> But coercing symbolic constants into RR or CC is not a simple, (or > even well-defined?) matter. Just think of many-valued nested > radicals; or if a=sqrt(2), b=sqrt(3), c=sqrt(6), would a*b-c > simplify/coerce to 0? This is not stratightforward at all.
Is it? I just would evaluate the expression in RR. And then sqrt(2)*sqrt(3)-sqrt(6) is not 0. Btw. I just realized that SymbolicRing does assert that not (sqrt(5+2*sqrt(2)*sqrt(3))-sqrt(2)-sqrt(3)).is_zero() which is wrong. While your example (sqrt(2)*sqrt(3)-sqrt(6)).is_zero() is properly recognized. I guess for radical expressions there is an algorithm that can decide zeroness. But if we also involve powers of radical expressions and perhaps logarithms this becomes more difficult. Take for example: sqrt(2)**log(9,2) = sqrt(2)**(2*log(3,2))=2**log(3,2)=3 which strangely enough is recognized by Sage: (sqrt(2)**log(9,2)-3).is_zero() I would be very grateful if anyone could point me to literature about those decidability problems (whether for radicals, algebraic numbers, or numbers involving log and exp, or even sin, cos, etc for which I think there are some undecidability results). --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
