#3587: [with patch, needs work] calculus -- wrap maxima's symbolic summation
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Reporter: was | Owner: whuss
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-4.1
Component: calculus | Keywords:
Reviewer: Burcin Erocal, Mike Hansen | Author: Wilfried Huss
Merged: |
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Comment(by burcin):
I uploaded a new patch in attachment:trac_3587-maxima_simplify_sum.patch.
This has both patches folded together, and renames `sum()` to
`symbolic_sum()` in `sage/calculus/calculus.py` and
`sage/misc/functional.py` eliminating the risk of people using the
symbolic sum instead of sum in library code without realizing, and the
need to import `__builtin__`.
I am OK with the patch, and ready to give it a positive review. However,
there is a problem, maxima returns wrong results in certain cases:
{{{
sage: sum(binomial(n,k), k, 1, n)
2^n - 2
sage: sum(binomial(n,k), k, 2, n)
2^n - 2*n - 2
sage: r=sum(binomial(n,k), k, 2, n-2)
sage: r.simplify()
2^n - 1/6*n^3 - 11/6*n - 2
}}}
It seems that maxima doesn't handle definite sums with "non natural"
bounds. I.e., in the examples above the bounds don't span the whole
support of the expression, so one needs further processing to get the
final result after calling Zeilberger's algorithm.
Indefinite sums seem to be fine. In this case, we could check the inputs,
and raise a warning if we have a definite sum. I'll try to do this, but
don't count on me since I already signed up for a lot this week.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3587#comment:9>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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