On Mon, Jun 30, 2014 at 9:29 AM, Ondřej Čertík <ondrej.cer...@gmail.com> wrote: > Thanks Volker for the tip, that does the job. More comments below:
Another comment. Evidently Sage uses **Maxima** for rational_simplify, hence the integer factorization that is required to do this is not-surprisingly insanely stupidly slow, by modern standards: sage: p = next_prime(10^10); q = next_prime(10^11) sage: a = sqrt(p^2*q)/p sage: %time a.rational_simplify() 1/10000000019*sqrt(10000000038300000037240000001083) CPU time: 1.12 s, Wall time: 3.52 s sage: %time factor(p^2*q) 10000000019^2 * 100000000003 CPU time: 0.00 s, Wall time: 0.03 s Don't even try increasing the size of p, q above... or it'll take forever. We should maybe consider sometime make our rational_simplify first factor or something (I don't know), so it can leverage sage's much better integer factorization code. William > > 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. -- William Stein Professor of Mathematics University of Washington http://wstein.org -- 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.
