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Question: How to use ToJet command when differential expression has composite differentiation ?

Question:How to use ToJet command when differential expression has composite differentiation ?

mskalsi 290 Maple 18
tojet
October 19 2016
0

Dear All

I am stucked at converting an differential expression in Jet notations. Maple is giving error as  expression contains composite derivatives. Please see attached file.


 

> 

with(PDEtools, D_Dx, declare, ToJet, FromJet):
> 

DepVars := [alpha(x, y, t), beta(x, y, t), xi(x, y, t), tau(x, y, t), eta(x, y, t), U(xi(x, y, t), tau(x, y, t), eta(x, y, t))]

[alpha(x, y, t), beta(x, y, t), xi(x, y, t), tau(x, y, t), eta(x, y, t), U(xi(x, y, t), tau(x, y, t), eta(x, y, t))]

 (1)
> 

alias(alpha = alpha(x, y, t), beta = beta(x, y, t), xi = xi(x, y, t), tau = tau(x, y, t), eta = eta(x, y, t), U = U(xi(x, y, t), tau(x, y, t), eta(x, y, t)))

alpha, beta, xi, tau, eta, U

 (2)
> 

declare(alpha, beta, xi, tau, eta, U)

alpha(x, y, t)*`will now be displayed as`*alpha

  

beta(x, y, t)*`will now be displayed as`*beta

  

xi(x, y, t)*`will now be displayed as`*xi

  

tau(x, y, t)*`will now be displayed as`*tau

  

eta(x, y, t)*`will now be displayed as`*eta

  

U(xi(x, y, t), tau(x, y, t), eta(x, y, t))*`will now be displayed as`*U

 (3)
> 

u := U*beta+alpha

beta*U+alpha

 (4)
> 

diff(u, x)

(diff(beta, x))*U+beta*((D[1](U))(xi, tau, eta)*(diff(xi, x))+(D[2](U))(xi, tau, eta)*(diff(tau, x))+(D[3](U))(xi, tau, eta)*(diff(eta, x)))+diff(alpha, x)

 (5)
> 

ToJet((diff(beta, x))*U+beta*((D[1](U))(xi, tau, eta)*(diff(xi, x))+(D[2](U))(xi, tau, eta)*(diff(tau, x))+(D[3](U))(xi, tau, eta)*(diff(eta, x)))+diff(alpha, x), DepVars)

Error, invalid input: PDEtools:-ToJet expects its 2nd argument, DepVars, to be of type Or(`PDEtools/F(...)`, name, And(Or(list({name, `PDEtools/F(...)`}), set({name, `PDEtools/F(...)`})), satisfies(proc (SL) options operator, arrow; evalb(0 < nops(SL)) end proc))), but received [alpha(x, y, t), beta(x, y, t), xi(x, y, t), tau(x, y, t), eta(x, y, t), U(xi(x, y, t), tau(x, y, t), eta(x, y, t))]

  

I guess ToJet is not working in case of composite function.

But how I can  display derivatived (D[1](U))(xi, tau, eta)as U[xi]


 

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