Hi Burcin, Many thanks! I see that with this patches, it would be esasy to have also a Weyl algebra implementation in Sage
Cheers, Pablo On Mon, Oct 24, 2011 at 10:11 AM, Burcin Erocal <bur...@erocal.org> wrote: > Hi Pablo, > > On Sat, 22 Oct 2011 18:49:39 -0300 > Pablo De Napoli <pden...@gmail.com> wrote: > >> On Thu, Oct 20, 2011 at 6:02 PM, Pablo De Napoli <pden...@gmail.com> >> wrote: >> > Hi, >> > >> > I need to perform computations with linear differential operators >> > whose coefficients are polynomials >> > in several variables (in Euclean space). >> > Has Sage some support for this kind of computation? >> > >> > Could you suggest me some tool for doing that? >> > >> > For instance assume that you have two first order differentian >> > operators (vector fields in the language of differential geometry) >> > like >> > >> > X = x D_x - y D_y >> > >> > Y= x D_x - y D_z >> > >> > where D_x is the partial derivative with respect to x. I would like >> > to compute XY >> > [which is a second order operator], or things like the Lie bracket >> > [X,Y]=XY-YX) [which is a first order one] > > You can also do this in Sage, after applying the patches at #4539: > > http://trac.sagemath.org/sage_trac/ticket/4539 > > This is a generic interface to the noncommutative part of Singular. > > http://www.singular.uni-kl.de/Manual/latest/sing_387.htm#SEC427 > > sage: F.<x,y,z,dx,dy,dz> = FreeAlgebra(QQ, 6) > sage: G = F.g_algebra({dx*x: x*dx + 1, dy*y: y*dy + 1, dz*z: z*dz + 1}) > sage: G.inject_variables() > Defining x, y, z, dx, dy, dz > sage: X = x*dx - y*dy > sage: Y = x*dx - y*dz > sage: X*Y > x^2*dx^2 - x*y*dx*dy - x*y*dx*dz + y^2*dy*dz + x*dx + y*dz > sage: X*Y - Y*X > y*dz > > > Cheers, > Burcin > -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
