The fact that i is not in CC doesn't bother me too much, since i is a
"formal square root of -1":
sage: i in CC
False
I can force it to be in CC by doing this:
sage: CC(i)
1.00000000000000*I
But then I think I should be able to do this:
sage: GF(5)(i)
Someone who knows more number theory than I do can come up with a
better solution, but coercion code like this ought to work: replace
the end ("raise TypeError...") of the _coerc_impl() method for
Finite_Field_prime_modn (in sage.rings.finite_field_prime_modn.py)
with this:
from sage.functions.constants import I
from sage.rings.arith import primitive_root
p = self.__char
if x == i and p % 4 == 1:
return self(primitive_root(p))**((p-1)/4)
raise TypeError, "no canonical coercion of x"
But this isn't the right place to patch. When I do this,
GF(5)._coerce_(i) works, but GF(5)(i) doesn't.
Perhaps IntegerMod in the file integer_mod.pyx should be patched, but
I don't want to mess around with Cython. Perhaps some other file
should be patched. Can anyone help?
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