Dear mailing list, I was wondering if there is any interest in a Sage package to compute with differential forms. Right now, I have the rudiments of a differential form class with the obvious operations (wedge product, exterior differential, Hodge star, ...) but I want to take this somewhat further: my goal is to be able to deal with Cartan's structure equation, exterior differential systems, point symmetries for ODEs, ... These are all very algorithmic procedures, so they would be relatively easy to implement.
Secondly, a more detailed question: while my class works well from a Python point of view, I don't really know how to incorporate it into the Sage hierarchy. More specifically: the set of all differential forms is a module over the ring of functions on R^n -- how would I incorporate this algebraic structure in Sage? Is there a parent representing a function ring on R^n? Since the result of "f = function(...); f.parent()" is "Symbolic Ring", and I want to be able to coerce functions into 0-forms, should I start with a module over the Symbolic Ring, or is another ring more appropriate? Last but not least, I noticed that there was some discussion on this mailing list on adding support for differential forms and exterior algebra using FriCAS and/or Reduce. There is also a Maxima package that looks interesting. Would this kind of solution be preferred over writing something from scratch? Either way, I would be really interested in developing Sage support for differential forms. Please let me know what you think. Sorry if I've overlooked anything! Sincerely, Joris -- 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
