Use cached_method for FractionField.is_exact

[nthiery]

Before the patch:

    sage: sage: P = ZZ['x']
    sage: R = P.fraction_field()
    sage: %timeit R.is_exact()
    625 loops, best of 3: 3.7 µs per loop

After the patch:

    sage: R=FractionField(ZZ['x'])
    sage: %timeit R.is_exact()
    625 loops, best of 3: 485 ns per loop

Thank you Simon King for #11115!

This is non negligible because is_exact is called basically each
time an element is constructed or arithmetic is performed. Here we
have a 10% improvement on constructing an element:

Before the patch:

    sage: x = P.gen()
    sage: y = x+1
    sage: %timeit R(x,y,coerce=False)
    625 loops, best of 3: 17.7 µs per loop

After the patch:

    sage: x = P.gen()
    sage: y = x+1
    sage: %timeit R(x,y,coerce=False)
    625 loops, best of 3: 16 µs per loop

CC: @simon-king-jena

Component: performance

Author: Nicolas M. Thiéry

Reviewer: David Loeffler

Merged: sage-5.0.beta9

Issue created by migration from https://trac.sagemath.org/ticket/12527

[nthiery]

comment:1

Attachment: trac_12527-fraction_field-is_exact_optimization-nt.patch.gz

Simon: you deserve this trivial review, for all your hard work on other related tickets :-)

[loefflerd]

comment:2

Isn't patchbot great? It makes reviewing patches like this a 10-second job. Sorry Simon!

[loefflerd]

Changed reviewer from Simon King to David Loeffler

[jdemeyer]

Merged: sage-5.0.beta9