I'm wondering if Sage has the following function for polynomials over
a field.  Mostly, I don't know if it is a common thing to expect, and
if so, I have no idea what it would be called.  So a pointer would be
of real help, if it  exists.  The paper I am cribbing from is about
matrices over ZZ, but I suspect it generalizes to any PID, so I may
not be translating everything exactly right (eg the degree condition).

Input:  p, q, r in F[x] with  gcd(p, q, r) = 1

Output: s  in F[x] such that  gcd(p + sq, r) = 1, degree(s) <
degree(r)

Thanks,
Rob

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