Gröbner basis design example

Length 10, 3 zero wavelet moments
(N=10, K=3)

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 64. Then that is converted in turn into a lexical Gröbner basis (gb.lp). The lexical lexical Gröbner basis is then factored into two Gröbner bases (gb.lp.1, gb.lp.2) each of degree 32. This is all done with the Singular program sfile which reads the design equations and computes the Gröbner bases.

The Gröbner basis gb.lp.1 has 18 real solutions. gb.lp.2 has 8 real solutions. The Maple programs result.1, result.2 numerically solve the Gröbner bases gb.lp.1, gb.lp.2 and write the solutions to respective Matlab files.