SR(infinity) / unsigned_infinity returns 0

[eviatarbach]

An error with division of infinities:

sage: infinity / unsigned_infinity
ValueError: unsigned oo times smaller number not defined
sage: SR(infinity)/unsigned_infinity
0
sage: gamma(SR(-2))/gamma(-4)
0

[zimmerma]

note also that limit returns "infinities" from the SymbolicRing? and not from the InfinityRing?, whereas it takes as input elements from the InfinityRing?:

sage: a=+Infinity
sage: b=limit(x, x=a)
sage: type(a), a.parent()
(sage.rings.infinity.PlusInfinity, The Infinity Ring)
sage: type(b), b.parent()
(sage.symbolic.expression.Expression, Symbolic Ring)

As a consequence, the equality a==b does not return True:

sage: a==b
+Infinity == +Infinity

Paul

[eviatarbach]

Hmm... But isn't that the case with anything in the Symbolic Ring? For example,

sage: SR(4) == 3
4 == 3
sage: type(limit(1/x, x=1))
<type 'sage.symbolic.expression.Expression'>

Calling bool with the equality returns a boolean:

sage: bool(a == b)
True

Calling .pyobject() on the result from limit would be sensible, I think. We have the following discrepancy now:

sage: type(diff(1))
<type 'sage.symbolic.expression.Expression'>
sage: type(integrate(0, x))
<type 'sage.rings.integer.Integer'>

It's very troubling how broken arithmetic and comparisons with infinities is at the moment, as shown in #11506.

[zimmerma]

ok I revert my comment 1.

Paul

[pbruin]

Fixed by #11506; the same error is now raised in all three cases. We should just add a doctest.

[pbruin]

Here is a doctest.

[jkeitel]

Looks good and works.