use of substitute

Question

I have a function of 3 variables F = F(a,b,c), 3 functions of 2 variables A(m,n), B(m,n) and C(m,n)

How do we input this in cadabra?

f(m,n) = F(A(m,n),B(m,n),C(m,n))

I also want to calculate the chain rule (partial derivative) and calculate the 2nd partial derivative.

Comments

What have you tried so far?

Answer 1

\mu,\nu::Coordinate; a,b,c::Coordinate; F:=F(a,b,c); A:=A(\mu,\nu); B:=B(\mu,\nu); C:=C(\mu,\nu); Seems to work

substitute(F, $a -> A$); substitute(F, $b -> B$); substitute(F, $c -> C$); Also seems to work

I tried this example from the site: https://cadabra.science/manual/PartialDerivative.html

\tau::Coordinate; \partial{#}::Derivative(\tau); f::Depends(\tau); ex:= \partial{f g}; unwrap(ex);

It returns 0 instead of g∂f

Comments

This last example works but you need to have a sufficiently recent cadabra.