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Bug in computing sum (of binomials)

asked 2019-01-22 18:38:13 +0200

Thrash gravatar image

updated 2023-01-09 23:59:49 +0200

tmonteil gravatar image

One gets a wrong output when running the following command:

sage: sum(binomial(1,n),n,0,oo)

The output should be $2$ instead of $3$. Compare:

sage: sum(binomial(1,n),n,0,oo,algorithm="sympy")
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answered 2019-01-22 19:31:45 +0200

rburing gravatar image

updated 2019-01-22 20:16:46 +0200

This bug originates from Maxima: if you evaluate


then it returns

from sage.calculus.calculus import symbolic_sum

which calls


which returns

from sage.interfaces.maxima_lib import max_to_sr, maxima_eval, max_ratsimp, max_simplify_sum, max_sum, sr_to_max
args = [binomial(1,n), n, 0, oo]
max_to_sr(maxima_eval([[max_ratsimp],[[max_simplify_sum],([max_sum],[sr_to_max(SR(a)) for a in args])]]))

Indeed we can see the bug in Maxima's simplify_sum:

(%i1) load("simplify_sum");
(%i2) simplify_sum(sum(binomial(1,n),n,0,inf));
(%o2)                                  3

I reported it upstream at Maxima, simplify_sum(sum(binomial(1,n),n,0,inf)) gives 3 instead of 2, and it is now tracked as trac ticket #27092.

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Thanks for the fast answer and the fast ticket report!

Thrash gravatar imageThrash ( 2019-01-22 20:51:07 +0200 )edit

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slelievre gravatar imageslelievre ( 2019-01-23 15:23:38 +0200 )edit

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Asked: 2019-01-22 18:38:13 +0200

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Last updated: Jan 22 '19