Hi, I plan to start implementing a user interface to symbolic summation soon and I want to get some opinions on how this interface should be.
The most natural construct for summation, either of a list or symbolic summation is of course "sum." Initially, I was thinking that it's a big sin to override the python "sum" function, since I also use it very often and consider it (performance) critical. However, I was encouraged to think again about this after Mike's comment here: http://trac.sagemath.org/sage_trac/ticket/3587#comment:3 For quick reference, here's the help for Python's sum function: sum(sequence, start=0) -> value Returns the sum of a sequence of numbers (NOT strings) plus the value of parameter 'start'. When the sequence is empty, returns start. We could easily extend this to check if the second parameter is a tuple which defines a range (e.g., (x, 1, n) where the upper and lower bounds are inclusive). If it is, try to solve the sum symbolically, otherwise call the python sum function. (Actually, I recall that there were plans to overwrite this function anyway with one that does balanced summation if the argument is a list.) So I propose the following: sage: var('i,n') (i, n) sage: sum(2^i, (i, 0, n)) 2^(n+1) - 1 sage: sum(1/i, (i, 1, n)) harmonic_number(1, n) (As far as I can see, Sage doesn't have a construct for harmonic numbers yet.) These still will work of course: sage: sum(range(5)) 10 sage: sum(i for i in range(5)) 10 sage: sum(range(5), 2) 12 Similarly, I suggest we extend prod the same way. Any comments or objections? I should also add that I don't like to differentiate between upper and lowercase commands, so I don't think using "Sum" is an option. If overriding "sum" is not accepted, "SymbolicSum" might be an alternative. Thanks. Burcin --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
