What you need to define a coordinate system and vector calculus (div, curl, etc.) is a set of coordinate variables, a corresponding set of basis vectors, the dot products of all the basis vectors in terms of the coordinates (the metric tensor), and the derivatives of the basis vectors as a linear combination of the basis vectors with coefficients that depend only upon the coordinates (derivable from the Christoffel symbols which are derived from the metric tensor). Note that the metric tensor can be derived from the vector manifold function which you can write in rectangular coordinates with coefficients that are functions of the coordinates of the coordinate system you wish to define. Instead of hard coding a particular coordinate system just instantiate a member of the coordinate system class as needed with a given vector manifold function or a given metric tensor. For example if the class is called CoordinateSystem then for a spherical coordinate system you would have -
ShericalCooridinates = CoordinateSystem((r*cos(theta),r*sin(theta)*cos(phi),r*sin(theta)*sin(phi)),(r,theta,phi)) where (r*cos(theta),r*sin(theta)*cos(phi),r*sin(theta)*sin(phi)) is the vector manifold for spherical coordinates and (r,theta,phi) are the coordinate symbols. The if V is a vector function in terms of the spherical coordinates you could have ShericalCooridinates.div(V) returns the divergence and ShericalCooridinates.curl(V) returns the curl, and if A and B are two vectors in spherical coordinates then ShericalCooridinates.dot(A,B) returns the dot product and ShericalCooridinates.cross(A,B) returns the cross product. On Tue, Mar 21, 2017 at 4:21 PM, Sassi Aissa < sassi.aissa.takiedd...@gmail.com> wrote: > As I read the description of the Idea, I think I have to implement an > abstract class called: Coordinate System, then create several classes that > represent different types > of Coordinate system and inherent from the so called 'Coordinate System' > class. Is it like this? > > -- > 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/747ffaa1-3d64-4728-8e8e-8b76b59e4a31%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/747ffaa1-3d64-4728-8e8e-8b76b59e4a31%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-kNRNxOhxn7MvkKHO5MQb1dKFbio6c37cv0oF8MujHKMA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
