Steps To Reproduce

Substitutions in the fraction field of a polynomial ring are much slower than necessary:

sage: P = PolynomialRing(QQ, ["x%s" % i for i in range(1000)])
sage: PF = P.fraction_field()
sage: p = sum(i*P.gen(i) for i in range(50,52)) / sum(i*P.gen(i) for i in range(51,53)); v = P.gen(51)
sage: %time p.subs({v: 100})
CPU times: user 55.4 ms, sys: 0 ns, total: 55.4 ms
Wall time: 55.4 ms
(50*x50 + 5100)/(52*x52 + 5100)
sage: %time p.numerator().subs({v: 100}) / p.denominator().subs({v: 100})
CPU times: user 3.32 ms, sys: 0 ns, total: 3.32 ms
Wall time: 3.33 ms
(50*x50 + 5100)/(52*x52 + 5100)

Expected Behavior

There should be not much difference in timing.

Actual Behavior

The method called is Element.subs, which, first of all, creates a dictionary containing all the gens of the parent.

Additional Information

#1381 seems to be orthogonal to this.

Environment

irrelevant.

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide