Abstract
AbstractSeveral techniques for calculating the Galois resolvents of polynomial equations are discussed and implemented. In particular, the method of power sums, in conjunction with the symbolic algebra program muMATH, is used to derive a complete set of explicit algebraic resolvents for the general sextic equation. A simple example, drawn from the theory of crystal elasticity, illustrates the utility of these results in answering the question “When is a polynomial equation (with multinomial coefficients) solvable?”.
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