#15822: Tropical semiring cannot exponentiate infinity
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Reporter: darij | Owner:
Type: defect | Status: new
Priority: trivial | Milestone: sage-6.2
Component: algebra | Resolution:
Keywords: tropical semiring, border case | Merged in:
Authors: Darij Grinberg | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by darij:
Old description:
> Just found this while experimenting with my own semirings:
>
> {{{
> sage: T = TropicalSemiring(QQ)
> sage: T.infinity() ** 2
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call
> last)
> <ipython-input-28-b94a4a077331> in <module>()
> ----> 1 T.infinity() ** Integer(2)
>
> /scratch/sage-6.1.1/local/lib/python2.7/site-
> packages/sage/rings/semirings/tropical_semiring.so in
> sage.rings.semirings.tropical_semiring.TropicalSemiringElement.__pow__
> (sage/rings/semirings/tropical_semiring.c:4218)()
>
> /scratch/sage-6.1.1/local/lib/python2.7/site-
> packages/sage/structure/element.so in
> sage.structure.element.RingElement.__mul__
> (sage/structure/element.c:14520)()
>
> /scratch/sage-6.1.1/local/lib/python2.7/site-
> packages/sage/structure/coerce.so in
> sage.structure.coerce.CoercionModel_cache_maps.bin_op
> (sage/structure/coerce.c:8150)()
>
> TypeError: unsupported operand parent(s) for '*': 'Integer Ring' and
> '<type 'NoneType'>'
> }}}
>
> Here is a way to solve this (sage/rings/semirings/tropical_semiring.pyx):
>
> {{{
> def __pow__(base, exp, dummy):
> """
> Return ``self`` to ``exp``.
>
> EXAMPLES::
>
> sage: T = TropicalSemiring(QQ)
> sage: elt = T(2)
> sage: elt**3
> 6
> sage: elt**-2
> -4
> sage: elt**(3/7)
> 6/7
> sage: elt**0
> 0
>
> sage: elt = T.infinity()
> sage: elt**0
> 0
> sage: elt**(1/2)
> +infinity
> sage: elt*33
> +infinity
> """
> cdef TropicalSemiringElement self, x
> self = base
> if self._val is None:
> if exp > 0:
> return self
> elif exp == 0:
> return self.parent().one()
> raise ZeroDivisionError("Tropical division by infinity")
> x = self._new()
> x._val = exp*self._val
> return x
> }}}
>
> Is this good? (I cannot upload branches from here -- git fails
> authorization?)
New description:
Just found this while experimenting with my own semirings:
{{{
sage: T = TropicalSemiring(QQ)
sage: T.infinity() ** 2
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
<ipython-input-28-b94a4a077331> in <module>()
----> 1 T.infinity() ** Integer(2)
/scratch/sage-6.1.1/local/lib/python2.7/site-
packages/sage/rings/semirings/tropical_semiring.so in
sage.rings.semirings.tropical_semiring.TropicalSemiringElement.__pow__
(sage/rings/semirings/tropical_semiring.c:4218)()
/scratch/sage-6.1.1/local/lib/python2.7/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__mul__
(sage/structure/element.c:14520)()
/scratch/sage-6.1.1/local/lib/python2.7/site-
packages/sage/structure/coerce.so in
sage.structure.coerce.CoercionModel_cache_maps.bin_op
(sage/structure/coerce.c:8150)()
TypeError: unsupported operand parent(s) for '*': 'Integer Ring' and
'<type 'NoneType'>'
}}}
Here is a way to solve this (sage/rings/semirings/tropical_semiring.pyx):
{{{
def __pow__(base, exp, dummy):
"""
Return ``self`` to ``exp``.
EXAMPLES::
sage: T = TropicalSemiring(QQ)
sage: elt = T(2)
sage: elt**3
6
sage: elt**-2
-4
sage: elt**(3/7)
6/7
sage: elt**0
0
sage: elt = T.infinity()
sage: elt**0
0
sage: elt**(1/2)
+infinity
sage: elt*33
+infinity
"""
cdef TropicalSemiringElement self, x
self = base
if self._val is None:
if exp > 0:
return self
elif exp == 0:
return self.parent().one()
raise ZeroDivisionError("Tropical division by infinity")
x = self._new()
x._val = exp*self._val
return x
}}}
Is this good? (I cannot upload branches from here -- "fatal: remote error:
access denied or repository not exported: /sage.git")
--
--
Ticket URL: <http://trac.sagemath.org/ticket/15822#comment:1>
Sage <http://www.sagemath.org>
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