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Contents:
Quick start
Installation guide
Documentation
Theory
The algebra of truncated polynomials
Elementary functions
Inverse functions
Practical Examples (to be done by hand)
Taylor models
Basic Python Tutorials:
The very basics
Understanding gduals and floats
Using vectorized doubles
Advanced Python Tutorials:
Differential Intelligence
Training Artificial Neural Networks
High Order Taylor Maps I
High Order Taylor Maps II
Map (series) inversion
Taylor Model Tutorials:
Taylor models of univariate functions
Taylor models of multivariate functions
Exploration of Volterra ODE system
Exploration of Kepler dynamics with a Neural network
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Theory
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Theory
Contents:
The algebra of truncated polynomials
Formal definition
Elementary functions
Exponential
Logarithm
Sine and cosine
Exponentiation
Inverse functions
Inverse hyperbolic tangent
Inverse tangent
The other inverse functions
Practical Examples (to be done by hand)
Example 1 - A multiplication
Example 2 - A division
Example 3 - An exponential
Taylor models
Taylor’s theorem
Formal definition
Arithmetic
References