Gcdex
inert gcdex function
Calling Sequence
Parameters
Description
Examples
Gcdex(a, b, x, 's', 't')
a, b
-
multivariate polynomials
x
main variable
s, t
(optional) unevaluated names
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,x<degreeb,x and degreet,x<degreea,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.
Gcdexx2+x+1,x2−x+1,x,s,tmod11
1
s,t
5x+6,6x+6
aliassqrt2=RootOfx2−2:
evalaGcdexx2−2,x2−sqrt2x,x,s,t
−sqrt2+x
sqrt22,−sqrt22
See Also
evala
Gcd
gcdex
mod
RootOf
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