SageMath has a built-in method for performing the extended Euclidean algorithm for two numbers (or polynomials), called xgcd. The algorithm also works for several arguments, by recursion. One can implement this easily with a SageMath helper function, but I was wondering: does SageMath have a built-in extension of xgcd to several arguments?
Perhaps not. You are welcome to contribute the enhancement.
There is a related functionality implemented for multivariate polynomials via .lift() method, which works like this:
sage: R.<x,y> = QQ[]
sage: pols = [x^2-2*x+4,x^2-5*x+6,x^2-4]
sage: J = R.ideal(pols)
sage: gcd(pols).lift(J)
[1/4, -1/10, -3/20]
sage: sum(map(prod,zip(_,pols))) == gcd(pols)
True
Asked: 2023-09-28 09:59:24 +0200
Seen: 370 times
Last updated: Sep 30 '23
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