On Fri, Jul 19, 2013 at 1:48 AM, Thilina Rathnayake <[email protected]> wrote: > Ondrej, > > I thought of implementing the sieving method described in the book to verify > the answers > returned by the descent method. It's simple to implement. What actually we > need to check > in descent method is whether it finds a solution if one exist, base solution > returned by different > algorithms will be different and it's sufficient to check whatever the > solutions returned indeed > satisfy the equation. > > But I would say verifying descent with the algorithm in MAGMA would be more > convincing. > Only thing is that I don't know much about lattice reduction. But I can > always get help from > the SymPy community if something goes wrong. So I will give a try to > implement it.
That sounds like a good plan. > > Yes, next thing is to get the parametrized formula for all the solutions. I > am working on it Excellent, cannot wait to play with it. Ondrej > now. > > > Regards, > Thilina > > > > > On Fri, Jul 19, 2013 at 2:30 AM, Ondřej Čertík <[email protected]> > wrote: >> >> Thilina, >> >> On Thu, Jul 18, 2013 at 1:43 PM, Thilina Rathnayake >> <[email protected]> wrote: >> > Seems like they haven't implement it anywhere else. I found an algorithm >> > that >> > was implemented in MAGMA, but it involves lattice reduction and since I >> > am >> > almost finished with the descent method, I didn't try to implement that. >> > I >> > would >> > try that If I can find some free time or perhaps after completing all >> > the >> > deliverables of my >> > project proposal. >> >> But you should be able to check the final results, after you implement >> the calculation of all solutions. Right? >> >> > >> > And once again, Thank you very much mario. If not for your help, I would >> > have wasted a >> > lot of time with this. But sadly, there is still a few problems. The >> > programme ran infinitely >> > when an input like (-3 , -4) was given. It should return (None, None, >> > None) >> > in this case. >> > I fixed it by adding a if condition to return a None-tuple when both the >> > inputs are negative. >> > So now it's okay. I have attached the modified version herewith. >> > >> > Also when I gave the input (3, 3), it runs infinitely. I couldn't fix >> > it. >> > But I found a >> > workaround to get rid of all of these bugs. I used a slightly modified >> > version of your first >> > programme and before I call descent() method in it, I made the two >> > inputs A >> > and B square >> > free and did some after-processing to recover the solutions for the >> > original >> > inputs. >> > Now it's all fine. >> >> Excellent! Great job. >> >> > >> > If not for the case with the input (3, 3) ( same thing happens with (7, >> > 7), >> > ..) your second >> > programme produces simpler answers than the first one. However there is >> > a >> > way to reduce >> > the magnitude of the answers returned by the descent method so we can >> > use it >> > with the >> > current implementation if needed. I plan to give the user the choice to >> > specify whether >> > the base solutions should be reduced before using them in the >> > parametrization to find all the >> > solutions for the equation. >> >> So I think the next step is to implement the retrieval of all the >> solutions, >> as described by the book, isn't it? >> >> Ondrej >> >> > >> > Thank you and best regards, >> > Thilina >> > >> > >> > >> > On Thu, Jul 18, 2013 at 7:10 PM, Ondřej Čertík <[email protected]> >> > wrote: >> >> >> >> Thanks Mario! >> >> >> >> I really appreciate your help. That's quite amazing that they had few >> >> bugs in the algorithm. Do you think they didn't actually implement it >> >> in any software? >> >> >> >> Ondrej >> >> >> >> On Thu, Jul 18, 2013 at 5:36 AM, mario <[email protected]> wrote: >> >> > The attached version works in the mentioned cases; the bug is fixed >> >> > reducing >> >> > to the case ``A > 0, B > 0`` >> >> > >> >> > >> >> > On Thursday, July 18, 2013 11:28:22 AM UTC+2, Thilina Rathnayake >> >> > wrote: >> >> >> >> >> >> I should try making input coefficients to be square free. I think >> >> >> the >> >> >> algorithm in general, >> >> >> does not work when the coefficients are not square free. >> >> >> >> >> >> >> >> >> >> >> >> On Thu, Jul 18, 2013 at 2:53 PM, Thilina Rathnayake >> >> >> <[email protected]> >> >> >> wrote: >> >> >>> >> >> >>> We can add descent(23, 616) to the bug list too. It also return >> >> >>> (None, >> >> >>> None, None) >> >> >>> but (6, 1, 38) is a solution. By finding more and more test cases >> >> >>> which >> >> >>> fail, I think we can >> >> >>> identify a pattern and then the cause for the bug. >> >> >>> >> >> >>> Regards, >> >> >>> Thilina >> >> >> >> >> >> >> >> > -- >> >> > You received this message because you are subscribed to the Google >> >> > Groups >> >> > "sympy" 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/sympy. >> >> > For more options, visit https://groups.google.com/groups/opt_out. >> >> > >> >> > >> >> >> >> -- >> >> You received this message because you are subscribed to the Google >> >> Groups >> >> "sympy" 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/sympy. >> >> For more options, visit https://groups.google.com/groups/opt_out. >> >> >> >> >> > >> > -- >> > You received this message because you are subscribed to the Google >> > Groups >> > "sympy" 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/sympy. >> > For more options, visit https://groups.google.com/groups/opt_out. >> > >> > >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" 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/sympy. >> For more options, visit https://groups.google.com/groups/opt_out. >> >> > > -- > You received this message because you are subscribed to the Google Groups > "sympy" 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/sympy. > For more options, visit https://groups.google.com/groups/opt_out. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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