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General Formulas for Solving Solvable Sextic Equations

✍ Scribed by Thomas R. Hagedorn

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
414 KB
Volume
233
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let G be a transitive, solvable subgroup of S . We show that there is a common 6 Ž .

w x formula for finding the roots of all irreducible sextic polynomials f x g Q x with Ž . Gal f s G. Moreover, once the roots r are calculated, there is an explicit i Ž . procedure for numbering them so that the Galois group acts via r s r for

g G ; S . We also demonstrate new criteria for determining the Galois group of 6 Ž . w x an irreducible sextic polynomial f x g Q x . The first two results generalize Ž .

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A generalized maclaurin transform for so
A generalized maclaurin transform for solving difference equations
✍ H.E. Heatherly 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 320 KB

The Maclaurin transform (or generating function method) is generalized to have as its range a ring of formal power series. All the usual operations needed for solving difference equations via this method are then carried out in the quotient division algebra of this ring. This allows one to solve dif