Computing and Using Minimal Polynomials
| Autor: | Abbott, John, Bigatti, Anna Maria, Palezzato, Elisa, Robbiano, Lorenzo |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | JSC 2019 |
| Druh dokumentu: | Working Paper |
| Popis: | Given a zero-dimensional ideal I in a polynomial ring, many computations start by finding univariate polynomials in I. Searching for a univariate polynomial in I is a particular case of considering the minimal polynomial of an element in P/I. It is well known that minimal polynomials may be computed via elimination, therefore this is considered to be a "resolved problem". But being the key of so many computations, it is worth investigating its meaning, its optimization, its applications (e.g. testing if a zero-dimensional ideal is radical, primary or maximal). We present efficient algorithms for computing the minimal polynomial of an element of P/I. For the specific case where the coefficients are in Q, we show how to use modular methods to obtain a guaranteed result. We also present some applications of minimal polynomials, namely algorithms for computing radicals and primary decompositions of zero-dimensional ideals, and also for testing radicality and maximality. Comment: This is a fully revised version. To be published in Journal of Symbolic Computation, special Issue on Symbolic Computation and Satisfiability Checking |
| Databáze: | arXiv |
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