The gcd function computes the greatest common divisor of two polynomials A and B.

The optional argument x specifies the dependant variable.  If unspecified, findsym(A,1) or findsym(B,1) is used (whichever returns a non-NULL result first).  Note that if the input polynomials are multivariate then, in general, s and t will be rational functions in variables other than x.

The extended Euclidean algorithm is applied by gcd to compute unique polynomials s, t and g in x such that s*A + t*B = g where g is the monic greatest common divisor of A and B. The results computed satisfy degree(s) < degree(B/g) and degree(t) < degree(A/g). The greatest common divisor g is returned as the function value.

If A and B are arrays, the gcd(A,B) function computes the element-wise greatest common divisor of A and B.

If A is a scalar and B is an array then gcd computes the greatest common divisor of A and each element of B.

Arrays A and B must be the same size.

$\mathrm{with}\left(\mathrm{MTM}\right)\&colon;$

$A≔\mathrm{Matrix}\left(2\&comma;3\&comma;'\mathrm{fill}'=12x\right)\&colon;$

$B≔\mathrm{Matrix}\left(2\&comma;3\&comma;'\mathrm{fill}'=27xy\right)\&colon;$

$\gcd \left(A\&comma;B\right)$

$\left[\begin{array}{ccc}x& x& x\\ x& x& x\end{array}\right]$

$g,c,d≔\gcd \left(⟨x^3-10x^2+31x-30\&comma;x^2-1⟩\&comma;⟨x^3-12x^2+41x-42\&comma;x^2+2x+1⟩\right)$

$g,c,d≔\left[\begin{array}{c}{x}^2-5x+6\\ x+1\end{array}\right],\left[\begin{array}{c}\frac{1}{2}\\ -\frac{1}{2}\end{array}\right],\left[\begin{array}{c}-\frac{1}{2}\\ \frac{1}{2}\end{array}\right]$