Hi Amritpal, > If we can make a function of "computation of expressions" then we have a > certificate or proof that how Sage solve the particular equation. If this > thing is physically (internally) happening with Sage then, why can't we do > it?
Just giving a transcript of all elementary computations done when calling some function f does not constitute a good certificate of the correctness of the output of f: to verify it, the user would have to verify every single step, and this would be as computationally expensive as doing the computation himself. "Certificates" are supposed to be small and easy to verify. See e.g. this paper on certificates for linear algebra computations, such as the rank: http://www.math.ncsu.edu/~kaltofen/bibliography/14/DuKa14.pdf > Not only asking for GSOC, but can you guide me regarding this. Because I'm > willing to implement this thing in Sage. If we are able to implement this > in Sage then Sage will go to a next level which can't be imagined by > anyone. Also, you cleared all my doubts in a single email. Thank you for > that. Sorry, apart from answering the odd email on this list, I'm not going to guide such a project. I'm not particularly interested in the "print_computation"-idea, and for the other idea on certificates, I simply don't know enough about certificated algorithms to be of significant help there. It's great that you're motivated about contributing to Sage though! Best, Johan Amritpal Singh writes: > On Wednesday, March 9, 2016 at 2:24:22 PM UTC+5:30, Johan S. R. Nielsen > wrote: >> Hi Amritpal, > <snip> >> A related, and mathematically quite important feature, is that of >> "certificates": that a function returns together with its output a >> certificate, a kind of proof, that output is really correct. For >> instance, say I call M.rank() on a matrix M. How do I know that the >> output 5 is correct? It would be nice to have a proof that I could >> check, possibly in a probabilistic way, and preferably much faster than >> the rank computation itself, to be certain that 5 is indeed the rank of >> M. Making fast algorithms that also output certificates is an active >> area of research and would be a cool addition to Sage. (I wouldn't be >> able to mentor such a project though: I don't know much about >> certificates, and I will likely be mentoring another project). > > Thanks for the reply and guidance. > You explained it very well that how this thing can be implemented with > Sage. According to you, we can make a separate function i.e. > print_computation which will take input in the form of string and print all > its occurrences which can be processed for solving the equation. It is a > good idea that it's very difficult to hack all of the Sage so we can create > different functions which deal with computation of expression. > > If we can make a function of "computation of expressions" then we have a > certificate or proof that how Sage solve the particular equation. If this > thing is physically (internally) happening with Sage then, why can't we do > it? > > Not only asking for GSOC, but can you guide me regarding this. Because I'm > willing to implement this thing in Sage. If we are able to implement this > in Sage then Sage will go to a next level which can't be imagined by > anyone. Also, you cleared all my doubts in a single email. Thank you for > that. > > > -- > Amritpal Singh > http://www.amritpals.com/ > https://github.com/amrit3701 -- -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
