SYM Paclet Symbol

LinearDependency

LinearDependency[op, {op₁, op₂, ...}, {x₁, x₂, ...}]
yields a list representing differential operator op as a linear compination of operators op_i.

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

The list {x₁,x₂,...} defines the set of operands the operators op, op_i act upon.

If op can be expressed as a linear compination of the operators op_i the vector of this linear compination will be returned otherwise, the empty set {}.

Let the operator x

_x+2y

_y. This operator can be expressed with the base {x

_x, y

_y} as:

Indeed,