FiniteField: make GF(p,n) the same as GF(p^n)

[user202729]

It is not uncommon for the user to accidentally call GF(p,n) while they want to call GF(p^n) or GF(p^n).

This raises an error when the user try to do so. Suggested by @videlec in #38376 (comment) .

(Actually if backwards compatibility isn't that important we can just make this equivalent to GF((p,n)). I doubt any existing code specifically relies on GF(p,n) called this way with n an integer.)

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[grhkm21]

Actually I'm more in favour of treating GF(p, n, ...) as GF((p, n), ...).

[videlec]

Actually I'm more in favour of treating GF(p, n, ...) as GF((p, n), ...).

I tend to agree but the (serious) drawback is an extra type checking and hence more time needed to construct the object GF(5, 'mygen').

[user202729]

I tend to agree but the (serious) drawback is an extra type checking and hence more time needed to construct the object GF(5, 'mygen').

Timing data:

sage: %time GF(5^2, "a")
CPU times: user 176 ms, sys: 9.28 ms, total: 186 ms
Wall time: 234 ms
Finite Field in a of size 5^2
sage: %time isinstance(2, (int, Integer))
CPU times: user 7 μs, sys: 1 μs, total: 8 μs
Wall time: 9.54 μs
True
sage: %time GF(5^2, "a")
CPU times: user 0 ns, sys: 259 μs, total: 259 μs
Wall time: 264 μs
Finite Field in a of size 5^2

9.54 μs versus 264 μs. So around 3-4% increase if the field is already cached.

Is it that bad? (On the other hand, small changes pile up…?)

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On the other hand that might break some backwards compatibility in unexpected cases e.g. the (actual) PSL code in Sage above. (Fortunately in that case the second argument is 1 anyway, and it's an IntegerMod instead of Integer so it's safe, right?)

[user202729]

I modify the code to make GF(p, n) = GF((p, n)).

Thoughts?