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Explicit Galois resolvents for sextic equations
Author(s) -
Hurley A. C.,
Head A. K.
Publication year - 1987
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560310306
Subject(s) - mathematics , polynomial , algebra over a field , galois theory , multinomial distribution , simple (philosophy) , symbolic computation , set (abstract data type) , galois group , pure mathematics , computer science , mathematical analysis , programming language , philosophy , statistics , epistemology
Several 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?”.