fast_callable can return ipow with exponents in the base ring

[bhutz]

fast_callable returns a string of operations. However, due to how caching of constants is done, the integer power function (ipow) can have constants in the base ring. This is because it checks the list of constants by comparing with == without taking into consideration the parent/type.

[bhutz]

Made the comparison to be by type and value instead of just value

---

New commits:

​27663fe

Trac 16051: comparing fast_callable constants by value and type

[nbruin]

I think parent, when it is available, is a more reliable attribute to determine the mathematical identity of an element (and hence with what constants it can be folded). I think sage.structure.parent is the right routine to use, because it will fall back on type if parent is not available:

sage: parent(1)
Integer Ring
sage: parent(int(1))
<type 'int'>
sage: parent(ZZ)
<type 'sage.rings.integer_ring.IntegerRing_class'>

One example where going by parent is ostensibly better than going by type is:

sage: a=RealField(1000)(1)
sage: b=RealField(200)(1)
sage: a==b
True
sage: (type(a),a)==(type(b),b)
True
sage: (parent(a),a)==(parent(b),b)
False

We shouldn't be folding constants that have different precision.

I don't have examples available, but it's certainly not ruled out that elements of different types could have the same parent (to allow for different representation methods in the same parent, for instance). I don't know if we should be folding constants in those cases.

In any of the cases where this matters other than to distinguish integer powers from from other constants one is really stretching the application domain of fast_callable anyway.

[git]

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

​9eb0789

Trac #16051: changed type to parent for constant comparison

[bhutz]

I wasn't aware of the instance of parent. That is definitely better, so I've changed it.

The instances I'm looking at is evaluating polynomials where the base ring can be something interesting like a powerseries ring, i.e. morphisms of projective space where base of projective space is something interesting. Mostly, when we implement fast evaluation for morphisms of projective space in #15920, we just don't want to break anything that currently works.

[bhutz]

opps. I meant #15780.

[drose]

I have run the complete doctest against this ticket.  Everything is good.