gcdex - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Algebra : Polynomials : Operations : gcdex

gcdex

extended Euclidean algorithm for polynomials

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

gcdex(A, B, x, 's', 't')

gcdex(A, B, C, x, 's','t')

Parameters

A, B, C

-

polynomials in the variable x

x

-

variable name

s, t

-

(optional) unevaluated names

Description

• 

If the number of parameters is less than six, gcdex applies the extended Euclidean algorithm to compute unique polynomials s, t and g in x such that sA+tB=g where g is the monic GCD (Greatest Common Divisor) of A and B. The results computed satisfy degrees<degreeBg and degreet<degreeAg. The GCD g is returned as the function value.

• 

In the case of six parameters, gcdex solves the polynomial Diophantine equation sA+tB=C for polynomials s and t in x. Let g be the GCD of A and B. The input polynomial C must be divisible by g. The polynomial s computed satisfies degrees<degreeBg. If degreeCg<degreeAg&plus;degreeBg then the polynomial t will satisfy degreet<degreeAg. The NULL value is returned as the function value.

• 

Note that if the input polynomials are multivariate then, in general, s and t will be rational functions in variables other than x.

Examples

gcdexx31&comma;x21&comma;x&comma;&apos;s&apos;&comma;&apos;t&apos;

1&plus;x

(1)

s&comma;t

1&comma;x

(2)

gcdexx2&plus;a&comma;x21&comma;x2a&comma;x&comma;&apos;s&apos;&comma;&apos;t&apos;

s&comma;t

1&plus;aa&plus;1&comma;2aa&plus;1

(3)

gcdex1&comma;x&comma;12x&plus;4x2&comma;x&comma;&apos;s&apos;&comma;&apos;t&apos;

s&comma;t

1&comma;4x2

(4)

See Also

degree

gcd

Gcdex

igcdex

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam