Opened 10 months ago

# Incorrect (Maxima) symbolic sum

Reported by: Owned by: charpent major sage-9.5 symbolics Not yet reported upstream; Will do shortly.

### Description

See this `ask.sagemath.org` 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)))
```

### comment:1 Changed 9 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 `ask.sagemath.org` 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).

### comment:2 Changed 7 months ago by mkoeppe

• Milestone changed from sage-9.3 to sage-9.4

Moving to 9.4, as 9.3 has been released.

### comment:3 Changed 3 months ago by mkoeppe

• Milestone changed from sage-9.4 to sage-9.5
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