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

 > $\mathrm{Gcd}\left(x+2,x+3\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}7$
 ${1}$ (1)
 > $\mathrm{Gcd}\left({x}^{2}+3x+2,{x}^{2}+4x+3,'s','t'\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}11$
 ${x}{+}{1}$ (2)
 > $s,t$
 ${x}{+}{2}{,}{x}{+}{3}$ (3)
 > $\mathrm{evala}\left(\mathrm{Gcd}\left({x}^{2}-x-{2}^{\frac{1}{2}}x+{2}^{\frac{1}{2}},{x}^{2}-2,'\mathrm{s1}','\mathrm{t1}'\right)\right)$
 ${x}{-}\sqrt{{2}}$ (4)
 > $\mathrm{s1},\mathrm{t1}$
 ${x}{-}{1}{,}{x}{+}\sqrt{{2}}$ (5)
 > $\mathrm{evala}\left(\mathrm{Gcd}\left({\left({x}^{2}-z\right)}^{2},{\left(x-\mathrm{RootOf}\left({\mathrm{_Z}}^{2}-z\right)\right)}^{3}\right)\right)$
 ${\left({x}{-}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{-}{z}\right)\right)}^{{2}}$ (6)