On 7 October 2014 12:13, Kurt Pagani <[email protected]> wrote: > > On Tuesday, 7 October 2014 05:36:26 UTC+2, Bill Page wrote: >> ... >> Your examples look good to me, except I would definitely prefer not to >> have to pass a metric for each function call. > > In the first place I had included the functions, > > g:SMR := diagonalMatrix([1 for j in 1..dim]) > > showMetric(x) == g > > setMetric(x,m) == > symmetric? m => g:=m > error("metric tensor should be symmetric.") > > to (re)set it when needed (Euclidean as default). Then I asked here what's > better, parameter or inline. There is by now 2:1 against including :) I > believe most users will not write dot(a,b,g)/hodgeStar(a,g) anyway a lot but > writing a macro or prefix/matchfix operator where you can hide the metric. >
I also definitely don't like the idiom of stateful/destructive operations on domains like 'setMetric'. I would strongly prefer either a package call or a new domain with additional static parameter. > >> we were to create a >> new domain that allows metric to be part of the definition, >> what should it be called? > > I have no idea. You tell me? I can't yet overview how the final module(s) > should look like. How about: DifferentialGeometry It is consistent with your objectives below and gives some room to add more. It is a pretty obvious name for most applications even if the orientation remains suitably abstract and generic in the FriCAS/Axiom tradition.. > What I have in mind is first to complete this by functions like proj > (projection on homogeneous parts, subspaces), push forward/pull > back, interior product i_X and Lie derivative L_X which is possible > which little effort, second to have simplicial homology (e.g. a type Simplex) > then using FreeAbelianGroup(Simplex), defining boundaryOperator and > so on such that one can deal with integration of differential forms over > simplicial complexes (Stokes theorem, Hodge pairing and so on you > know). It's almost all there but one has to organize it. It should be a > teamwork to becoming really useful, so any suggestions welcome. Yes! I think your orientation and objectives are perfect. I would be very glad to help where I can. Bill Page. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
