Re: [sage-support] Solve system of non linear equations
> On Sat, Dec 08, 2012 at 11:44:19AM +0530, Santanu Sarkar wrote: > > Dear all, > > I have a system of non linear equations over GF(2). How to solve > > them in Sage? How large is your system ? (how many variables ?). What is the largest degree in an equation ? Depending on the answer to these questions, your system may be solved by exhaustive search, using a library I wrote (and that can be called from sage after a little bit of black magic). Charles -- 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] Re: Groebner Basis over finite field
Hi! On 2012-12-13, Santanu Sarkar wrote: > When I want to calculate > Groebner basis, I have following error. > > > verbose 0 (3292: multi_polynomial_ideal.py, groebner_basis) Warning: > falling back to very slow toy implementation. This is not an error but a warning. > P1=next_prime(2^100) > R.=GF(P1)[] The warning tells you that your finite field is so big that it can not be dealt with in (lib)Singular. Hence, if you want to compute a Gröbner basis over such a big finite prime field, Sage can not use the fast implementation in (lib)Singular; instead, Sage will try to use a generic implementation of Buchberger's algorithm (that's what is called "toy implementation" in the warning message). If you are lucky, the computation will succeed soon, if you aren't lucky, then there is not much one can do about it. Are you sure that you need this particularly large finite field? Would a smaller finite field do? Would QQ do? Best regards, Simon -- 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] Groebner Basis over finite field
I have a set of non-linear equations over a prime field. I want to solve them using Groebner basis technique. When I want to calculate Groebner basis, I have following error. verbose 0 (3292: multi_polynomial_ideal.py, groebner_basis) Warning: falling back to very slow toy implementation. P1=next_prime(2^100) R.=GF(P1)[] M=[x-2,x^2+y^2-1] I=M*R B=I.groebner_basis() -- 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.
Re: [sage-support] Solve system of non linear equations
Thank you very much for your help. On 9 December 2012 12:18, Georgi Guninski wrote: > On Sat, Dec 08, 2012 at 11:44:19AM +0530, Santanu Sarkar wrote: > > Dear all, > > I have a system of non linear equations over GF(2). How to solve > > them in Sage? > > > > If you need to solve large nonlinear systems over GF(2) and don't > insist on using sage I suspect a better choice is to convert > them to conjunctive normal form (CNF) and then use state of the > art SAT solver like lingeling/cryptominisat. > > There are sage programs for converting ANF to CNF, don't know if > they are in vanilla sage. > -- 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] Re: Simplifying expression, 'x' vs. 'y'
> >> might each be considered "simpler" depending on the context, which is the >> way a lot of people who don't know about decidability would perceive this >> question (or so my experience has been interacting with a lot of people who >> ask about why Sage doesn't "simplify" this or that). I suppose the answer >> to my example would depend on what you pick for your axiomoids? RJF always >> seems to have a useful comment about these things as well. >> > Carette would argue that 1-x^2 requires fewer characters (or tree nodes, > or whatever), so is definitely 'simpler'. > I would add 'if the user wants 'factor', he/she should ask for it! > > Of course! I guess my point is that that's not always what people mean by simplify, but sometimes it is, because people (esp. if they're not computer scientists) don't have an expression tree in mind when they use that word colloquially :-) -- 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.
