Aaron, it would be wonderful if we could discuss the implementation of the Frac function.
On Jun 2, 10:37 pm, Aaron Meurer <asmeu...@gmail.com> wrote: > I use Matrices in the Risch algorithm. > Seehttps://github.com/asmeurer/sympy/blob/integration3/sympy/integrals/p.... > The function in the test > athttps://github.com/asmeurer/sympy/blob/integration3/sympy/integrals/t... > should give you an idea of a typical usage. > > The matrices are rational functions, with possible symbolic > coefficients, though the computability problems for symbolic > coefficients is something we know we will have to deal with (see the > comment at the top of constant_system()). At the moment, it doesn't > get very large with what is implemented, but it could when more things > are implemented. The main things that I need to do are rref(), with > correctness assured with rational functions, and the ability to > compute null spaces (mainly with rational entries, but I suppose they > could be any symbolic entries). This is the only part of the Risch > algorithm code that uses Expr instead of Poly, since Matrix doesn't > work with Poly (we would need a Frac class for that). I don't like > how I have to manually make sure rref calls cancel to assure > correctness (actually, if we had Frac, I could remove a ton of calls > to Poly.cancel in my code). > > Like Mateusz pointed out, heurisch() solves a huge linear system. The > sizes he gives are a little misleading, since those are only for the > integrals that run fast enough to be in the tests. If you try to run > an integral like the one from issue 1441, it hangs because of a sparse > system of about 600 equations in about 450 variables (put a print > statement in the code). > > Aaron Meurer > > > > > > > > On Tue, May 31, 2011 at 9:51 PM, Brian Granger <elliso...@gmail.com> wrote: > > Hi, > > > In sympy.physics.quantum we use sympy Matrix instances all over the > > place. These can be quite large (100x100 up to many 1000x1000. In > > the future we could get even bigger) and always have symbolic entries. > > At times we do like to convert them to numerical numpy arrays, but in > > many cases we really want the symbolic forms. > > > On Sat, May 28, 2011 at 6:56 AM, SherjilOzair <sherjiloz...@gmail.com> > > wrote: > >> I would like to know how and where Sympy's matrices are used. > >> Is Sympy matrices used for numeric computing anywhere ? > >> Are Sympy Matrices expected to offer any advantage that matrices in > >> numpy/scipy or other libraries cannot offer ? > > >> Is its use limited to symbolic ? What size of Matrices with symbolic > >> content is used ? > >> Operations on Expr are way costlier than operations on numerics. So, > >> knowing the size of the symbolic matrices that are required would help > >> me in optimization when writing algorithms for sparse matrices, and > >> also when refactoring Matrix. > > >> I expect that one cannot use too large symbolic matrices, as solving/ > >> inversing/etc. would result in expression blowup. > > >> I would be glad if you could also tell what running time you would > >> expect from the matrices that you use. > > > instant ;) > > > When we are dealing with large symbolic matrices, we are typically > > just doing matrix/vector multplies. But for small matrices we do > > other things like linear solves, decompositions and eigenvalue > > problems. symbolic eigenvalues are great, but expressions quickly get > > out of hand as the matrix size increases. > > > Cheers, > > > Brian > > >> -- > >> You received this message because you are subscribed to the Google Groups > >> "sympy" group. > >> To post to this group, send email to sympy@googlegroups.com. > >> To unsubscribe from this group, send email to > >> sympy+unsubscr...@googlegroups.com. > >> For more options, visit this group > >> athttp://groups.google.com/group/sympy?hl=en. > > > -- > > Brian E. Granger > > Cal Poly State University, San Luis Obispo > > bgran...@calpoly.edu and elliso...@gmail.com > > > -- > > You received this message because you are subscribed to the Google Groups > > "sympy" group. > > To post to this group, send email to sympy@googlegroups.com. > > To unsubscribe from this group, send email to > > sympy+unsubscr...@googlegroups.com. > > For more options, visit this group > > athttp://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 sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
