Sage mixes Infinity and +Infinity

[zimmermann6]

This is related to #8942. The limit function can output either
+Infinity, -Infinity, or Infinity, the later
meaning a complex infinity. For example:

sage: limit(1/x, x=0, dir='above')
+Infinity
sage: limit(1/x, x=0, dir='below')
-Infinity
sage: limit(1/x, x=0)             
Infinity

However Sage does not distinguish +Infinity and Infinity:

sage: l1=limit(1/x, x=0, dir='above')
sage: l2=limit(1/x, x=0, dir='below')
sage: l3=limit(1/x, x=0)
sage: l1==l3
True

Component: coercion

Keywords: infinity, equality

Issue created by migration from https://trac.sagemath.org/ticket/9480

[burcin]

comment:1

This is more of a problem with the equality checking rules in Sage and the coercion system than symbolics, so I'm changing the component to coercion.

If the arguments compare equal when coerced to a common parent, Sage returns True for the equality. In this case, the coercion goes to the UnsignedInfinityRing, where +Infinity is mapped to unsigned_infinity.

sage: UnsignedInfinityRing.has_coerce_map_from(InfinityRing)
True
sage: Infinity
+Infinity
sage: UnsignedInfinityRing.coerce(Infinity)
Infinity

BTW, isn't there an inconsistency in the capitalization of Infinity. Shouldn't it be lowercase according to Python conventions?

[burcin]

Changed keywords from none to infinity, equality

[tscrim]

comment:2

Sometimes it's infinity and others its Infinity. At the very least this should be consistent. Also there are other issues with infinity: #11506 #9547.

[zimmermann6]

comment:4

in Sage 5.11 we get:

sage: l1=limit(1/x, x=0, dir='right'); l1
+Infinity
sage: l2=limit(1/x, x=0, dir='left'); l2 
-Infinity
sage: l3=limit(1/x, x=0); l3             
Infinity
sage: bool(l1==l2), bool(l2==l3), bool(l3==l1)
(False, False, False)

however the objects returned are in SR and not in the infinity class:

sage: type(l1), l1.parent()
(sage.symbolic.expression.Expression, Symbolic Ring)
sage: p1=+Infinity
sage: type(p1), p1.parent()
(sage.rings.infinity.PlusInfinity, The Infinity Ring)

I propose to close that ticket, and open a new one about the above issue (or add it to an existing ticket).

Paul

[zimmermann6]

comment:5

or add it to an existing ticket

I've added a comment in #14857

Paul

[nathanncohen]

comment:6

No patch to review on this ticket...

Paul : when you want to close a ticket, you should set its milestone to wontfix/duplicate, say why on a comment, and change the status to positive_review so that the release manager will see it.

Nathann

[zimmermann6]

comment:7

in Sage 6.0 we get:

sage: l1=limit(1/x, x=0, dir='above')
sage: l3=limit(1/x, x=0)
sage: bool(l1==l3)
False

thus the issue is fixed now, and I change the status to "fixed".

Paul

[zimmermann6]

comment:8

sorry when changing to "fixed" (which made more sense to me than invalid or wontfix) the status was changed automatically to "closed"...

Paul

[tscrim]

comment:9

I also verified that it works in 6.1.beta2.