extended Euclidean algorithm for polynomials
gcdex(A, B, x, 's', 't')
gcdex(A, B, C, x, 's', 't')
A, B, C
polynomials in the variable x
(optional) unevaluated names
For the first calling sequence (when 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 s⁢A+t⁢B=g where g is the monic GCD (Greatest Common Divisor) of A and B. The results computed satisfy degree⁡s<degree⁡Bg and degree⁡t<degree⁡Ag. The GCD g is returned as the function value.
If arguments s and t are specified, they are assigned the cofactors.
In the second calling sequence, gcdex solves the polynomial Diophantine equation s⁢A+t⁢B=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; otherwise, an error message is displayed. The polynomial s computed satisfies degree⁡s<degree⁡Bg. If degree⁡Cg<degree⁡Ag+degree⁡Bg then the polynomial t will satisfy degree⁡t<degree⁡Ag. The NULL value is returned as the function value.
In this case, s and t are not optional.
Note that if the input polynomials are multivariate then, in general, s and t will be rational functions in variables other than x.
Error, (in `gcdex/diophant`) the Diophantine equation has no solution
The gcdex command was updated in Maple 2018.
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