On Fri, Apr 13, 2018 at 7:26 AM, John Cremona <john.crem...@gmail.com> wrote: > This looks like a bug to me: > > sage: F=GF(3) > sage: R.<X,Y,Z>=F[] > sage: C=Curve(X^8+Y^8-Z^8) > sage: C.count_points(1) # correct count over GF(3^1) > [4] > sage: C.count_points(8) # should give counts over GF(3^n) for n=1..8 but it > crashes > > TypeError: F (=[X^8 + Y^8 - Z^8]) must be a list or tuple of polynomials of > the coordinate ring of A (=Projective Space of dimension 2 over Finite > Field in z2 of size 3^2) > > -- note that the error message looks suspicious. > > Also the more naive > > sage: F=GF(3^8) > sage: R.<X,Y,Z>=F[] > sage: C=Curve(X^8+Y^8-Z^8) > sage: C.count_points(1) > [4696] > > works but is so slow it must be doing something very basic such as testing > every point in the plane (of which there are 3^16+3^8+1...) > > John >
Agreed. Moreover, according to http://doc.sagemath.org/html/en/constructions/algebraic_geometry.html, "The option algorithm="bn uses Sage’s Singular interface and calls the brnoeth package." However, when I look at the doc string in C.rational_points? it says the option algorithm is ignored. Times seem to bear this out: sage: x,y,z = PolynomialRing(GF(3^7), 3, 'xyz').gens() sage: C = Curve(z^8 - y^8 - x^8) sage: time Cpts = C.rational_points() CPU times: user 10.9 s, sys: 243 ms, total: 11.1 s Wall time: 10.9 s sage: time Cpts = C.rational_points(algorithm="bn") CPU times: user 10.8 s, sys: 182 ms, total: 11 s Wall time: 10.8 s sage: x,y,z = PolynomialRing(GF(3^8), 3, 'xyz').gens() sage: C = Curve(z^8 - y^8 - x^8) sage: time Cpts = C.rational_points() CPU times: user 22.8 s, sys: 97.2 ms, total: 22.9 s Wall time: 22.8 s sage: time Cpts = C.rational_points(algorithm="bn") CPU times: user 22.8 s, sys: 97.2 ms, total: 22.9 s Wall time: 22.9 s > > On 13 April 2018 at 11:55, David Joyner <wdjoy...@gmail.com> wrote: >> >> Hi: >> >> The question below is posted for Gary McGuire, who is not a subscriber >> to this list: >> >> "I would like to know the number of rational points on the (projective) >> curve >> x^8+y^8=z^8 >> over the field of order 3^{18}. >> >> My question is, can Sage do this calculation, and how?" >> >> - David >> >> PS: About 3 years ago, a related question was posted: >> https://groups.google.com/forum/#!topic/sage-support/s59iDjhu2zU >> For some reason, the method described there is no longer implemented. >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-support" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sage-support+unsubscr...@googlegroups.com. >> To post to this group, send email to sage-support@googlegroups.com. >> Visit this group at https://groups.google.com/group/sage-support. >> For more options, visit https://groups.google.com/d/optout. > > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
