+\frac{y}{x}\right)\:$

$\mathrm{numden}\left(M\right)$

$\left[\begin{array}{ccc}{x}^2+y^2& x^2+y^2& x^2+y^2\\ x^2+y^2& x^2+y^2& x^2+y^2\end{array}\right],\left[\begin{array}{ccc}yx& yx& yx\\ yx& yx& yx\end{array}\right]$