is_algebraic in the new assumptions means algebraic over the rationals. Your definition of algebraic means algebraic over a rational function field over the rationals. In other words, Q.algebraic(a) means a satisfies a polynomial over QQ (the rational numbers), a.is_algebraic_function() means that a satisfies a polynomial over QQ(x, y, ...), the field of rational functions in (x, y, ...) over the rationals, where (x, y, ...) are all symbols in a. For example, sqrt(2) is an algebraic in the first sense, and sqrt(x) is algebraic in the second sense.
It looks like the paper is using the less rigorous form of "algebraic", if I am understanding it correctly, which just means, "an expression". Aaron Meurer On Wed, Jun 12, 2013 at 12:19 AM, Sean Vig <sean.v....@gmail.com> wrote: > The heuristic is in a paper on the arxiv [1] (the second heuristic, on page > 10). It may be that they just meant a quotient of polynomials, but I think > it would work fine for anything that is algebraic, though I haven't tried > anything that ends up being that complex. > > There is also an is_algebraic handler in the new assumptions, the logic from > there could be adapted until such a time that the new assumptions are moved > into the core. > > Sean > > [1] http://arxiv.org/abs/gr-qc/9607037v1 > > > On Tue, Jun 11, 2013 at 11:00 PM, Aaron Meurer <asmeu...@gmail.com> wrote: >> >> I'm curious what the heuristic is, though, that requires this class of >> expressions. Sometimes people who deal with ODEs abuse (misuse) the >> term "algebraic". >> >> Aaron Meurer >> >> On Tue, Jun 11, 2013 at 10:58 PM, Aaron Meurer <asmeu...@gmail.com> wrote: >> > is_rational_function could easily be extended to handle such cases >> > (one just needs to allow rational instead of integer exponents). >> > >> > Aaron Meurer >> > >> > On Tue, Jun 11, 2013 at 10:48 PM, Manoj Kumar >> > <manojkumarsivaraj...@gmail.com> wrote: >> >> >> >> >> >> >> >> On Wed, Jun 12, 2013 at 12:33 AM, Aaron Meurer <asmeu...@gmail.com> >> >> wrote: >> >>> >> >>> What do you mean by algebraic? There is is_polynomial or >> >>> is_rational_function. >> >>> >> >>> >> >>> >> >> I was referring to this, >> >> http://en.wikipedia.org/wiki/Algebraic_expression , >> >> is_Polynomial wouldn't work if I want to identify cases like sqrt(1 - >> >> x**2/1 >> >> + x**2) , so thats where I thought a function might come in handy. >> >> >> >> >> >> >> >> -- >> >> Regards, >> >> Manoj Kumar, >> >> Mech Undergrad. >> >> GSoC 2013, SymPy >> >> BPGC >> >> http://manojbits.wordpress.com >> >> >> >> -- >> >> 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 sympy+unsubscr...@googlegroups.com. >> >> To post to this group, send email to sympy@googlegroups.com. >> >> Visit this group at http://groups.google.com/group/sympy?hl=en-US. >> >> 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 sympy+unsubscr...@googlegroups.com. >> To post to this group, send email to sympy@googlegroups.com. >> Visit this group at http://groups.google.com/group/sympy?hl=en-US. >> 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 sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at http://groups.google.com/group/sympy?hl=en-US. > 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 sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
