On Fri, Oct 31, 2014 at 6:37 AM, Christophe Bal <[email protected]> wrote: > Thanks for the answers. > > Maybe integration will be a good candidate. When I talk about formal output, > I think of special case where the formula given is correct but certainl not > the one a human will see first.
I see. I was thinking more of cases where the human wouldn't see how to solve it at all. A possible idea here is integrals using square roots. Humans tend to make simplifications on square roots which are not true in general, leading to "simpler" output, whereas computer algebra systems try to be more cautious about them. For instance, sqrt(1/x) != 1/sqrt(x). Aaron Meurer > > One day, a student had shown me an integral which was evaluate by its formal > calculator to a formula containing arctan whereas my solution do not use it, > and was more simple. The problem is that I have not noted this example... > > Maybe solving some polynomial of degree 3 can give such "complicated" > formulas that a human would not use. > > Christophe BAL > > 2014-10-30 23:53 GMT+01:00 Richard Fateman <[email protected]>: >> >> There are even simpler examples. For instance, some systems multiply >> polynomials by some evaluation/interpolation scheme in finite fields. Or >> by FFT >> or by so-called Karatsuba or Cooke-Toom methods or a Kronecker method >> evaluating a polynomial to a single huge integer... >> >> Risch integration is certainly another one. >> >> >> On Wednesday, October 29, 2014 3:40:58 AM UTC-7, Christophe Bal wrote: >>> >>> Hello. >>> >>> I'm looking for formal outputs that are not calculated as a human can do >>> (this is for a free french "book"). Do you know such kind of examples ? >>> >>> Christophe BAL >>> >>> PS : this questions has been posted on both Sage and Sympy lists. >> >> -- >> 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. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/a2c48c91-3bc3-4761-bef7-7a8bdebc7297%40googlegroups.com. >> >> For more options, visit https://groups.google.com/d/optout. > > > -- > 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. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAAb4jGmGUqW1vGBkYLieOYhBGJT%3DOn7nfZDyHVNFW524%3DGfN7w%40mail.gmail.com. > > For more options, visit https://groups.google.com/d/optout. -- 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. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6JH_tCkVtKsmFxcJ4Ucbajc8pmxBnzzr3dtNTiWUhMpAg%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
