Using Galois ideals for computing relative resolvents

DOI10.1006/jsco.2000.0376zbMath0989.12004OpenAlexW2012218416MaRDI QIDQ5927988

Philippe Aubry, Annick Valibouze

Publication date: 19 March 2001

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/0ce2bd5f16223ba98b3408d0ad81552e4b0c749f

zbMATH Keywords

algorithmscharacteristic polynomialsGalois idealsreduced Gröbner basisrelative resolventsseparable triangular set of polynomials

Mathematics Subject Classification ID

Related Items (16)

PARALLEL COMPUTATION OF RESOLVENTS BY MULTIMODULAR TECHNIQUES AND DECOMPOSITION FORMULA ⋮ A parallel multi-modular algorithm for computing Lagrange resolvents ⋮ Dynamic Galois theory ⋮ New simple algorithms for computing the minimal polynomial of cos(2π/n) ⋮ Algebraic certification of numerical algorithms computing Lagrange resolvents ⋮ Gröbner basis of the alternating Galoisian ideal ⋮ Efficient arithmetic in successive algebraic extension fields using symmetries ⋮ Algebraic computation of resolvents without extraneous powers ⋮ Homotopy techniques for multiplication modulo triangular sets ⋮ Bit-size estimates for triangular sets in positive dimension ⋮ Galois theory, splitting fields and computer algebra ⋮ Computing strong regular characteristic pairs with Gröbner bases ⋮ On approximate triangular decompositions in dimension zero ⋮ Change of order for regular chains in positive dimension ⋮ Computation of the decomposition group of a triangular ideal ⋮ ON THE FIELD INTERSECTION PROBLEM OF SOLVABLE QUINTIC GENERIC POLYNOMIALS

Uses Software

• FGb

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computing Galois groups over the rationals
• Solving zero-dimensional algebraic systems
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• A modular method for computing the Galois groups of polynomials
• Triangular sets for solving polynomial systems: a comparative implementation of four methods
• Study of algebraic relations between the roots of a univariate polynomial
• Computational verification of M₁₁and M₁₂as galois groups over Q
• The transitive groups of degree up to eleven⁺
• Calculs d'invariants primitifs de groupes finis
• Symmetric Functions, m-Sets, and Galois Groups
• The Determination of Galois Groups
• Calcul de résolvantes avec les modules de Cauchy
• Lagrange resolvents
• Galois group computation for rational polynomials

This page was built for publication: Using Galois ideals for computing relative resolvents