[sage-support] modular symbols mod 3
Hi Everyone, I'm getting what I perceive to be an error when I compute some spaces of modular symbols mod 3. (Probably the same phenomenon occurs mod 2.) Specifically: sage: N=7*13 sage: for l in primes(20): ... ModularSymbols(Gamma0(N),2,base_ring=GF(l)).cuspidal_submodule().dimension() 14 17 14 14 14 14 14 14 The genus of X_0(91) is 7, so I expected to see a string of 14's. The 17 stands out like a sore thumb. Actually, I get an analogous error if I remove cuspidal_submodule: the 14's become 17's and the 17 becomes a 20. The consistent increment of 3 has to do with the fact that there are four cusps. Thanks in advance! Best, Ken -- 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 http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] weird comparison of rational numbers
Hi Sage Gurus, Am I doing something stupid here: sage: print 1/2 3/7 sage: L=[] sage: for i in range(2,3): ... for j in range(1,2): ... L.append([i,j]) ... sage: print L sage: for P in L: ... print P[1], P[0] ... P[1]/P[0] 3/7 False [[2, 1]] 1 2 True In plain language: I ask sage whether 1/2 is less than 3/7, and sage tells me false. I then create the list L = [[2,1]] and loop through L (which has only one element). For P=[2,1], I ask sage whether P[1]/P[0] is less than 3/7 and get true. The conundrum is that P[1]/P[0] is 1/2, so mathematically I'm getting the answers false and then true for the same question. So what's going on? I'm sure that there's a simple explanation. Thanks, Ken -- You received this message because you are subscribed to the Google Groups sage-support group. To post to this group, send email to sage-support@googlegroups.com. To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en.
[sage-support] strange behavior in sage 5.0
Any advice here? Am I doing something wrong: sage: 1+1 2 sage: (0.8*0.15)/(0.8*0.15 + 0.2*0.85) Unhandled SIGILL: An illegal instruction occurred in Sage. This probably occurred because a *compiled* component of Sage has a bug in it and is not properly wrapped with sig_on(), sig_off(). You might want to run Sage under gdb with 'sage -gdb' to debug this. Sage will now terminate. /Users/kribet/Desktop/sage/spkg/bin/sage: line 312: 70167 Illegal instruction: 4 sage-ipython $@ -i Ken -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] elliptic curve extension degree
Consider this short sage transcript: sage: E=EllipticCurve(GF(3),[1,1]) sage: for i in range(3): ... print i,E.order(extension_degree=i) 0 4 1 4 2 16 Sage seem to think that E has 4 points over the field with 1 element. Was this intended? Ken -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] gcd's of numbers mod N
Hi everyone, If a is an integer mod m (and m is a positive integer), then the gcd of a and m is well defined; it's the gcd of A and m were A is any integer representing a mod m. Consider this transcript in sage: sage: a = Mod(1,6) sage: b = Mod(3,6) sage: print gcd(a-b,6) # is this a bug? sage: print gcd(b-a,6) 4 2 sage seems to think that the gcd of 6 and (-2 mod 6) is -2 mod 6, which it converts to 4. A mathematician would say that the gcd is 2. Is this a bug, or does sage have a higher purpose here? Thanks, Ken -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] surprised by behavior of torsion_subgroup
Hi,Maybe this is a frivolous comment, but I'd like to express my surprise at the use of "torsion_subgroup" to mean two very different things for an abelian variety and for an elliptic curve:sage: E=EllipticCurve('11a')sage: E.torsion_subgroup()Torsion Subgroup isomorphic to Multiplicative Abelian Group isomorphic to C5 associated to the Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Fieldsage: A=J0(11)sage: A.torsion_subgroup()Traceback (most recent call last):...TypeError: torsion_subgroup() takes exactly 2 arguments (1 given)sage: A.torsion_subgroup(5)Finite subgroup with invariants [5, 5] over QQ of Abelian variety J0(11) of dimension 1sage: A.rational_torsion_subgroup()Torsion subgroup of Abelian variety J0(11) of dimension 1sage: A.rational_torsion_subgroup().order()5sage: A.rational_torsion_subgroup().abelian_group()Traceback (most recent call last):...AttributeError: 'RationalTorsionSubgroup' object has no attribute 'abelian_group'I'm surprised that "torsion_subgroup" for an elliptic curve over Q refers to *rational* torsion while for an abelian variety over Q it refers to *all* torsion. Further, it's frustrating to me that the rational torsion subgroup of an abelian variety over Q has an order but not the structure of an abelian group. I'm sure that there are good reasons for this, but this end user is kind of amazed. Before the sage session above, I used to think that elliptic curves and abelian varieties of dimension 1 were the same thing! Live and learnBest,Ken
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[sage-support] points on elliptic curves mod N
Hi, I'd like to present Lenstra's elliptic curve factoring method to a class. This means that I'd like to define an elliptic curve over Integers(N), where N is composite, and then add points on that curve in sage. I may be doing something stupid, but I'm getting a NotImplementedError with the method I'm using: sage: E=EllipticCurve([0,Mod(1,59)]); E Elliptic Curve defined by y^2 = x^3 + 1 over Ring of integers modulo 59 sage: E([0,1]) (0 : 1 : 1) sage: E=EllipticCurve([0,Mod(1,5963)]); E Elliptic Curve defined by y^2 = x^3 + 1 over Ring of integers modulo 5963 sage: E([0,1]) Traceback (most recent call last): ... NotImplementedError Is there a workaround? Does an alternative approach allow the desired computations? Thanks much in advance! Best, Ken R -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org To unsubscribe, reply using remove me as the subject.
[sage-support] standard deviations in sage
Hello All, I asked myself how I could use sage to compute the standard deviation of a grade distribution for one of my courses. Rooting around, I found that I can compute for example sage: vector(RDF,[1,2,2,1]).standard_deviation() and get the answer 0.57735026919. However, if I try the same command with RDF replaced by RR, I get anAttributeError. My first question is: What's going on here; how come RDF and RR are so different in this context? Their respective descriptions look very similar -- An approximation to the field of real numbers using double precision floating point numbers. Answers derived from calculations in this approximation may differ from what they would be if those calculations were performed in the true field of real numbers. This is due to the rounding errors inherent to finite precision calculations. An approximation to the field of real numbers using floating point numbers with any specified precision. Answers derived from calculations in this approximation may differ from what they would be if those calculations were performed in the true field of real numbers. This is due to the rounding errors inherent to finite precision calculations. If I had found some documentation about the standard deviation command, I would probably have have found the answer to my first question. This leads to my second question: Why I don't I see information about standard_deviation when I type standard_deviation? at the command line? Thanks in advance for the help! Ken Ribet -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org To unsubscribe, reply using remove me as the subject.
