Sym Paclet Symbol

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EulerOperator

EulerOperator[0, functions][expr]
gives the action of the Euler operator or variational derivative, in respect to a given set of functions, on an expression expr.

EulerOperator[order, functions][expr]
gives the action of the higher Euler operator or Lie-Euler operator of order order, in respect to a given set of functions, on an expression expr.

MORE INFORMATION

To use EulerOperator, you first need to load the SYM Package using Needs["SYM`"].

The order can be a vector of integers with dimension equal with dimension of the variable space of the functions.

functions is given as a list of functions.

expr can be any expression including the functions and the derivatives of them.

Basic Examples (2)

For the same expression different orders gives:

Application of the EulerOperator for multivariable functions and for mixed orders

Applications (2)

Neat Examples (1)

HomotopyOperator

SYM Overview