Thanks Volker for the tip, that does the job. More comments below: On Sun, Jun 29, 2014 at 11:52 PM, John Cremona <john.crem...@gmail.com> wrote: > Be careful though: > > sage: (sqrt(-2)*sqrt(-3)).simplify_radical() > -sqrt(3)*sqrt(2) > > i.e. you cannot use sqrt(a)*sqrt(b)=sqrt(a*b) everywhere without > reaching a contradiction. > > sage: bool( (sqrt(-2)*sqrt(-3)) == sqrt(2)*sqrt(3) ) > False
Right, e.g. in sympy: >>> sqrt(-2)*sqrt(-3) -sqrt(6) Coming to the original example, sympy returns >>> sqrt(3)/sqrt(15) sqrt(5)/5 And Mathematica returns 1/sqrt(5). Here is a more difficult example, in SymPy: >>> 2**(S(1)/3) * 6**(S(1)/4) 2**(7/12)*3**(1/4) Mathematica returns the same thing. Sage, on the other hand, does not simplify this: sage: 2**(1/3) * 6**(1/4) 6^(1/4)*2^(1/3) sage: _.rational_simplify() 6^(1/4)*2^(1/3) What is interesting though, is that Sage does perform some factorization automatically, e.g.: sage: sqrt(12) 2*sqrt(3) Mathematica and SymPy do the same here. Here is even better example, in Sage: sage: sqrt(12)/sqrt(6) 1/3*sqrt(6)*sqrt(3) sage: _.rational_simplify() 1/3*sqrt(6)*sqrt(3) SymPy or Mathematica: >>> sqrt(12)/sqrt(6) sqrt(2) So the Sage rule seems to be --- factorize simple sqrt(N) into the form a*sqrt(b), do this for all sqrt() in the expression, and then just convert 1/sqrt(n) -> sqrt(n)/n, and return the result, after canceling common factors. I think a better rule is to either a) factor everything, like SymPy or Mathematica 2) do not factor anything, and just leave sqrt(12)/sqrt(6) as is. Then rational_simplify() should return the result from a). Ondrej -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
