I have updated the proposal in GSOC portal. I updated the following things - Breakdown of Project Synopsis - Added phases of development - Updated the schedule - Added Appendix for extra details ( diagrams )
I submitted my proposal for the topic : *" Implement matrix spaces over commutative semirings <https://wiki.sagemath.org/GSoC/2024#Implement_matrix_spaces_over_commutative_semirings> "* These are my basic details - Name: Animesh Shree ( Shay2Shay ) - College: Indian Institute of Information Technology, Sri City, India - Employment : Student ( 2021-25 Batch, 3rd Year, B.Tech. CSE ) - Skill: Python, Cython, C-API On Sunday, March 31, 2024 at 2:52:35 PM UTC+5:30 Animesh Shree wrote: > Sorry, I mistakenly attached wrong file. > This is the correct one > > On Sunday, March 31, 2024 at 11:36:25 AM UTC+5:30 Animesh Shree wrote: > >> Actually I was facing few errors. >> The 4th error made me feel like coercion was required. >> >> >> On Sunday, March 31, 2024 at 3:24:02 AM UTC+5:30 tcscrims wrote: >> >>> First, coercion is not in any way essential for polynomial rings. It >>> makes some things a bit more cumbersome, but it is certainly workable by >>> putting elements in the tropical semiring. >>> >>> Second, the operations between, e.g., integers and tropical ring >>> elements does *not* make sense. What is T(1) + 1? Is it 1 or 2? There's no >>> good way to answer this. The case with (integer) 0 under addition is a >>> special case that I would like to not have, but changing that would be more >>> work than the benefit. >>> >>> Best, >>> Travis >>> >>> >>> On Sunday, March 31, 2024 at 6:45:12 AM UTC+9 anime...@iiits.in wrote: >>> >>>> I read about Matrix Algebra over Tropical Semiring and found that there >>>> is "tropical determinant" for this purpose (Page 3 : Eq 4 >>>> <http://www.math.uni-konstanz.de/~michalek/may22.pdf>). This >>>> formulation does not use (additive) inversion. >>>> >>>> I was also trying different operations between tropical elements and >>>> other elements(like Integers). It looks like there is a need for >>>> implementation of coercion maps between few datatypes and tropical >>>> elements. >>>> One can check this by running few commands like >>>> sage: T = TropicalSemiring(QQ) >>>> sage: a = T(1); b = T(0) >>>> sage: a + 0; b + 0 >>>> sage: a * 0; b * 0 >>>> sage: a + 1; b + 1 >>>> sage: a * 1; b * 1 >>>> >>>> Coercion maps and models are crucial for polynomial element >>>> implementation. >>>> For example : between >>>> 'Symbolic Ring' and 'Tropical semiring over Rational Field' >>>> 'Univariate Polynomial Ring in x over Tropical semiring over Rational >>>> Field' and 'Tropical semiring over Rational Field' >>>> 'Tropical semiring over Rational Field' and 'Integer Ring' >>>> On Friday, March 29, 2024 at 12:16:44 AM UTC+5:30 tcscrims wrote: >>>> >>>>> One needs to be *very* careful about what operations mean. -T(2), the >>>>> (tropical) additive inverse of 2, is *not* T(-2). There is no way to >>>>> have min(2, a) = \infty (note that this is the (tropical) additive unit). >>>>> >>>>> I am not sure how (or if) determinants over the tropical semiring are >>>>> defined, but one could define it by having the sign included in each >>>>> term. >>>>> So for the 2x2 case, it could be T(a*b) + T(-b*d), but I don’t know if >>>>> this >>>>> makes det a group homomorphism. >>>>> >>>>> Best, >>>>> Travis >>>>> >>>>> >>>>> On Wednesday, March 27, 2024 at 2:17:39 AM UTC+9 anime...@iiits.in >>>>> wrote: >>>>> >>>>>> This problem can be seen clearly if we use *Matrix_generic_dense* as >>>>>> element class for matrix space. >>>>>> >>>>>> >>>>>> On Tuesday, March 26, 2024 at 9:42:45 PM UTC+5:30 Animesh Shree wrote: >>>>>> >>>>>>> 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 anime...@iiits.in >>>>>>>>> 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? >>>>>>>>>> >>>>>>>>> -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. 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