mvPolynomial

This is an implementation of multi-variable polynomial in C++.

Idea

This library treats multi-variable polynomial as a map from indexes to coefficients. For example, x^2 * y^2 - 2 * x * y ^2 + 3 is

{
  {{2, 2}, 1},
  {{1, 2}, -2},
  {{0, 0}, 3}
}

Install

First, you clone this repository.

git clone https://github.com/sukeya/mvPolynomial.git

Next, add the following codes in your CMakeLists.txt.

add_subdirectory(mvPolynomial)

Finally, add linked libraries.

target_link_libraries(your_exe PRIVATE mvPolynomial)

Then, you will be able to use this library.

How to use

The namespace is mvPolynomial. The examples exist in "test" directory.

Multi-variable polynomial

A class MVPolynomial implements multi-variable polynomials.

#include "mvPolynomial/mvPolynomial.hpp"

using MP2 = mvPolynomial::MVPolynomial<int, double, 2>;

You can construct a polynomial from an initializer list of (index, coefficient) pairs.

auto p = MP2({
    {{0, 0}, 1.0},
    {{1, 0}, 2.0},
    {{0, 1}, 3.0},
});

The constant term is the zero index.

double c = p.get(Eigen::Array2i::Zero());
p.set(Eigen::Array2i({2, 0}), 5.0);

If you want to read a term that may be absent, use try_get.

auto maybe_xy = p.try_get(Eigen::Array2i({1, 1}));
if (maybe_xy.has_value()) {
  double coeff = *maybe_xy;
}

set(index, 0.0) removes the term, and zero-coefficient terms are normalized away automatically.

The class provides basic polynomial arithmetic.

auto q   = MP2({
    {{0, 0}, 4.0},
    {{1, 0}, 1.0},
});
auto sum = p + q;
auto sub = p - q;
auto mul = p * q;
auto div = p / 2.0;
auto pw  = p.pow(3);

p /= scalar and p / scalar are supported. Division by zero scalar throws std::invalid_argument.

You can evaluate a polynomial at a point.

double value = p(Eigen::Vector2d({2.0, 3.0}));

You can also substitute a polynomial for one axis.

auto x = MP2({
    {{0, 0}, 1.0},
    {{1, 0}, 2.0},
});
auto composed = p(x, 1);

Differentiation and integration are available both as member functions and as free functions.

auto dx_member = p.D(0);
auto iy_member = p.Integrate(1);

auto dx = mvPolynomial::D(p, 0);
auto iy = mvPolynomial::Integrate(p, 1);

Negative indices are not supported and cause std::invalid_argument.