Using Galois Ideals for Computing Relative Resolvents
Copyright policy )Using Galois Ideals for Computing Relative Resolvents
In this paper we show that some ideals which occur in Galois theory are generated by triangular sets of polynomials. This geometric property seems important for the development of symbolic methods in Galois theory. It may and should be exploited in order to obtain more efficient algorithms, and it enables us to present a new algebraic method for computing relative resolvents which works with any polynomial invariant.
galois theory, Algebra and Number Theory, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], Separable extensions, Galois theory, characteristic polynomials, idéal de galois, resolvent, separable triangular set of polynomials, [INFO] Computer Science [cs], Symbolic computation and algebraic computation, algorithms, ideal of relations, résolvante, galois ideal, [INFO.INFO-OH] Computer Science [cs]/Other [cs.OH], Computational Mathematics, relative resolvents, Computational aspects of field theory and polynomials, Galois ideals, idéal des relations, théorie de galois, reduced Gröbner basis
galois theory, Algebra and Number Theory, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], Separable extensions, Galois theory, characteristic polynomials, idéal de galois, resolvent, separable triangular set of polynomials, [INFO] Computer Science [cs], Symbolic computation and algebraic computation, algorithms, ideal of relations, résolvante, galois ideal, [INFO.INFO-OH] Computer Science [cs]/Other [cs.OH], Computational Mathematics, relative resolvents, Computational aspects of field theory and polynomials, Galois ideals, idéal des relations, théorie de galois, reduced Gröbner basis
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