Gröbner basis design example

Length 10, 4 zero wavelet moments
(N=10, K=4)

The first step of the design procedure is to generate the design equations. The Maple program setup generates the design equations and writes them to the file eqs.

The set of nonlinear design equations is first converted into a grevlex Gröbner basis (gb.dp) of degree 40. Then that is converted in turn into a lexical Gröbner basis (gb.lp). This is done with the Singular program sfile which reads the design equations and computes the Gröbner bases. The lexical lexical Gröbner basis gb.lp does not factor.

The Gröbner basis gb.lp has 40 solutions, but 24 of them are complex so are ignored. The remaining 16 real solutions are computed numerically from gb.lp by the Maple program result. The numerical solutions are written to the Matlab files.