Polynomials with frobenius galois groups

Cangelmi, Leonardo

doi:10.1080/00927870008826864

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Some Preliminary Results1

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2003

2022

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Cited by 2 publications

(2 citation statements)

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“…The complexity of the entire algorithm is a polynomial function of |G| (≤ A|G| 4 ). For those solvable polynomials with small Galois groups [9,11,12], we can even solve them manually with the help of this algorithm and the corresponding numerical roots. However, when the order of the Galois group is large, high demands are placed on the precision of the numerical roots.…”

Section: Discussionmentioning

confidence: 99%

An Algorithm for Solving Solvable Polynomial Equations of Arbitrary Degree by Radicals

Li¹

2022

Preprint

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This work provides a method(an algorithm) for solving the solvable unary algebraic equation f (x) = 0 (f (x) ∈ Q[x]) of arbitrary degree and obtaining the exact radical roots. This method requires that we know the Galois group as the permutation group of the roots of f (x) and the approximate roots with sufficient precision beforehand. Of course, the approximate roots are not necessary but can help reduce the quantity of computation. The algorithm complexity is approximately proportional to the 4th power of the size of the Galois group of f (x). The whole algorithm doesn't need to deal with tremendous polynomials or reduce symmetric polynomials.

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Section: Discussionmentioning

confidence: 99%

An Algorithm for Solving Solvable Polynomial Equations of Arbitrary Degree by Radicals

Li¹

2022

Preprint

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“…We recall and reorganize some basic facts about Frobenius groups in Cangelmi 2000 andRobinson (1982) for our purposes. Let f (x) 2 Z[x ] satisfy all the assumptions of the Theorem.…”

Section: Some Preliminary Resultsmentioning

confidence: 99%