On Inner-Product Algorithm in Calculating Normal-Forms and Realization with Computer Algebra

Calculating normal-forms is one of the main algorithms on studying nonlinear dynamical system. There are matrix-expressing, conjugate-operator and Lie-algebra algorithms which can be used in the calculation. It is well known that calculating with conjugate-operator is the main step in finding all orders of normal forms. In this paper, a Mathematica package is presented for calculating normal-forms with inner-product algorithm. The package we compiled possesses generality in calculating high order normal-forms of nonlinear dynamical systems.