 Gcd - Maple Programming Help

Gcd

inert gcd function

 Calling Sequence Gcd(a, b) Gcd(a, b, 's', 't')

Parameters

 a, b - multivariate polynomials s, t - (optional) unevaluated names

Description

 • 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.

Examples

 > Gcd(x+2,x+3) mod 7;
 ${1}$ (1)
 > Gcd(x^2+3*x+2,x^2+4*x+3,'s','t') mod 11;
 ${x}{+}{1}$ (2)
 > s, t;
 ${x}{+}{2}{,}{x}{+}{3}$ (3)
 > evala(Gcd(x^2-x-2^(1/2)*x+2^(1/2), x^2-2, 's1', 't1'));
 ${x}{-}\sqrt{{2}}$ (4)
 > s1, t1;
 ${x}{-}{1}{,}{x}{+}\sqrt{{2}}$ (5)
 > evala(Gcd((x^2-z)^2, (x-RootOf(_Z^2-z))^3));
 ${\left({x}{-}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{-}{z}\right)\right)}^{{2}}$ (6)