Abstract
A method for calculating the location of all types of level lines of a real polynomial on the real plane is proposed. To this end, the critical points and critical curves of the polynomial and then its critical values (there are a finite number of them) should be calculated. Using this data, all critical level lines and one representative for each noncritical level line corresponding to intervals of values between adjacent critical level lines are found. A scheme for calculating level lines based on algorithms of polynomial computer algebra—Gröbner bases and primary ideal decomposition—is proposed. Software for implementing these calculations is indicated. Nontrivial examples are discussed.
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Bruno, A.D., Batkhin, A.B. Level Lines of a Polynomial on a Plane. Program Comput Soft 48, 19–29 (2022). https://doi.org/10.1134/S0361768822010030
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DOI: https://doi.org/10.1134/S0361768822010030