Engineering↗
Buchmann's Sub-exponential Algorithm: Overview
Buchmann's algorithm for class groups and units of arbitrary number fields, its structure, and where its cost concentrates.
Every page in the KEVOS library tagged Number Field. 4 pages.
Buchmann's algorithm for class groups and units of arbitrary number fields, its structure, and where its cost concentrates.
Factoring polynomials whose coefficients lie in a number field, by reduction to the rational case via norms.
Number fields as finite extensions of the rationals, their embeddings and signature, and the presentation on which all computation depends.
Algebraic numbers and integers, minimal polynomials, number fields as finite extensions of Q, real and complex embeddings, the signature, and the primitive element theorem.