failing calculation with limit

[sagetrac-casamayou]

In all three calculations below, the first result is false, whereas in a previous version of Sage, he returned Und what is the correct answer.

sage:f(x) = (cos(pi/4-x) - tan(x)) / (1 - sin(pi/4+x))
sage:limit(f(x), x = pi/4) 
+Infinity
sage: limit(f(x), x = pi/4, dir='plus')            
-Infinity
sage: limit(f(x), x = pi/4, dir='minus')           
+Infinity

CC: @jasongrout @sagetrac-mvngu @mwhansen

Component: calculus

Keywords: limit

Author: Karl-Dieter Crisman

Reviewer: Paul Zimmermann

Merged: sage-4.5.2.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/8942

[kcrisman]

comment:1

This was fixed when we improved our recognition of Maxima's unsigned infinity.

sage: sage: limit(f(x), x = pi/4, dir='minus')           
+Infinity
sage: sage: limit(f(x), x = pi/4, dir='plus')            
-Infinity
sage: sage:limit(f(x), x = pi/4) 
Infinity

So I guess this can be closed? Or should we whip up a patch to document this...?

[sagetrac-casamayou]

comment:2

Replying to @kcrisman:

This was fixed when we improved our recognition of Maxima's unsigned infinity.

sage: sage: limit(f(x), x = pi/4, dir='minus')           
+Infinity
sage: sage: limit(f(x), x = pi/4, dir='plus')            
-Infinity
sage: sage:limit(f(x), x = pi/4) 
Infinity

So I guess this can be closed? Or should we whip up a patch to document this...?

This can be closed. Thanks a lot !

[kcrisman]

comment:3

Thanks. One thing to point out is http://www.sagemath.org/doc/developer/trac.html#closing-tickets, so that in theory only the release manager should close a ticket. For instance, we might want to document this somewhere (which is what I was really asking about).

I will now violate that same web page by re-opening it; since it hasn't actually been merged (nothing to merge) hopefully that is ok, Minh or Mike :)

[kcrisman]

Attachment: trac_8942-unsigned-inf.patch.gz

Based on 4.4.2

[kcrisman]

Author: Karl-Dieter Crisman

[kcrisman]

comment:4

If we want more documentation that we have fixed this, here it is. Ready for review.

[zimmermann6]

comment:5

positive review (I've checked that all doctests still pass).

A small comment: maybe the documentation could say more explicitly that the output Infinity
indicates a complex infinity, whereas +Infinity means plus infinity.

By the way, there is a problem since Sage parses Infinity as +Infinity:

sage: Infinity
+Infinity
sage: Infinity == +Infinity
True
sage: a=limit(1/x, x=0)
sage: a == +Infinity
True

but this could be in a different ticket.

[zimmermann6]

comment:6

but this could be in a different ticket.

see #9480

[qed777]

Merged: sage-4.5.2.alpha0

[qed777]

Reviewer: Paul Zimmermann