#10682: sum fails with lower bound != 0 or 1
-------------------------+--------------------------------------------------
Reporter: fmaltey | Owner: burcin
Type: defect | Status: new
Priority: critical | Milestone: sage-5.0
Component: symbolics | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
-------------------------+--------------------------------------------------
Changes (by was):
* priority: major => critical
Comment:
This is not some general issue where sum fails on all inputs with lower
bound != 0, 1. For example, this is fine:
{{{
sage: var('n,k')
(n, k)
sage: sum(k, k, 1, n)
1/2*n^2 + 1/2*n
sage: sum(k, k, 2, n)
1/2*n^2 + 1/2*n - 1
}}}
Starting at 2, I guess this should be the answer:
{{{
sage: (sum (binomial(n,k)*k^2, k, 1, n) - sum (binomial(n,k)*k^2, k, 1,
1))
(n^2 + n)*2^(n - 2) - n
}}}
The answer seems fine for starting at 3,4, by the way:
{{{
sage: a = (sum (binomial(n,k)*k^2, k, 1, n) - sum (binomial(n,k)*k^2, k,
1, 2))
sage: b = sum (binomial(n,k)*k^2, k, 3, n)
sage: bool(a==b)
True
sage: a = (sum (binomial(n,k)*k^2, k, 1, n) - sum (binomial(n,k)*k^2, k,
1, 3))
sage: b = sum (binomial(n,k)*k^2, k, 4, n)
sage: bool(a==b)
True
}}}
This is probably a serious bug in Maxima, since the real work is done by
the function
{{{
sage.calculus.calculus.maxima.sr_sum
}}}
which just calls maxima in some complicated way.
I am raising the priority since this is a subtle and very serious
mathematically incorrect result. Also, somebody needs to isolate this to
a pure-maxima session exhibiting the bug (if it is in maxima!) and report
upstream. I tried for a minute and failed.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10682#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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