Computing minimal polynomials and the degree of unfaithfulness |
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| Authors: | Wei Li Jie-Tai Yu |
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| Institution: | 1. Department of Mathematics and Statistics , McGill University , Montreal, Quebec, H3A 2K6, Canada;2. Department of Decision Sciences and Engineering Systems , Rensselaer Polytechnic Institute , Current addresses, Troy, NY, 12180;3. Department of Mathematics , University of Notre Dame , Notre Dame, IN, 46556, U.S.A;4. Department of Mathematics , Cornell University , Curent addresses, Ithaca, NY, 14853 |
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| Abstract: | We show how to compute, based on the Gröbner basis computation, the minimal polynomial of n polynomials in n- 1 variables which contain n- 1 algebraically independent elements. We apply this result to automorphisms of polynomial rings.We also generalize these to rational functions and obtain a criterion for a rational map of an affne space to be birational. |
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