Some better information about this is at http://planetmath.org/encyclopedia/ContentOfPolynomial.html.
Aaron Meurer On Sat, Dec 10, 2011 at 1:08 AM, Aaron Meurer <asmeu...@gmail.com> wrote: > I don't think this is a good idea. The problem is that these > algebraic domains are not in general unique factorization domains > (http://en.wikipedia.org/wiki/Unique_factorization_domain, see the > non-examples section). I believe the content can be defined regardless > of this fact (see http://en.wikipedia.org/wiki/Content_(algebra) and > http://en.wikipedia.org/wiki/Highest_common_factor), but many of the > properties, such as Gauss's lemma > (http://en.wikipedia.org/wiki/Gauss%27s_lemma_(polynomial)) only hold > in UFDs. > > And anyway, I've always seen the content defined over QQ, though I > haven't had as much exposure to algebra as I would like have to stand > strongly behind this statement. > > If the goal is to make factorization work, why not just modify > factor_terms() (or something like it) to do this instead? Contents and > primitives are useful for more than just these things, because of > things like Gauss's lemma. > > Also, I should point out that Gauss's lemma is useful for actually > computing the content, if the input polynomial is already factored. > Since this doesn't hold in the more general algebraic domains that you > want to extend this to, you can no longer use it in that case. > > Maybe Mateusz can comment on all of this? > > Aaron Meurer > > On Tue, Dec 6, 2011 at 5:19 AM, smichr <smi...@gmail.com> wrote: >> as_content_primitive removes Rational content from an expression. Does >> it make sense to remove radical content, too, but leave it as a factor >> with the primitive portion? >> >> >>> (sqrt(2+2*x)+sqrt(10+10*x)).as_content_primitive() >> (1, sqrt(2)*(sqrt(x + 1) + sqrt(5)*sqrt(x + 1))) >> >> >> see https://github.com/sympy/sympy/pull/824 >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To post to this group, send email to sympy@googlegroups.com. >> To unsubscribe from this group, send email to >> sympy+unsubscr...@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/sympy?hl=en. >> -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
