Hi, I've submitted a patch
http://sagetrac.org/sage_trac/ticket/628 for making "binomial" work as one would expect for symbolic expressions, in cases like this: sage: n=var('n') sage: binomial(n+1,n-1) n*(n + 1)/2 by defining binomial(x,m)=binomial(x,x-m) whenever x-m is an integer. This would be consistent with the way in which Maxima defines the binomial function. http://maxima.sourceforge.net/docs/manual/en/maxima_31.html#SEC126 is it reasonable to treat the symbolic variable n as an integer?. In this case, I think that this will give the results that one would exprect. However, in gemeral, I think that having domains for symbolic variables would be essential for performing symbolic calculations, and get correct results (but certainly could make a CAS much more complex). Currently Sage does not have a way to specify that a symbolic variable belongs to a certain domain (for example that n is a symbolic variable representing an integer). I think that, the calculus package implicitly assumes that symbolic variable represents a real number. [In fact, I think that Axiom is the only free CAS with this feature, but I'm not sure about that] Consider for example the expression sqrt(x**2) If x is a real number, it can be simplified to abs(x) However, if x where known to be a positive real number, it could be simplified to x On the other hand, if x is a complex number, that expression could be problematic (since it depends on choosing a branch for the square root) Another classical example is the binomial (x+y)^2=x^2 + 2xy + y^2 that holds if x and y commute. If one wants to build a CAS that can operate on non commuting objects, it is essential to have domains for symbolic variables. just to share some ideas on that... Pablo --~--~---------~--~----~------------~-------~--~----~ 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://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
