On Nov 14, 6:11 pm, William Stein <wst...@gmail.com> wrote: > 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?
I do not need these modulus, but they are used for instance in NumberField even for degree one extensions. > > 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 This problem is solved in #11784, that has positive review. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
