[Maxima-bugs] [maxima:bugs] #5717 limit() returns ind when the one-sided limits are different forms of the same number

[David S. <tom...@us...>]

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**[bugs:#5717] limit\(\) returns ind when the one-sided limits are different forms of the same number**

**Status:** open
**Group:** None
**Labels:** limit 
**Created:** Mon Oct 26, 2026 08:22 AM UTC by David Scherfgen
**Last Updated:** Mon Oct 26, 2026 08:22 AM UTC
**Owner:** nobody


By Claude:

`limit()` computes a two-sided limit from both sides. When the two come out as different forms of the same number, it does not see that they are equal and returns `ind`:

```
(%i1) f : unit_step(x)*%e^(log(6)/2) + unit_step(-x)*sqrt(6)$
(%i2) [limit(f, x, 0, plus), limit(f, x, 0, minus), limit(f, x, 0)];
(%o2) [%e^(log(6)/2),sqrt(2)*sqrt(3),ind]
(%i3) g : unit_step(x)*%e^(log(x + 3)/3)/3 + unit_step(-x)/(x + 9)^(1/3)$
(%i4) [limit(g, x, 0, plus), limit(g, x, 0, minus), limit(g, x, 0)];
(%o4) [%e^(log(3)/3)/3,1/9^(1/3),ind]
```

`%e^(log(6)/2)` is `sqrt(6)` and `%e^(log(3)/3)/3` is `1/9^(1/3)`, so both limits exist. For the same reason `limit()` does not see that a numerator vanishes:

```
(%i5) limit((x^(1/3)*%e^(log(x)/3) - 9^(1/3))/(x - 3), x, 3);
(%o5) infinity
```

The numerator is `x^(2/3) - 9^(1/3)`, which is `0` at `x = 3`, so the limit is the derivative of `x^(2/3)` there, `2/3^(4/3)`.


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