Hi, Could it be that you are looking for the pushforward operator associated to a differentiable map between two manifolds? cf. https://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/differentiable/diff_map.html#sage.manifolds.differentiable.diff_map.DiffMap.pushforward
Eric. Le dimanche 5 février 2023 à 12:56:05 UTC+1, chris.patr...@gmail.com a écrit : > 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.patr...@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...@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/7aa4c9d9-62ec-4f19-b4de-2f83e9d7eab3n%40googlegroups.com.
