I was going through this code and got error. But I could not understand why
this is the case.
sage: T = TropicalSemiring(QQ)
sage: T(1)
1
sage: T(2)
2
sage: T(-2)
-2
sage: -T(2)
---------------------------------------------------------------------------
ArithmeticError Traceback (most recent call last)
Cell In[26], line 1
----> 1 -T(Integer(2))
File ~/sage/src/sage/rings/semirings/tropical_semiring.pyx:278, in
sage.rings.semirings.tropical_semiring.TropicalSemiringElement.__neg__()
276 if self._val is None:
277 return self
--> 278 raise ArithmeticError("cannot negate any non-infinite element")
279
280 cpdef _mul_(left, right) noexcept:
ArithmeticError: cannot negate any non-infinite element
sage:
It looks like starting with T(-2) and reaching to -2 from T(2) by comparing
with zero(+Inf) are different things.
T(-2) = -2
T(2) -T(2) = T.zero(+inf) = T(2) + (-T(2))
My doubt is : if we cannot negate the elements, then how can we compute
the determinant of a Matrix over Tropical Semiring.
For example in 2x2 matrix : [[a,b], [c,d]] the determinant should be ad -
bc
But can it be expressed as ad + (-bc) -->> min ( add(a,d), -1*add(b,c) )?
In fact we connot even do matrix subtraction directly.
What can be done in these cases??
On Thursday, March 21, 2024 at 8:48:26 PM UTC+5:30 Animesh Shree wrote:
> Hello Sir,
>
> I have submitted my proposal.
> Please review it and let me know necessary updates and improvements.
>
> I want to verify soundness of my approach and extend the proposal for
> Multivariate Polynomials.
>
> Thank You
> Animesh Shree
> On Tuesday, March 12, 2024 at 12:26:38 AM UTC+5:30 tcscrims wrote:
>
>> Mathematically speaking, you can always weaken axioms. However, there are
>> some extra advantages that additive groups have that commutative semirings
>> don't have (mainly 0, the additive identity).
>>
>> That being said, there isn't anything prevent you from constructing the
>> appropriate categories. It would be good to have a more specific use-case
>> in mind, but that isn't necessary. However, one should be careful with the
>> name because it would conflict with what "most" people would call an
>> algebra (which is why we have MagmaticAlgebras).
>>
>> Best,
>> Travis
>>
>>
>> On Tuesday, March 12, 2024 at 2:57:29 AM UTC+9 [email protected] wrote:
>>
>>> Hello Sir,
>>>
>>> I was going through "Algebras" and I had a doubt.
>>> Does MagmaticAlgebra and AssociativeAlgebra have to be implemented over
>>> Ring only?
>>> I went through internet and google uses rings to define those algebras,
>>> but the axioms that those algebra follow (Unital, Associative) are also
>>> preserved by commutative semirings.
>>> Would it be good to define MagmaticAlgebra and AssociativeAlgebra over
>>> other objects that follow those axioms too or come-up with alternative
>>> Algebra?
>>>
>>
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