Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Algorithms in invariant theory
Algorithms in invariant theory
Computing bases for rings of permutation-invariant polynomials
Journal of Symbolic Computation
Algorithm 305: symmetric polynomial
Communications of the ACM
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Term Reduction Systems and Algebraic Algorithms
GWAI '81 Proceedings of the German Workshop on Artificial Intelligence
Algorithms for symmetrical polynomials
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
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This note presents a fast version of the classical algorithm to represent any symmetric function in a unique way as a polynomial in the elementary symmetric polynomials by using power sums of variables. We analyze the worst case complexity for both algorithms, the original and the fast version, and confirm our results by empirical run-time experiments. Our main result is a fast algorithm with a polynomial worst case complexity w.r.t. the total degree of the input polynomial compared to the classical algorithm with its exponential worst case complexity.