Defining it as sage: BB=lambda(c): factorial(c-1)*(mu/(B*mu+1))^2*sum(((c-1/(B*mu+1))^i)/factorial(i),i,0,c-1) sage: BB(1) mu^2/(B*mu + 1)^2
gives the evaluated sum. In other words it's a function which returns a symbolic expression instead of a symbolic expression which can be evaluated. I don't know if there are disadvantages to this in terms of evaluation speed if you use BB a lot, or things like taking derivatives etc. but hopefully it will work for what you need. -Ivan On Feb 3, 2012, at 6:17 PM, Vincent Knight wrote: > Thanks kcrisman, > > I was holding out for someone to suggest something a bit more straightforward > but I'll try and implement this. Very much appreciated (as always). > > Best wishes, > Vince > > On 2 February 2012 19:32, kcrisman <[email protected]> wrote: > > > On Feb 2, 1:53 pm, Vince <[email protected]> wrote: > > Hi all, > > > > I'm working with some formulas including summations and sage doesn't > > always do what I was hoping. I program a function called BB(c) > > including (factorials): > > > > sage: var('i,mu,B') > > sage: BB(c)=factorial(c-1)*(mu/(B*mu+1))^2*sum(((c-1/(B*mu+1))^i)/ > > factorial(i),i,0,c-1) > > > > When I compute it I get the following output which sadly hasn't > > evaluated the symbolic summation: > > > > sage: BB(1) > > mu^2*sum((B*mu + 1)^(-i)*(B*mu)^i/factorial(i), i, 0, 0)/(B*mu + 1)^2 > > > > However if I copy and past the previous output sage does indeed > > compute everything I expect: > > > > sage: mu^2*sum((B*mu + 1)^(-i)*(B*mu)^i/factorial(i), i, 0, 0)/(B*mu + > > 1)^2 > > mu^2/(B*mu + 1)^2 > > > > Am I missing something here? I'd obviously like BB(1) to directly > > compute my result. > > > > I think the following simpler examples might be illuminating. > > > sage: var('i') > i > sage: g(x) = sum(i,i,0,x) > sage: g > x |--> 1/2*x^2 + 1/2*x > sage: g(x) = sum(i^2,i,0,x) > sage: g > x |--> 1/3*x^3 + 1/2*x^2 + 1/6*x > sage: g(x) = sum(factorial(i),i,0,x) > sage: g > x |--> sum(factorial(i), i, 0, x) > sage: g(3) > sum(factorial(i), i, 0, 3) > > So the summing, if it knows a formula *before* you plug in i, will > work; otherwise it will be an unevaluated sum. This is undoubtedly > due to the preparser's syntax. > > > sage: preparse('g(x) = sum(factorial(i),i,0,x)') > '__tmp__=var("x"); g = > symbolic_expression(sum(factorial(i),i,Integer(0),x)).function(x)' > > > So we get a callable thing, and passing in x simply substitutes. > > d = dict(zip(map(repr, self.arguments()), args)) > d.update(kwds) > return SR(_the_element.substitute(**d)) > > So we're just doing > > sage: SR(g.subs({x:3})) > sum(factorial(i), i, 0, 3) > > The only workaround I see right now is to evaluate the string output > you got. > > sage: h = SR(g.subs({x:3})) > sage: eval(str(h)) > 10 > > > I really hope someone else sees a better way around this, though. > > - kcrisman > > -- > To post to this group, send email to [email protected] > To unsubscribe from this group, send email to > [email protected] > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > > > > -- > Dr Vincent Knight > Cardiff School of Mathematics > Senghennydd Road, > Cardiff > CF24 4AG > (+44) 29 2087 5548 > www.vincent-knight.com > @drvinceknight > Skype: drvinceknight > > > -- > To post to this group, send email to [email protected] > To unsubscribe from this group, send email to > [email protected] > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
