Faster arithmetic with function field ideals

[klee]

We make ideal arithmetic faster for ideals with two-generators representation.

sage: K.<x> = FunctionField(GF(2)); _.<Y> = K[]
....: L.<y> = K.extension(Y^7 - x^3*Y - x)
....: O = L.maximal_order()
....: I = O.ideal(y)
....: J = O.ideal(x + y)
sage: def naive_power(i, n):
....:     j = i
....:     for s in range(n - 1):
....:         j *= i
....:     return j
....: 
sage: n = 100
sage: i = I / J
sage: %timeit naive_power(i, n)
683 ms ± 8.82 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
sage: %timeit i^n
34.3 ms ± 454 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
sage: p, q = i.gens_two()
sage: %timeit naive_power(i, n)  # faster multiplication
147 ms ± 4.08 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
sage: %timeit i^n                # faster powering
16.2 ms ± 149 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
sage: naive_power(i, n) == i^n
True

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​a165300

Speed up ideal multiplication

[tscrim]

One trivial little change:

      def _gens_two(self):
-         """
+         r"""

Once done, you can set a positive review on my behalf.

I do find this line

if len(self._gens_two.cache) == 2:

to be a little strange though.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​5d190dd

Use raw docstring to prevent invalid escape warning

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​0a77fa5

Drop use of _gens_two.cache

[klee]

Replying to tscrim:

Sorry for the mess. I somehow lost a commit that I thought I uploaded.

One trivial little change:

      def _gens_two(self):
-         """
+         r"""

Once done, you can set a positive review on my behalf.

Done now.

I do find this line

if len(self._gens_two.cache) == 2:

to be a little strange though.

I had deleted this in the lost commit. Now done again.

I will wait for a green bot. Thank you for quick review.

[tscrim]

Thanks. Sounds good. Green bot => positive review.