#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-4.1.2
Component: calculus | Keywords:
Reviewer: Burcin Erocal, Mike Hansen | Author: Wilfried Huss
Merged: |
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Comment(by kcrisman):
I installed this, but it does not seem to work as advertised. Namely,
{{{
sage: var('n,k')
(k, n)
sage: sum(binomial(n,k),k,0,n)
simplify_sum(sum(binomial(n,k),k,0,n))
}}}
It does behave as desired if I go to Maxima and load(simplify_sum) etc.,
but that's not the same. Somehow it's staying symbolic for some reason.
This is off of 4.1.1 on Mac OSX.5.
> 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.
Looks like this problem is fixed in Maxima 5.19 (at least they work
properly in 5.19.1), so this is another good reason to get that in Sage
soon (there was an experimental spkg posted at
[http://sage.math.washington.edu/home/kirkby/Solaris-
fixes/maxima-5.19.0/maxima-5.19.0.spkg] at one point). Incidentally,
apparently it never got to as heavy a hitter as Zeilberger, but I'm not
sure where the problem was.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3587#comment:10>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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