Thank you very much for the reply. What I was looking for was a tensor which I could manipulate and then choose the basis at a later time. With your example, which is similar to what I started with, I am unable to do things like take the covariant derivative with respect to an arbitrary metric. Or if I wished to check relationships with an arbitrary tensor
On Thursday, May 26, 2016 at 8:58:05 AM UTC-4, Eric Gourgoulhon wrote: > > Hi, > > Le mercredi 25 mai 2016 18:40:57 UTC+2, Zach Elgood a écrit : >> >> I recently started using Sage Manifolds, and was wondering if it was >> possible to define tensor expression independent of basis. For example, I >> am working with some quantum field theory, and am trying to define the >> following tensor >> >> U_mu=partial_mu (psi)/(sqrt(partial_nu(psi) nabla^nu (psi)) >> >> where psi is a scalar field. I want this to be valid independent of the >> choice of basis. >> >> > With SageManifolds, all tensor expressions are independent of basis, > although internally computations are made in one or more bases. > For instance, your example could be written as (assuming that (M,g) is a > Lorentzian manifold): > > psi = M.scalar_field(...) > dpsi = psi.differential() > U = dpsi / sqrt( g.inverse()(dpsi, dpsi) ) > > There is no mention of any basis in the definition of U. > > Best wishes, > > Eric. > -- You received this message because you are subscribed to the Google Groups "sage-support" 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 https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
