Mathematics

A modular header-only C++ mathematics library providing generic types (such as complex numbers and dual numbers) and functions for general use.

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Features

• Header-only — no build system required, just #include what you need
• Generic — all types are templated over any numeric type (float, double, long double, etc.)
• Operator-overloaded — arithmetic works naturally with +, -, *, /, ==, !=
• No dependencies — only the C++ standard library (<cmath>)
• Modular — each type lives in its own header; include only what you use

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Modules

Complex<T> — Complex numbers (Complex.hpp)

Represents numbers of the form a + bi where i² = −1.

Method / Operator	Description
+, -, *, /	Arithmetic between two complex numbers
+, -, *, / with scalar	Mixed arithmetic with real scalars
==, !=	Equality testing
~, .conj	Conjugate
.abs()	Modulus |z| = √(a² + b²)
.abssqr()	Squared modulus a² + b²
.ang()	Argument θ = atan2(b, a) in radians
.re	The real part a
.im	The imaginary part b

#include "Complex.hpp"

Complex<double> z1(3.0, 4.0);   // 3 + 4i
Complex<double> z2(1.0, -2.0);  // 1 - 2i

auto sum  = z1 + z2;            // 4 + 2i
auto prod = z1 * z2;            // 11 - 2i
double r  = z1.abs();           // 5.0
double th = z1.ang();           // atan2(4, 3)

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Dual<T> — Dual numbers (Dual.hpp)

Represents numbers of the form a + bε where ε² = 0.

Dual numbers propagate derivatives automatically through arithmetic, making them ideal for forward-mode automatic differentiation — compute a function and its exact derivative in a single pass, with no numerical error.

Method / Operator	Description
+, -, *, /	Arithmetic between two dual numbers
+, -, *, / with scalar	Mixed arithmetic with real scalars
==, !=	Equality testing
~, .conj	Conjugate
.re	The real part a
.eps	The dual (infinitesimal) part b

#include "Dual.hpp"

// Differentiate f(x) = x² + 3x at x = 2
// Seed with Dual(x, 1) — the 1 seeds the derivative
Dual<double> x(2.0, 1.0);
Dual<double> f = x * x + x * 3.0;

double value = f.re;  // f(2)  = 10.0
double derivative = f.eps; // f'(2) = 7.0

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Usage

Since this is a header-only library, simply copy the headers you need into your project and include them:

#include "Complex.hpp"
#include "Dual.hpp"

No installation, no cmake, no linking required.

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Requirements

• A standard-conforming C++ compiler (GCC, Clang, MSVC)

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Roadmap

Planned additions to the library:

• Split-complex (hyperbolic) numbers
• Gegenbauer polynomials
• Common mathematical functions extended to all numeric types

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License

See LICENSE for details.