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Introduction
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ALIAS-C++
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Generalized inverse trigonometric functions
Contents
Analyzing univariate polynomials
Subsections
Introduction
Finding bounds on the roots
First Cauchy theorem
Mathematical background
Implementation
Example
Second Cauchy theorem
Mathematical background
Implementation
Example
Third Cauchy theorem
Mathematical background
Implementation
Lagrange-MacLaurin theorem
Mathematical background
Implementation
Example
Laguerre method
Mathematical background
Implementation
Example
Laguerre second method
Mathematical background
Implementation
Newton method
Mathematical background
Implementation
Newton theorem
Mathematical background
Implementation
Joyal bounds
Mathematical background
Implementation
Pellet method
Mathematical background
Implementation
Global implementation
Example
Kantorovitch theorem
Implementation
Example
Bounds on the product and sum of roots
Newton relations
Mathematical background
Implementation
Viète relations
Mathematical background
Implementation
Maximum number of real roots
Number of real roots
Descartes Lemma
Mathematical background
Implementation
Budan-Fourier method
Mathematical background
Implementation
Example
Sturm method
Mathematical background
Implementation
Example
Du Gua-Huat-Euler theorem
Mathematical background
Implementation
Separation between the roots
Rump theorem
Mathematical background
Implementation
Example
Analyzing the real roots
Analyzing the real part of the roots
Utilities
Addition of two polynomials
Multiplication of two polynomials
Evaluation of a polynomial
Evaluation in centered form
Safe evaluation of a polynomial
Sign of a polynomial
Implementation
Derivative of a polynomial
Euclidian division
Expansion of
Centered form
Unitary polynomial
Safe evaluation of a vector
Jean-Pierre Merlet 2012-12-20
