Indeed I was (am) only interested in the case of char != 2,3. Its should be easy to add the missing cases, tough.
On Friday, May 9, 2014 5:05:30 PM UTC+2, John Cremona wrote: > > It is quite likely that the implementation of Jacobian for plane cubics > does not work in characteristic 3 (at least in general). I had something > to do with early implementations but then it was all rewritten in terms of > Jacobians, so I cannot remember the details. Perhaps Volker Braun can > comment. You yourself can look at the code which is run to see what you > think -- and of course you are more than welcome to add code for char. 3. > > John Cremona > > > On 9 May 2014 12:16, Gabriel Furstenheim Milerud > <[email protected]<javascript:> > > wrote: > >> I'd like to create an elliptic curve from a degree 3 polynomial without a >> base point, but when I use the Jacobian method I get a "division by zero" >> error. >> >> This is my data: >> A=GF(3^2,'c') >> S.<a,b,c>=A[] >> gS=a^3 - a^2*b + b^3 - a^2*c - a*b*c + b^2*c + a*c^2 + b*c^2 + c^3 >> Jacobian(gS) >> >> My intuition is that Jacobian tries to compute a short Weierstrass >> polynomial and this is not necessarily possible in characteristic 3 (I >> didn't have any problem in characteristic 5). I also checked that the curve >> was smooth, so it is indeed genus 1 >> >> Is there any way to make it work? >> >> >> This is the error I get: >> >> "Traceback (most recent call last): >> File "sag.py", line 16, in <module> >> Jacobian(gS) >> File >> "/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/jacobian.py", >> >> line 116, in Jacobian >> return Jacobian_of_equation(X, **kwds) >> File >> "/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/jacobian.py", >> >> line 225, in Jacobian_of_equation >> f, g = WeierstrassForm(polynomial, variables=variables) >> File >> "/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/toric/weierstrass.py", >> >> line 506, in WeierstrassForm >> return WeierstrassForm_P2(polynomial, variables) >> File >> "/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/schemes/toric/weierstrass.py", >> >> line 771, in WeierstrassForm_P2 >> S = cubic.S_invariant() >> File >> "/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/rings/invariant_theory.py", >> >> line 1769, in S_invariant >> a,b,c,a2,a3,b1,b3,c1,c2,m = self.scaled_coeffs() >> File >> "/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/rings/invariant_theory.py", >> >> line 1753, in scaled_coeffs >> 1/F(3)*a[3], 1/F(3)*a[4], 1/F(3)*a[5], >> File "element.pyx", line 1813, in >> sage.structure.element.RingElement.__div__ (sage/structure/element.c:15219) >> File "coerce.pyx", line 783, in >> sage.structure.coerce.CoercionModel_cache_maps.bin_op >> (sage/structure/coerce.c:7325) >> File "element.pyx", line 1811, in >> sage.structure.element.RingElement.__div__ (sage/structure/element.c:15198) >> File "element_givaro.pyx", line 1201, in >> sage.rings.finite_rings.element_givaro.FiniteField_givaroElement._div_ >> (sage/rings/finite_rings/element_givaro.cpp:10695)" >> >> -- >> 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 [email protected] <javascript:>. >> To post to this group, send email to [email protected]<javascript:> >> . >> Visit this group at http://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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
