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Gcdex

inert gcdex function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Gcdex(a, b, x, 's', 't')

Parameters

a, b

-

multivariate polynomials

x

-

main variable

s, t

-

(optional) unevaluated names

Description

• 

The Gcdex function is a placeholder for the extended Euclidean algorithm applied to a and b which are polynomials in x over a field.  Gcdex computes g, the greatest common divisor of a and b, which is a monic polynomial in x.  Additionally s and t are (if present) assigned polynomials in x such that  as+bt=g  with degrees&comma;x<degreeb&comma;x and degreet&comma;x<degreea&comma;x. Gcdex is used in conjunction with either mod or evala as described below, both of which define the coefficient domain.

• 

The call Gcdex(a, b, x, 's', 't') mod p performs the computation modulo p a prime integer. The multivariate polynomials a and b must have rational coefficients or coefficients in a finite field specified by RootOfs.

• 

The call evala(Gcdex(a, b, x, 's', 't')) does likewise. The multivariate polynomials a and b must have algebraic number (or function) coefficients specified by RootOfs.

Examples

Gcdex(x^2+x+1,x^2-x+1,x,'s','t') mod 11;

1

(1)

s, t;

5x+6,6x+6

(2)

alias(sqrt2=RootOf(x^2-2)):

evala(Gcdex(x^2-2,x^2-sqrt2*x,x,'s','t'));

sqrt2+x

(3)

s, t;

sqrt22,sqrt22

(4)

See Also

evala

Gcd

gcdex

mod

RootOf