faster coercion from Integer to Quadratic Number fields

[vdelecroix]

As suggested in ​this thread on sage-devel, the patch implements a faster coercion from the integers to quadratic number fields.

To avoid rebase I put dependencies on #13213 and #13256.

[vbraun]

There is a block of commented-out code under

# we ignore the code below because of the morphism 

If its not used then delete it, don't leave commented-out chunks of code lying around. Is there a performance difference with this branch removed? It looks like an attempt to deliberately circumvent the morphism to me.

[vdelecroix]

Thanks for having a look.

I commented the code because it was never used because of the coercion system (see the __call__ of Parent). It was the case even before my patch. I think the gain is minor but the fact is that it was unused. I will remove it.

Here are some timings, the improvement is somwhere around x10.

without

sage: K=QuadraticField(2)
sage: q = 12   
sage: %timeit K(q)
100000 loops, best of 3: 10.3 us per loop
sage: g = K.gen()
sage: %timeit q*g
1000000 loops, best of 3: 1.66 us per loop
sage: %timeit q+g
100000 loops, best of 3: 13.2 us per loop

with

sage: K=QuadraticField(2)
sage: q = 12   
sage: %timeit K(q)
1000000 loops, best of 3: 660 ns per loop
sage: g = K.gen()
sage: %timeit q*g
1000000 loops, best of 3: 1.74 us per loop
sage: %timeit q+g
100000 loops, best of 3: 2.76 us per loop

There is no difference for the multiplication because the methods _lmul_ or _rmul_ are called directly and there is not a call to the coercion morphism.

[vbraun]

Looks good to me...