Online Help

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.

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

$1$

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

$x+1$

$s,t$

$x+2,x+3$

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

$x-\sqrt{2}$

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

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

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

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