Make choosing irreducible polynomials independent of finite field implementations

[pjbruin]

This patch makes the FiniteField constructor call the implementation-independent code for choosing irreducible polynomials from #14832.

With this patch, the generic constructor always passes an actual polynomial (not a string specifiying an algorithm to construct one) to the finite field implementation class. For backwards compatibility, the existing classes still recognise a string modulus. Checking if the finite field is a Conway polynomial is now done by an implementation-independent function.

This is a dependency of #12142.

Apply: attachment: trac_14833-FiniteField_polynomial_choice.patch

Depends on #14832

CC: @xcaruso

Component: finite rings

Keywords: polynomials

Author: Peter Bruin

Reviewer: Jean-Pierre Flori

Merged: sage-5.12.beta2

Issue created by migration from https://trac.sagemath.org/ticket/14833

[pjbruin]

Description changed:

--- 
+++ 
@@ -2,3 +2,7 @@
 
 With this patch, the generic constructor always passes an actual polynomial (not a string specifiying an algorithm to construct one) to the finite field implementation class.  For backwards compatibility, the existing classes still recognise a string `modulus`.  Checking if the finite field is a Conway polynomial is now done by an implementation-independent function.
 
+This will be a dependency of #12142.
+
+Apply: [attachment: trac_14833_finite_fields_polynomial_choice.patch](https://github.com/sagemath/sage-prod/files/10658072/trac_14833_finite_fields_polynomial_choice.patch.gz)
+

[jpflori]

comment:3

It may be better to use a function decorator to do the caching of the is_conway method, i.e. use @cached_method.

And is there any point to prevent setting the default return value for finite fields explicitely constructed with conway polynomials?
(i.e. removing what would be the equivalent of "self._is_conway = True" after the "modulus == "conway"" tests? to set the default value of the cached_method you can use "self.is_conway.set_cache(True)".)

[pjbruin]

comment:4

Replying to @jpflori:

It may be better to use a function decorator to do the caching of the is_conway method, i.e. use @cached_method.

OK, I'll fix this as soon as I have time, unless you or someone else does it first.

And is there any point to prevent setting the default return value for finite fields explicitely constructed with conway polynomials?
(i.e. removing what would be the equivalent of "self._is_conway = True" after the "modulus == "conway"" tests? to set the default value of the cached_method you can use "self.is_conway.set_cache(True)".)

That might be slightly more elegant, but the test for modulus == 'conway' is now in PolynomialRing.irreducible_element, which is not directly related to finite fields, so we would need an additional check in the finite field constructor. I'm not sure if it is worth it: checking whether we have a Conway polynomial is (hopefully) very fast (since the database was loaded when we looked up the Conway polynomial), and is_conway() is currently only used for Sage <-> Gap conversion.

[pjbruin]

based on 5.11.beta3 + #14832, use @cached_method

[pjbruin]

comment:5

Attachment: trac_14833-FiniteField_polynomial_choice.patch.gz

[pjbruin]

Description changed:

--- 
+++ 
@@ -2,7 +2,7 @@
 
 With this patch, the generic constructor always passes an actual polynomial (not a string specifiying an algorithm to construct one) to the finite field implementation class.  For backwards compatibility, the existing classes still recognise a string `modulus`.  Checking if the finite field is a Conway polynomial is now done by an implementation-independent function.
 
-This will be a dependency of #12142.
+This is a dependency of #12142.
 
-Apply: [attachment: trac_14833_finite_fields_polynomial_choice.patch](https://github.com/sagemath/sage-prod/files/10658072/trac_14833_finite_fields_polynomial_choice.patch.gz)
+Apply: [attachment: trac_14833-FiniteField_polynomial_choice.patch](https://github.com/sagemath/sage-prod/files/10658071/trac_14833-FiniteField_polynomial_choice.patch.gz)
 

[jpflori]

Reviewer: Jean-Pierre Flori

[jpflori]

comment:6

Ok, looks ok for me.