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Perhaps not. You are welcome to contribute the enhancement.

There is a related functionality implemented for multivariate polynomials via .lift() functions, which works like this:

sage: R.<x,y> = QQ[]
sage: J = R.ideal([x^2-2*x+4,x^2-5*x+6,x^2-4])
sage: gcd(J.gens()).lift(J)
[1/4, -1/10, -3/20]
sage: sum(map(prod,zip(_,J.gens()))) == gcd(J.gens())
True

Perhaps not. You are welcome to contribute the enhancement.

There is a related functionality implemented for multivariate polynomials via .lift() functions, 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([x^2-2*x+4,x^2-5*x+6,x^2-4])
R.ideal(pols)
sage: gcd(J.gens()).lift(J)
gcd(pols).lift(J)
[1/4, -1/10, -3/20]
sage: sum(map(prod,zip(_,J.gens()))) sum(map(prod,zip(_,pols))) == gcd(J.gens())
gcd(pols)
True

Perhaps not. You are welcome to contribute the enhancement.

There is a related functionality implemented for multivariate polynomials via .lift() functions, 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