> Is there a way to compute the gradient and hessian matrices of a vector > field like u = (x) i + (2yz) j + (3xy) k. >
I know you didn't ask for this, but just in case it is of any help, here's how you do it in Cadabra (https://cadabra.science). Cadabra uses Sympy under the hood, so it's at least a partial Sympy answer. Set-up with: {x,y,z}::Coordinate; {i,j,k,l}::Indices(values={x,y,z}); \partial{#}::PartialDerivative; rl:= { u_{x} = x, u_{y} = 2 y z, u_{z} = 3 x y }; The gradient can then be computed using: grad:= g_{i j} = \partial_{i}{ u_{j} }; evaluate(grad, rl, rhsonly=True); and the Hessian with: H:= H_{i j k} = \partial_{i j}{ u_{k} }; evaluate(H, rl, rhsonly=True); Hope this helps. Kasper -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/6f06c7ac-46d7-499f-af4d-392e9399be24o%40googlegroups.com.
