On 11/14/11 8:44 AM, David Roe wrote:
I think I'd describe it as a feature to reduce the number of GF(7)s
floating around. There's no coercion from ZZ[x] to GF(p), regardless
of the choice of modulus. The modulus function on
FiniteField_prime_modn is there for consistency of interface with the
other finite fields. Is there a reason you need different copies of
GF(p) with different variable names or moduli? Or should we just
update the documentation?
David
On Mon, Nov 14, 2011 at 08:06, luisfe<lftab...@yahoo.es> wrote:
I find that this is not coherent with documentation of Finite Field.
"""
sage: G=GF(7,'a',modulus=QQ[x](x+2))
sage: G.modulus()
x + 6
sage: G.variable_name()
'x'
sage: G.polynomial_ring().hom([G.gen()])
Ring morphism:
From: Univariate Polynomial Ring in x over Finite Field of size 7
To: Finite Field of size 7
Defn: x |--> 1
"""
Is this intended for cache reasons or is a bug? I mean cache eficiency
for the following doctest in finite_rings/constructor.py
"""
sage: K = GF(7, 'a')
sage: L = GF(7, 'b')
sage: K is L
True
"""
Which esentially says that the generator name is ignored in this case.
Bug or not, this is indeed "worrisome", because it could cause
significant confusion:
sage: F=GF(7,'a',modulus=QQ[x](x+3))
sage: G=GF(7,'a',modulus=QQ[x](x+2))
sage: F.modulus()
x + 6
sage: G.modulus()
x + 6
sage: F is G
True
It appears that the modulus isn't used elsewhere:
sage: F=GF(7,'a',modulus=QQ[x](x+3))
sage: F(x)
TypeError
However, that is in itself inconsistent, since when the degree of the
finite field is bigger than 1, then we *do* use the modulus to implement
this coercion (correctly):
sage: F=GF(7^2,'a',modulus=x^2+4)
sage: F(x)
a
sage: F(x^2)
3
There is also a nearby bug though which I easily stumbled on, since
evidently the degree of the modulus isn't even checked! (I would expect
an error here -- a user might think they're getting a GF(7^2,...)).
sage: F=GF(7,'a',modulus=QQ[x](x^2+3))
sage: G=GF(7,'a',modulus=QQ[x](x^2+5))
sage: F is G
True
sage: F
Finite Field of size 7
Worse here's another bug coming from I guess not checking the degree, etc.:
sage: R.<x> = QQ[]
sage: F=GF(7^2,'a',modulus=QQ[x](x+3))
sage: F(x)
0
sage: F(x+1)
1
-- William
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