Engineering↗
Transcendence Degree and Finite Field Extensions
Field extensions have algebraic notions of dimension. Transcendence degree measures the number of algebraically independent parameters; finite extensions are ordinary finite-dim…
Tag
minimal polynomial
Every page in the KEVOS library tagged minimal polynomial. 5 pages.
Engineering↗
Algebraic Numbers and Minimal Polynomials
Algebraic numbers, minimal polynomials, algebraic integers, and the computational tests that distinguish them.
Engineering↗
Detecting Algebraic and Linear Dependence with LLL
Recovering exact integer relations from numerical approximations using LLL, and the precision requirements that make the method reliable.
Engineering↗
The Characteristic Polynomial and the Hessenberg Method
Computing the characteristic polynomial via Hessenberg reduction, and its role in producing minimal polynomials of algebraic numbers.
Engineering↗
Algebraic Numbers and Number Fields
Algebraic numbers and integers, minimal polynomials, number fields as finite extensions of Q, real and complex embeddings, the signature, and the primitive element theorem.
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