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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&plus;bt&equals;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

Gcdexx2&plus;x&plus;1&comma;x2x&plus;1&comma;x&comma;&apos;s&apos;&comma;&apos;t&apos;mod11

1

(1)

s&comma;t

5x&plus;6&comma;6x&plus;6

(2)

aliassqrt2&equals;RootOfx22&colon;

evalaGcdexx22&comma;x2sqrt2x&comma;x&comma;&apos;s&apos;&comma;&apos;t&apos;

sqrt2&plus;x

(3)

s&comma;t

12sqrt2&comma;12sqrt2

(4)

See Also

evala

Gcd

gcdex

mod

RootOf

 


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