#9635: symbolic sum gives wrong answer
--------------------------------------------------------------+-------------
Reporter: Henryk.Trappmann | Owner:
burcin
Type: defect | Status:
new
Priority: major | Milestone:
Component: calculus | Resolution:
Keywords: | Work issues:
Report Upstream: Fixed upstream, in a later stable release. | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
--------------------------------------------------------------+-------------
Changes (by kcrisman):
* upstream: Reported upstream. Developers acknowledge bug. => Fixed
upstream, in a later stable release.
Comment:
The
[http://sourceforge.net/tracker/?func=detail&aid=3036579&group_id=4933&atid=104933
bug report] got updated over a year ago.
In the current Sage:
{{{
(%i1) load(simplify_sum);
(%o1) /Users/karl-
dietercrisman/Downloads/sage-5.0/local/share/maxima/5.26.0/s\
hare/contrib/solve_rec/simplify_sum.mac
(%i2) simplify_sum(sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j
+1,n));
Is j + 1 positive, negative, or zero?
pos;
(%o2) 1
}}}
So just need a doctest.
{{{
sage: (n,k,j)=var('n,k,j')
sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n)
-sum((-1)^(-j + k)*binomial(k - 1, j)*binomial(n, k), k, j + 1, n)
sage: assume(j>-1)
sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n)
1
sage: forget()
sage: assume(n>=j)
sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n)
-sum((-1)^(-j + k)*binomial(k - 1, j)*binomial(n, k), k, j + 1, n)
sage: forget()
sage: assume(j==-1)
sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n)
1
sage: forget()
sage: assume(j<-1)
sage: sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j+1,n)
-sum((-1)^(-j + k)*binomial(k - 1, j)*binomial(n, k), k, j + 1, n)
}}}
Was the original report here wrong? Maxima currently says that the sign
of `j+1` is all that matters, which sort of makes sense
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9635#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
