SYM Paclet Symbol

HomotopyOperator

HomotopyOperator[fun][expr]
gives the result of the action of the Homotopy operator on an expression expr with respect to a set of functions, fun.

MORE INFORMATION

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

fun is the list of functions.

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

Let the expression between the two functions u,

:

When the Euler Operator is 0 a vector function can be found that its divergence gives back the expression using the Homotopy operator. For the one dimensional case this is equivalent to integrating the function:

Indeed,