tax¶

tax is a header-only C++23 library for Truncated Algebraic eXpansions — a framework for computing truncated multivariate Taylor polynomials as first-class objects.

Write natural mathematical expressions and tax automatically propagates the full Taylor series, giving you the function value and all partial derivatives up to order \(N\) in a single evaluation pass.

Features¶

Compile-time fixed order \(N\) and variable count \(M\) via TruncatedTaylorExpansionT<T, N, M>
Lazy expression templates with automatic sum/product flattening and leaf fast-paths
Comprehensive math: arithmetic, trigonometric, hyperbolic, transcendental, power, and special functions
Direct derivative access: coefficients, partial derivatives, gradient, Jacobian, and higher-order derivative tensors
Eigen integration: adapters for Eigen vectors, matrices, and tensors
Taylor ODE integrator: adaptive high-order integration for scalar and vector ODEs
Automatic Domain Splitting: adaptive polynomial approximation over large domains

Quick Example¶

#include <tax/tax.hpp>
#include <iostream>

int main() {
    // sin(x) expanded at x₀ = 0, up to order 9
    auto x = tax::TE<9>::variable(0.0);
    tax::TE<9> f = tax::sin(x);

    std::cout << f.value()         << "\n";   // sin(0) = 0
    std::cout << f.derivative({1}) << "\n";   // cos(0) = 1
    std::cout << f.eval(0.3)       << "\n";   // ≈ sin(0.3)
}

Modules¶

Module	Description
Core	Truncated Taylor polynomials, expression templates, and mathematical functions
Vector (Eigen)	Eigen integration for vectors, matrices, Jacobians, and higher-order tensors
Automatic Domain Splitting	Adaptive polynomial approximation over large domains
Taylor Integrator	High-order adaptive ODE integration with DA-based flow maps

Requirements¶

C++23 compiler (GCC 13+, Clang 17+, Apple Clang 16+)
CMake 4.2+
Eigen 3.4+

License¶

BSD 3-Clause. See LICENSE for details.