Engineering↗
Galois Groups of Cubic and Quartic Fields
Complete determination of Galois groups in degrees three and four, where the discriminant and one cubic resolvent decide everything.
Tag
Galois Group
Every page in the KEVOS library tagged Galois Group. 7 pages.
Engineering↗
Galois Groups of Quintic Fields
Determining Galois groups in degree five, where solvability by radicals first fails and the resolvent degrees grow.
Engineering↗
Galois Groups of Sextic and Septic Fields
Degrees six and seven, where the number of candidate groups and the resolvent degrees make careful strategy essential.
Engineering↗
Test Polynomials for Galois Group Software
Why Galois group implementations need a curated test set, what a good set covers, and how to build one.
Engineering↗
The Galois Group Computation Problem
What computing a Galois group means, why the splitting field cannot be constructed, and the transitive group classification that makes the problem finite.
Engineering↗
The Resolvent Method for Galois Groups
Constructing resolvent polynomials whose factorisation distinguishes candidate Galois groups, and the practical issues in using them.
Engineering↗
Computing Galois Groups of Number Fields
The resolvent method for determining Galois groups, the Frobenius cycle-type approach via Dedekind's theorem, transitive group classification by degree, and test polynomials.
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