Hi Pablo, On Sat, 22 Oct 2011 18:49:39 -0300 Pablo De Napoli <[email protected]> wrote:
> On Thu, Oct 20, 2011 at 6:02 PM, Pablo De Napoli <[email protected]> > 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 [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
