Possibly the problem is that MPolynomial.gcd calls 
UniqueFactorizationDomains.ParentMethods._gcd_univariate_polynomial, which 
recurses on MPolynomial.gcd, but the setup done by MPolynomial.gcd is 
possibly not cheap.

On Sunday 3 November 2024 at 12:31:44 UTC+1 Martin R wrote:

> Are the following timings to be expected?
>
> sage: R = SymmetricFunctions(QQ).h().fraction_field()
> sage: P = PolynomialRing(R, 200, "x")
> sage: e = P.gen(199); e
> x199
> sage: %time e.gcd(e)
> CPU times: user 41.1 s, sys: 2.24 s, total: 43.4 s
> Wall time: 43.5 s
> x199
>
> sage: R = QQ
> sage: P = PolynomialRing(R, 200, "x")
> sage: e = P.gen(199); e
> x199
> sage: %time e.gcd(e)
> CPU times: user 41 µs, sys: 0 ns, total: 41 µs
> Wall time: 47 µs
> x199
>
> sage: R = QQbar
> sage: P = PolynomialRing(R, 200, "x")
> sage: e = P.gen(199); e
> x199
> sage: %time e.gcd(e)
> CPU times: user 3.02 s, sys: 183 ms, total: 3.2 s
> Wall time: 3.21 s
> x199
>

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