cancellation of two indefinite limits

[dkrenn]

We get

sage: limit(cos(x),x=oo) - limit(sin(x),x=oo)
0

This comes from the fact that the return value of each of these limits is a symbolic variable:

sage: limit(sin(x), x=oo)
ind
sage: type(limit(sin(x), x=oo))
<type 'sage.symbolic.expression.Expression'>
sage: limit(sin(x), x=oo).variables()
(ind,)

CC: @sagetrac-jakobkroeker

Component: symbolics

Keywords: symbolic, cancellation, limit, indefinite

Stopgaps: wrongBehaviourMarker

Issue created by migration from https://trac.sagemath.org/ticket/16422

[dkrenn]

Description changed:

--- 
+++ 
@@ -5,7 +5,7 @@
 0
 ```
 
-This comes from the fact that the return value of each limit is a symbolic variable:
+This comes from the fact that the return value of each of these limits is a symbolic variable:
 
 ```
 sage: limit(sin(x), x=oo)

[nbruin]

comment:2

This is an upstream problem (in maxima). It seems "ind" isn't a special symbol there either:

Maxima 5.29.1 http://maxima.sourceforge.net
using Lisp ECL 12.12.1
(%i3) limit(sin(x),x,inf)-limit(cos(x),x,inf);
(%o3)                                  0

We could intercept ind whenever it comes by (from limit) and raise an exception to limit the damage, but I imagine the bad simplifications could already happen internal to maxima.

This seems to happen with infinity as well, by the way:

(%i14) limit(1/x^2,x,0)-limit(1/x^4,x,0);
(%o14)                                 0

Sage catches those (when they happen in a way sage can see it happen), so perhaps we should recognize ind and a special value--leading to an exception if we can't do anything with it.

[dkrenn]

comment:4

Still there in 6.6.

[sagetrac-jakobkroeker]

Stopgaps: wrongBehaviourMarker