Abstract
Let R be a commutative ring with 1, let R[X 1…,X n ] be the polynomial ring in X 1,…, X n over R, let G be a permutation group acting on the indeterminates and let σ1, …, σ n be the elementary symmetric polynomials.
This paper presents a detailed analysis and implementation issues of an algorithm for computing a representation of an arbitrary G-invariant polynomial in R[X 1…,X n ] as a finite R[σ1, …, σ n ]-linear combination of G-invariant polynomials with a total degree of at most max{n,n(n - 1)/2}. In addition, we show how the degree bounds can be improved for a certain class of permutation groups.
The results of this note are based on the author’s Ph. D. thesis written under the supervision of Proof. Loos(Tübingen) and Prof. Weispfenning(Passau). The author would like to thank Prof. Smith(Güttingen) and N. Killius (Güttingen) for discussion and support. Special thanks to the anonymous referees for their comments and remarks.
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Göbel, M. (1998). On the Reduction of G-invariant Polynomials for Arbitrary Permutation Groups G . In: Bronstein, M., Weispfenning, V., Grabmeier, J. (eds) Symbolic Rewriting Techniques. Progress in Computer Science and Applied Logic, vol 15. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8800-4_4
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DOI: https://doi.org/10.1007/978-3-0348-8800-4_4
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