more user friendly finite field extensions

[videlec]

GF(p).extension(xxx) does not accept symbolic polynomials... and the error is cryptic

sage: Fp = GF(3)
sage: Fp2.<i> = Fp.extension(x^2+1)
Traceback (most recent call last):
...
UnboundLocalError: local variable 'E' referenced before assignment

We make it more user friendly by allowing the above in some duck typing fashion.

Component: number theory

Work Issues: merge conflict

Author: Vincent Delecroix

Branch/Commit: u/vdelecroix/24526 @ ba84546

Issue created by migration from https://trac.sagemath.org/ticket/24526

[videlec]

Author: Vincent Delecroix

[videlec]

Description changed:

--- 
+++ 
@@ -7,3 +7,5 @@
 ...
 UnboundLocalError: local variable 'E' referenced before assignment

+ +We make it more user friendly by allowing the above in some duck typing fashion.

[videlec]

New commits:

ba84546

24526: more user friendly finite field extension

[videlec]

Commit: ba84546

[videlec]

Branch: u/vdelecroix/24526

[mezzarobba]

comment:3

It may be better to keep the branch dealing with tuples/lists for speed reasons... Perhaps it doesn't matter (I don't know how much it is used or what alternatives exist for constructing extensions without too much overhead), but your patch makes the call to extension() in GF(3).extension([1, 0, 1], 'a') 70% slower on my system.

[darijgr]

comment:4

Should this ducktyping really all be happening under the hood without notifying the user? I think a more readable error message would be better, or at least a warning. We don't want people to use SR for polynomials in their code, do we?

Also, is this

+                else:
+                    modulus = modulus.change_ring(self)

necessary? The GF constructor already does modulus = R(modulus).monic(), where R = PolynomialRing(FiniteField(p), 'x').

[dkrenn]

comment:5

Does not apply anymore.

[dkrenn]

Work Issues: merge conflict

[slel]

comment:6

Recent user report for the same problem:

• Ask Sage question 56220: Finite field extension

[slel]

comment:7

Please rebase, and I can review.