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Gcd

inert gcd function

 

Calling Sequence

Parameters

Description

Examples

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'));

x2

(4)

s1, t1;

x1,x+2

(5)

evala(Gcd((x^2-z)^2, (x-RootOf(_Z^2-z))^3));

xRootOf_Z2z2

(6)

See Also

evala

gcd

Gcdex

mod

RootOf