# Ticket #4142(closed defect: fixed)

Opened 5 years ago

## limit bug: should be -Infinity, but gives +Infinity

Reported by: Owned by: ddrake burcin major sage-4.3.1 calculus Fixed upstream, in a later stable release. Dan Drake Karl-Dieter Crisman sage-4.3.1.alpha0

### Description

```sage: f = sqrt(1-x^2)
sage: g = diff(f, x); g
-x/sqrt(1 - x^2)
sage: limit(g, x=1, dir='below')
+Infinity
```

The last command should give -Infinity, of course, since f is a semicircle. At the other endpoint, the limit is correct (+Infinity).

## Change History

### comment:1 Changed 4 years ago by kcrisman

As it happens, this is still a problem in Sage 4.1.x - but the problem is somewhat more subtle than just some Maxima bug, or Sage incorrectly parsing Maxima output:

```(%i1) limit(-x/sqrt(1-x^2),x,1,minus);
(%o1)                                            infinity
```

BUT Maxima's infinity is not Sage's infinity; it is the complex infinity! If the answer is +infinity, Maxima would return 'inf'. I've asked the Maxima list about this, so we'll see what happens.

### comment:2 Changed 4 years ago by kcrisman

This is fixed in the latest Maxima CVS version, so whenever we upgrade again, this one will hopefully be closed.

```Maxima 5.19post http://maxima.sourceforge.net
using Lisp SBCL 1.0.24
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) limit(-x/sqrt(1-x^2),x,1,minus);
(%o1)                                minf
```

### comment:3 Changed 3 years ago by kcrisman

• Report Upstream set to N/A

This is now correct in Maxima 5.20.1, so it just needs a doctest once the new spkg is merged.

### comment:4 Changed 3 years ago by kcrisman

• Status changed from new to needs_review
• Report Upstream changed from N/A to Fixed upstream, in a later stable release.
• Authors set to Karl-Dieter Crisman

The patch here depends on the spkg at #7745 to work properly. It also depends on the patch there, and at #6423, but will probably still apply if someone forgot to apply them first.

### Changed 3 years ago by kcrisman

Based on 4.3.alpha1

### comment:5 Changed 3 years ago by ddrake

• Status changed from needs_review to positive_review
• Reviewers set to Dan Drake

The spkg and patch at #7745 fix this problem, and the doctest passes. Positive review; this can be merged as soon as #7745 is in.

### comment:6 Changed 3 years ago by mhansen

• Status changed from positive_review to closed
• Resolution set to fixed
• Merged in set to sage-4.3.1.alpha0
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