Apologies, must read email when my brain is working. The deformation gradient has a covariant index on M and a contravariant index on S. As such it maps a vector on M to a (deformed m) vector on S i.e., x^i = F^i_J X^J where F^i_J = \del chi(X^i) / X^J where x = \chi(X).
On Sun, 5 Feb 2023 at 10:05 PM, Chris Bradley < chris.patrick.brad...@gmail.com> wrote: > Hi all, > I'm new to Sage so forgive me if this is a dumb question but does Sage > deal with two-point tensors? By this I mean a second order tensor with one > contravariant index in the tangent space of one manifold and one > contravariant index in the tangent space of another manifold. The > particular application is in solid mechanics and is the deformation > gradient tensor which is given by the derivative of the map between the two > manifolds i.e., \chi: M -> S where M has chart coordinates X and S has > chart coordinates x and the deformation gradient tensor is given by F = > \del \chi/ \del X. All I've managed to find, documentation wise, involves > creating tensors from the tangent/cotangent space of a single manifold > rather than a tensor from the tangent space of M and the tangent space of > S. Thanks in advance. > > Best wishes > Chris > > -- > You received this message because you are subscribed to a topic in the > Google Groups "sage-support" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sage-support/XDQHDYuKwRs/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > sage-support+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/94042d7b-7772-4778-818f-21bcea9646b6n%40googlegroups.com > <https://groups.google.com/d/msgid/sage-support/94042d7b-7772-4778-818f-21bcea9646b6n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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 sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAMYg_1tRhOG21CGRYpHxAp%3DXHk8R%2BLmWq4uNMD04dYPYoGaXdw%40mail.gmail.com.
