Opened 3 months ago

Last modified 2 months ago

#31418 new defect

Incorrect (Maxima) symbolic sum

Reported by: charpent Owned by:
Priority: major Milestone: sage-9.3
Component: symbolics Keywords:
Cc: Merged in:
Authors: Reviewers:
Report Upstream: Not yet reported upstream; Will do shortly. Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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See this question for details.

sage: sum((1+r)^i, i, 1, n)
((r + 1)^(n + 1) - r - 1)/r

which is incorrect if r==0.

Mathematica faills in the same trap :

sage: sum((1+r)^i, i, 1, n, algorithm="mathematica")
((r + 1)^n - 1)*(r + 1)/r

Workaround : use sympy algorithm :

sage: sum((1+r)^i, i, 1, n, algorithm="sympy")
cases(((r + 1 == 1, n), (1, ((r + 1)^(n + 1) - r - 1)/r)))

Change History (1)

comment:1 Changed 2 months ago by gh-DaveWitteMorris

I don't think the simplification is actually a bug, because the result is equal to the sum as a symbolic expression, so the code is behaving as advertised. More precisely, the rule in ginac is that a simplification can be made if it is "algebraically correct, possibly except for a set of measure zero (e.g. x/x is transformed to 1 although this is incorrect for x=0)".

The user in this particular question, seems to be interested in numerical calculations, rather than symbolic manipulations, so perhaps they should have defined a python function, instead of using a symbolic expression.

However, I agree that it would be good to have a way to evaluate the symbolic expression at r = 0 (without having to take a limit).

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