The Gcd function is a placeholder for representing the greatest common divisor of a and b where a and b are polynomials. If s and t are specified, they are assigned the cofactors. Gcd is used in conjunction with either mod, modp1 or evala as described below which define the coefficient domain.

The call Gcd(a, b) mod p  computes the greatest common divisor of a and b modulo p a prime integer. The inputs a and b must be polynomials over the rationals or over a finite field specified by RootOf expressions.

The call modp1(Gcd(a, b), p) does likewise for a and b, polynomials in the modp1 representation.

The call  evala(Gcd(a, b))  does likewise for a and b, multivariate polynomials with algebraic coefficients defined by RootOf or radicals expressions. See evala,Gcd for more information.

$\mathrm{Gcd}\left(x+2\,x+3\right)\mathbf{mod}7$

$1$

$\mathrm{Gcd}\left(x^2+3x+2\,x^2+4x+3\,'s'\,'t'\right)\mathbf{mod}11$

$x+1$

$s,t$

$x+2,x+3$

$\mathrm{evala}\left(\mathrm{Gcd}\left(x^2-x-2^{\frac{1}{2}}x+2^{\frac{1}{2}}\,x^2-2\,'\mathrm{s1}'\,'\mathrm{t1}'\right)\right)$

$x-\sqrt{2}$

$\mathrm{s1},\mathrm{t1}$

$x-1,x+\sqrt{2}$

$\mathrm{evala}\left(\mathrm{Gcd}\left({\left(x^2-z\right)}^2\,{\left(x-\mathrm{RootOf}\left({\mathrm{\_Z}}^2-z\right)\right)}^3\right)\right)$

${\left(x-\mathrm{RootOf}\left({\mathrm{\_Z}}^2-z\right)\right)}^2$