bug fixes for profile functions for the Steenrod algebra

[jhpalmieri]

Profile functions for the Steenrod algebra, especially at odd primes, are a little buggy:

sage: P3 = SteenrodAlgebra(p=3, profile=(lambda n: Infinity, lambda n: 1))
sage: P3._has_nontrivial_profile()
False

This should be True.

sage: P3._profile
((+Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity, +Infinity), (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1))

All of the "Infinity"s should be omitted.

sage: SteenrodAlgebra(p=3, profile=((3,2,1), lambda n: 1))
Traceback (most recent call last)
...
TypeError: unsupported operand type(s) for -: 'NoneType' and 'int'

This error shouldn't happen.

These bugs are in the function steenrod_algebra_misc.normalize_profile_function and in the method _has_nontrivial_profile in steenrod_algebra.SteenrodAlgebra_generic. The attached patch fixes these, and it also speeds up `steenrod_algebra_misc.is_valid_profile:

sage: sage: from sage.algebras.steenrod.steenrod_algebra_misc import is_valid_profile, normalize_profile
sage: pro = normalize_profile(lambda n: n)
sage: timeit('is_valid_profile(pro[0], pro[1], p=2)') # before
5 loops, best of 3: 334 ms per loop

sage: timeit('is_valid_profile(pro[0], pro[1], p=2)') # after
125 loops, best of 3: 3.99 ms per loop

[was]

I don't know what a "profile" is, and maybe no other Sage developers do. But the code looks good and works. I think it makes sense to just trust our resident algebraic topologist in this case.