Hi Dmitri,
On Jan 10, 5:48 pm, Dima Pasechnik <dimp...@gmail.com> wrote:
> This is not good enough. It could be that the [1,1]-element lies in a
> proper subring.
> One should either test each matrix entry and take the biggest ring, or
> ask GAP to do it for you.
> Say, if A is a GAP matrix you can do
> gap> Field(Flat(A));
> to get the smallest field containing all the entries of A.
Ouch. That is easily doable, but will slow down quite a bit my
conjugacy classes code.
Oh well, better get it slow now and look for a way of passing a global
ring around later on...
Anyway I think it's better to use Ring() rather than Field() since the
former can always be coerced into the latter.
As of now, this is what I have (including methods for finite and
cyclotomic fields). I don´t like all these nested if's so any
alternative proposal will be welcome...
def _sage_(self):
r"""
Override of ExpectElement._sage_ method. Aiming for a better
conversion. Initially just for matrices!
EXAMPLES:
- Conversion of gap matrices into sage matrices, back and
forth
::
sage: h = matrix(GF(5),2,[1,2, -1, 1])
sage: hh = gap(h)
sage: hh.sage()
[1 2]
[4 1]
sage: hh.sage() == h
True
- Conversion of finite fields into the corresponding sage
fields
::
sage: R = gap("GF(16)")
sage: R.sage()
Finite Field in x16 of size 2^4
- Conversion of cyclotomic fields
::
sage: K = gap("CF(9)")
sage: K.sage()
Cyclotomic Field of order 9 and degree 6
"""
try:
if self.IsMatrix(): # Conversion of matrices
return self._matrix_()
if self.IsRing(): # Conversion of rings
if self.IsField(): # Fields
if self.IsFinite(): # Finite fields
from sage.rings.finite_field import GF
size = self.Size()
var = 'x'+str(size)
return GF(size, var) # What is the right
thing to use as generator name??
if self.IsCyclotomicField(): # Cyclotomic
fields
# Don't know if there is a gap way of getting
the number n for CF(n), so use the defining string "CF(n)" instead.
# The following strips the first three
characters, that should be "C", "F", "(" and the last ")".
from sage.rings.number_field.number_field
import CyclotomicField
n = int(str(self)[3:-1])
return CyclotomicField(n)
except NotImplementedError:
pass
return ExpectElement._sage_(self)
Is there a canonical or preferred way of calling the generator of GF
(q)? I went for "xq" (where q is a prime power) but that can easily
been changed.
The code for determining the ring has been replaced by
R = self.Flat().Ring().sage()
and moved to the _matrix_ method in the same class.
Cheers
J
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