Implement actions using _act_ instead of _call_

[jdemeyer]

We change the internal API of Action: instead of the existing _call_ method, we implement an _act_ method which always takes (g, x) as arguments, where g is the acting element and x is the acted-on element.

The current implementation using _call_ takes a left and right argument. This is less efficient because many actions can be left or right actions. This means that every _call_ method needs to "decode" its arguments as g and x.

Work on #24247 shows that a significant amount of time is spent in Action.__call__. This ticket optimizes that quite a bit. It also adds documentation to Action.

Timings (compared to before #24247 and #5574):

Note: "before" timings are without #24247, #5574 and #24500. "after" timings are with #24247, #5574 and #24500.

GF(2ⁿ)^ZZ

Before:

sage: k.<a> = GF(4, impl="ntl"); n = 2; timeit('a ^ n', number=100000, repeat=20)
100000 loops, best of 20: 383 ns per loop

After:

sage: k.<a> = GF(4, impl="ntl"); n = 2; timeit('a ^ n', number=100000, repeat=20)
100000 loops, best of 20: 635 ns per loop

RDF^ZZ

Before:

sage: a = RDF(2); n = ZZ(2); timeit('a ^ n', number=100000, repeat=20)
100000 loops, best of 20: 156 ns per loop

After:

sage: a = RDF(2); n = ZZ(2); timeit('a ^ n', number=100000, repeat=20)
100000 loops, best of 20: 185 ns per loop

ideal^ZZ

Before:

sage: a = ZZ.ideal(2); n = ZZ(2); timeit('a ^ n', number=10000, repeat=20)
10000 loops, best of 20: 13.3 µs per loop

After:

sage: a = ZZ.ideal(2); n = ZZ(2); timeit('a ^ n', number=10000, repeat=20)
10000 loops, best of 20: 14.1 µs per loop

AA^QQ

Before:

sage: a = AA(8); n = 1/3; timeit('a ^ n', number=10000, repeat=20)
10000 loops, best of 20: 12.8 µs per loop

After:

sage: a = AA(8); n = 1/3; timeit('a ^ n', number=10000, repeat=20)
10000 loops, best of 20: 16.6 µs per loop

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​dd3b5b5	Implement actions using _act_ instead of _call_
​f2b676e	Don't use Set_PythonType in IntegerAction

[tscrim]

Do you have timings with this ticket (at least, my understanding of the description is the "after" does not include this ticket)?

[jdemeyer]

Replying to tscrim:

Do you have timings with this ticket (at least, my understanding of the description is the "after" does not include this ticket)?

The "after" does include this ticket.