Level lines of a polynomial in the plane

We propose a method for computing the position of all level lines of a real polynomial in the real plane. To do this, it is necessary to compute its critical points and critical curves, and then to compute critical values of the polynomial (there are finite number of them). Now finite number of critical levels and one representative of noncritical level corresponding to a value between two neighboring critical ones enough to compute. We propose a scheme for computing level lines based on polynomial computer algebra algorithms: Gröbner bases, primary ideal decomposition. Software for these computations are pointed out. Nontrivial examples are considered.

Simple Algorithm of Wavelet Decomposition Depth and Program Realization

This paper is contraposed how to determine the decomposition depth of the wavelet transform. Based on the principle of the wavelet coefficient keep the “energy” of signal, combined with Mallat algorithm, the article designs a simple algorithm. Though it, we could confirm the ideal decomposition depth of the wavelet analysis. Finally, through an example, we could verify the effectiveness of the algorithm.