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The problem is that for these kind of inexact rings the methods are not implemented.

For the resultant, you can compute the resultant with

a.sylvester_matrix(b,x).det()

But I cannot promise performance nor numeric stability.

The gcd is more tricky. For instance, if you take univariate polynomials over an inexact rings and perform Euclides method, you will end with a gcd 1 due to numerical errors. You are asking for an approximate gcd which is not easy to compute.