On Thu, Nov 13, 2008 at 5:12 AM, Burcin Erocal <[EMAIL PROTECTED]> wrote: > > 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?
Just a simple: +1 Note that Robert Bradshaw wrote the current prod (in Cython), and it is balanced and very fast. > 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. I agree. I'm strongly opposed to that Maple-style case-has-meaning crap. > If overriding "sum" is not accepted, "SymbolicSum" might be an alternative. > > > Thanks. > > Burcin > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