Re: [sage-support] Re: Differential algebra support
Sorry for catching up so late, The Maple package for differential algebra, mostly written by François Boulier, has been ported to SAGE. It is not part of SAGE yet, but we hope that it will soon be. In any case, you can follow its progress there : http://trac.sagemath.org/sage_trac/ticket/13268 If you're feeling adventurous, you can apply the patches to your own SAGE installation, rebuild, and enjoy :) -- Charles Bouillaguet Le jeudi 30 juillet 2009 09:05:32 UTC+2, Martin Rubey a écrit : > William asked me to forward his reply... > > (One remark: William always developed for Axiom. In Sage, the variant > of Axiom usually provided is FriCAS. To the best of my knowledge, all > libraries developed for Axiom is provided by FriCAS as well.) > > "William Sit" writes: > > > Dear Martin: > > > > I just noticed that I can't post on the Sage support group. Would you > > please forward the following (revised for typos and grammar) to > > Daniel? thanks. > > > > William > > > > Dear Daniel and Martin: > > > > I have not kept up with all the newest development of software in > > differential algebra, but my impression is that Maple has the most > > abundance, particularly with regard to the Rosenfeld-Groebner > > algorithm. People most familiar with the Mape implementation are > > Elizabeth Mansfield, Evelyn Hubert, Francois Boulier, Ziming Li, > > Morena Maza, and perhaps a few more. I am not familiar at all with > > SAGE. > > > > That said, I don't believe the Ritt algorithm (if by this you mean > > the algorithm to decompose a radical differential ideal into its > > prime components) has ever been implemented, since there is no > > algorithm yet to test inclusion of prime differential ideals given by > > characteristic sets. I wonder whether even the Risch, or the Kovacic > > algorithm, has been fully implemented (emphasis on "fully"). The > > expert on these was Manuel Bronstein, who unfortunately passed away > > in 2006. I am not familar with what Bronstein has implemented, but I > > think it is mostly for linear ODE, second and third order. These are > > all related to differential Galois theory (more precisely, > > Picard-Vessiot theory). Jacque Artur-Weil would be one of the experts > > on this. > > > > As far as I know, there has been (was?) no abstract implementation of > > differential polynomial categories except in Axiom (I did that), and > > there the implementation is rudimentary; for example, there is no > > domain for differential ideals. Computationally, of course, one > > always deals with a finite set of differential polynomials and so it > > can be argued that there is no need to have an abstract > > implementation, but that was the question Daniel asked. > > > > Moreover, to implement abstractly partial differential polynomial > > rings is quite tricky. Many years ago, I had a project advising a > > student to implement that in Axiom. The student, a very bright one, > > was overwhelmed by the layers of abstraction even just to deal with > > input methods and notation, which I insisted should be very general, > > in accordance with the philosophy of Axiom. Later, the student > > quitted, my funds ran out and, alas, the commercial version of Axiom > > also died. I did not complete the project. > > > > I have implemented in Axiom the algorithm Leon Pritchard and I > > developed to handle initial value problems for general, first order, > > ODEs. I have not written up the documentation and hence the > > implementation is still private. I don't have time to do that, given > > the high standard required by Tim Daly, but the algorithms are > > straight forward, as described in our joint paper. > > > > I hope this brief reply will be helpful, > > > > William > > > > William Sit, Professor Emeritus > > Mathematics, City College of New York Office: > > R6/202C Tel: 212-650-5179 > > Home Page: http://scisun.sci.ccny.cuny.edu/~wyscc/ -- 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] Re: Simplifying expression, 'x' vs. 'y'
On Wednesday, 12 December 2012 02:28:19 UTC, kcrisman wrote: > > > > On Tuesday, December 11, 2012 6:52:53 PM UTC-5, JamesHDavenport wrote: > >> Pedantic Note. Jacques Carette's paper: Understanding Expression >> Simplification. >> Proc. ISSAC 2004 (ed. J. Gutierrez), ACM Press, New York, 2004, pp. 72-79. >> http://www.cas.mcmaster.ca/~carette/publications/simplification.pdf. >> defines it in a useful way, just not in a computable way (that I can see >> in practice). >> > > Very interesting paper. I guess I was referring to the sense that > > (1+x)(1-x) > > and > > 1-x^2 > > might each be considered "simpler" depending on the context, which is the > way a lot of people who don't know about decidability would perceive this > question (or so my experience has been interacting with a lot of people who > ask about why Sage doesn't "simplify" this or that). I suppose the answer > to my example would depend on what you pick for your axiomoids? RJF always > seems to have a useful comment about these things as well. > Carette would argue that 1-x^2 requires fewer characters (or tree nodes, or whatever), so is definitely 'simpler'. I would add 'if the user wants 'factor', he/she should ask for it! -- 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.
