@Aaron Thanks for the feedback, the KroneckerDelta anecdote is hilarious. I suspect that a lot of current work could be refactored with a good linear algebra module. There is even a current GSoC project discussing units that could make use of it. Lots of things that SymPy finds difficult are easily representable as vector spaces. Thanks also for updating the page, ground types is not something I know much about. I'll add to the projects page when I get some time.
@Alan I completely agree about abstract index notation. I have a small section of the wiki page on tensor indexing. There I pose that we might be able to use indexing as a way to define most operations. The tricky thing with this project is how to describe all tensor-ish operations with a single syntax that can be applied to a wide variety of applications. Can we create a single system which can be cleanly extended to include both Riemannian geometry and dense matrix computations? My current thought is that indexed expressions are a powerful-yet-general description that these representations all share. Any work done on indexed expressions (such as your idea of finding symmetries) would apply for all application projects. I really appreciate the input so far. I think that if only one person thinks about this project then it will likely end up as just-another-linear-algebra-module. Extra perspectives greatly reduce this risk. I would be interested in what people could see coming out of a general linear algebra system. What projects would this facilitate? On Mon, Feb 20, 2012 at 9:38 PM, Alan Bromborsky <[email protected]>wrote: > On 02/20/2012 10:00 PM, Aaron Meurer wrote: > >> I updated the section on that page about ground types to be a little >> clearer about what we want there. Many things will actually involve >> improvements to Poly() to get things to work (for example, the >> addition of a Frac() class). >> >> Aaron Meurer >> >> On Mon, Feb 20, 2012 at 7:40 PM, Aaron Meurer<[email protected]> wrote: >> >>> On Mon, Feb 20, 2012 at 2:19 PM, Matthew Rocklin<[email protected]> >>> wrote: >>> >>>> Hi Everyone, >>>> >>>> I would like to create a general tensor/linear algebra framework for >>>> SymPy. >>>> I'd like to hear ideas from the community about this. >>>> >>>> We already have a few linear algebraic projects within SymPy >>>> (i.e. Matrices, SparseMatrices, MatExprs, Indexed/IndexedBase code >>>> generation, Physics stuff, Geometric Algebra (sort of)) but they don't >>>> communicate well. It would be nice to create a general and abstract >>>> framework off of which these projects and others could hang and interact >>>> more naturally. >>>> >>>> I'm writing the community about this for two reasons. >>>> Reason one: I'd like feedback as to whether or not this sort of >>>> undertaking >>>> is a good idea. If it is I'd welcome some thoughts on how it should be >>>> done >>>> and how it could be useful for future work. >>>> >>> Definitely. One problem right now is that a lot of modules duplicate >>> work, because we don't really have a good centrailzed module for >>> things. For example, over GCI, a student merged together three >>> independent KroneckerDelta implementations (one in >>> sympy/physics/quantum, one in sympy/physics/secondquant, and one in >>> sympy/functions/special/**tensor_functions.py). No doubt there are >>> other things still duplicated. >>> >>> That's also why even if we are implementing some of these things to >>> help with physics, we should try to separate mathematical concepts >>> from physical concepts in the implementation. >>> >>> Reason two: I think I can separate this work into a few pieces, each of >>>> which would make for a good GSoC project for this year or next. Is this >>>> endeavor something into which the community would want to invest >>>> resources? >>>> >>> I think so. Some projects may depend on others (e.g., we're limited in >>> what we can do with slow matrices). But feel free to do this and add >>> the ideas to the GSoC ideas page. That page needs more ideas that >>> have more descriptions on them (like the ones at the bottom). Not >>> only will this help potential students, but it will help us a lot when >>> we apply. >>> >>> Aaron Meurer >>> >>> Here are some projects that interest me >>>> >>>> Framework design - we need a sufficiently general framework (this is >>>> hard >>>> and probably has to be half completed before GSoC time) >>>> Abstract Vector Spaces >>>> Tensor Math - Krastanov was talking about this and I think it's a great >>>> idea. There is a lot of good multilinear algebra out there that SymPy >>>> doesn't currently touch at all. >>>> General storage - Efficient NDArray classes (dense, mutable, sparse, >>>> functional, numpy, external programs) - views of NDArrays (transpose, >>>> slices). >>>> Theorem proving type system for >>>> tensors/matrices http://scicomp.stackexchange.** >>>> com/questions/74/symbolic-**software-packagbasic<http://scicomp.stackexchange.com/questions/74/symbolic-software-packagbasic>es-for-matrix-expressions >>>> >>>> I've dumped some thoughts on the following wiki page >>>> https://github.com/sympy/**sympy/wiki/Linear-Algebra-**Vision<https://github.com/sympy/sympy/wiki/Linear-Algebra-Vision> >>>> >>>> Comments or questions are welcome. >>>> >>>> -Matt >>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups >>>> "sympy" group. >>>> To post to this group, send email to [email protected]. >>>> To unsubscribe from this group, send email to >>>> sympy+unsubscribe@**googlegroups.com<sympy%[email protected]> >>>> . >>>> For more options, visit this group at >>>> http://groups.google.com/**group/sympy?hl=en<http://groups.google.com/group/sympy?hl=en> >>>> . >>>> >>> I am rewriting the geometric algebra module using noncommuting symbols > to represent base vectors and base multivectors and let general > multivectors be linear combinations of the base multivectors and let sympy > do the heavy > lifting with regard to simplification and other operations. The current > GA module was written before I understood what sympy could do and is a real > mess from the point of view of being an extensible module. > > Someone should employ all the inherent abilities of sympy to write a > module for Tensors using Penrose's abstract index > http://en.wikipedia.org/wiki/**Abstract_index_notation<http://en.wikipedia.org/wiki/Abstract_index_notation>notation > especially allowing for simplifications using tensor symmetries > and also allow for symbolic differentiation. > > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to sympy+unsubscribe@** > googlegroups.com <sympy%[email protected]>. > For more options, visit this group at http://groups.google.com/** > group/sympy?hl=en <http://groups.google.com/group/sympy?hl=en>. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
