You might find the following github project built upon sympy of interest - https://github.com/brombo/galgebra
and https://en.wikipedia.org/wiki/Conformal_geometric_algebra In conformal geometric algebra rotations, general rotation (about any point) translations, screws, inversions, and dilations in N dimensions are rotations about the origin in an N+2 dimensional Minkowski space. On Sat, Mar 18, 2017 at 6:48 AM, Дрынкин Роберт <rob.dryn...@gmail.com> wrote: > Hello, > My name is Robert Drynkin and I am first-year student of Applied > Mathematics and Computer Science in HSE and Mathematics in IUM. I have > never contributed to open source projects, but I was really exited by your > project, and I want to use it and make it better. I have found that > geometry module is small, and I want to rewrite it, make it more abstract. > You can have a look at the table explaining my idea and, if you have any > questions, continue reading. I would like to start from creating > N-dimensional projective space with homogeneous coordinates in N+1 > dimensional vector space. Inside this space we can find N-dimensional > Euclidian space like affine map. After that we can implement homograhies > and, as a particular case, affine transformations. Of course, we want to > have a usual plane with classic objects, and we, motivated by this aim, > start to write bilinear forms -> quadratic forms -> quadrics -> conics and > it is enough to calculate circles, ellipses, parabolas, hyperbolas and > lines on the projective plane and at the same time all conics for > projective space. Of course, if we have projective space, we should have > duality space. No less interesting object is projective line, and the fact > that on any smooth conic we can introduce homogeneous coordinates (and all > consequences from this fact, although I have no ideas so far how to > effectively implement it). In our construction we can easily add a > polyhedron to our Euqlidian space, like a convex cone in enclosing space. > In conclusion, we should add visualization module (there we face some > questions about dimensions of spaces). Also, there is a question about > which field we are working in (I don't want to limit it with R, at least > because it is not algebraically closed). It is the first idea, of course > there are much interesting things to add. > > > Also, me and my friend(looo...@gmail.com > <https://vk.com/write?email=looo...@gmail.com>) from MIPT have some ideas > about non-rigid body physics project. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at https://groups.google.com/group/sympy. > To view this discussion on the web visit https://groups.google.com/d/ > msgid/sympy/929de326-119a-4ee2-8a46-1016b8c752b2%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/929de326-119a-4ee2-8a46-1016b8c752b2%40googlegroups.com?utm_medium=email&utm_source=footer> > . > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CALOxT-mMxHs4eq0ZTvz80-Ng-LSmzrDOUq-Jrg2d6RYhbgH-qw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
