Dropping support for power with Finite Field Polynomial Element

[Shay2Shay]

Fixes issue : #32287
Reference : pow ( Int, Finite Field)
It was noticed that raising power with ModN field numbers and Gravio/NTL was not consistent.

• Finite Field = ModN : Coerced the FF element to Integer then performed Powering
• Finite Field = Gravio/NTL: Coerced the output to Gravio/NTL rather than Integer because it could only interpret non prime order field elements to be polynomials.

Change:
Removed support for Gravio/NTL/Pari_ffelt in powering scenario.

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[Shay2Shay]

@tscrim please have a look.

[tscrim]

I don't think this is the correct way to fix the issue. Adding very special cases in generic code for deciding coercion should not be done without a very good reason. Contrast your code with the generic base class IntegerModRing. Hence, my proposed change, get every other case that is not an IntegerModRing but a finite field.

[tscrim]

Suggested change

	from sage.rings.finite_rings.finite_field_pari_ffelt import FiniteField_pari_ffelt
	from sage.rings.finite_rings.finite_field_ntl_gf2e import FiniteField_ntl_gf2e
	from sage.rings.finite_rings.finite_field_givaro import FiniteField_givaro
	if isinstance(S, (FiniteField_pari_ffelt, FiniteField_ntl_gf2e, FiniteField_givaro)):
	elif isinstance(S, FiniteField):

You will also need to add

from sage.rings.finite_rings.finite_field_base import FiniteField

[tscrim]

Suggested change

	raise TypeError('Unable to raise power using finite field polynomial element')
	_record_exception()

I think this is the correct thing to do.

[Shay2Shay]

I understood the 1st part elif isinstance(S, FiniteField) and I made desired changes.

But I couldn't understand the second part _record_exception(). I originally intended the function call to throw error and halt.
But removing raise error will not stop the program and at it will coerce the base of power to be finite field element - this is what I am thinking.

[tscrim]

Sorry, I forgot what _record_exception does; yes, that is not the proper thing to do there. Errors definitely should not be raised in that code. In turn, this made me realize something: specific coercions between specific parents should not be (dis)allowed by the coercion code. Those specific parents should be the ones to handle them. So I do not think this is the correct fix. We probably need to dig deeper into what coercions are being called and figure out a better mechanism for disallowing it.

[Shay2Shay]

Understood

I will close this and look for another approach.

Those specific parents should be the ones to handle them.

Like ntl - old implementation.

sage: x = 123**GF(64, impl='ntl')(5); x, x.parent()
...
...
...
TypeError: unsupported operand parent(s) for ^: 'Finite Field in z6 of size 2^6' and 'Finite Field in z6 of size 2^6'

[Shay2Shay]

@tscrim
If I add here (Same with other variants):

if isinstance(exp.parent(), FiniteField) and not isinstance(exp.parent(), ModNField):
    raise TypeError("Cannot raise power with polynomial")

How would that be?? (This works locally)