**hypercube_integrals**,
a Python code which
returns the exact value of the integral of any monomial
over the interior of the unit hypercube in M dimensions.

The interior of the unit hypercube in M dimensions is defined by

0 <= X(1:M) <= 1.

The integrands are all of the form

F(X) = product ( 1 <= I <= M ) X(I)^E(I)where the exponents are nonnegative integers.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

**hypercube_integrals** is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version..

ball_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3d.

circle_integrals, a python code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2d.

cube_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.

disk01_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2d.

hyperball_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in m dimensions.

hypercube_grid, a python code which computes a grid of points over the interior of a hypercube in m dimensions.

hypercube_monte_carlo, a python code which applies a monte carlo method to estimate the integral of a function over the interior of the unit hypercube in m dimensions;

hypersphere_integrals, a python code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in m dimensions.

line_integrals, a python code which returns the exact value of the integral of any monomial over the length of the unit line in 1d.

polygon_integrals, a python code which returns the exact value of the integral of any monomial over the interior of a polygon in 2d.

pyramid_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.

simplex_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit simplex in m dimensions.

sphere_integrals, a python code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3d.

square_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit square in 2d.

tetrahedron_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.

triangle_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2d.

wedge_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3d.

- hypercube_integrals.py, the source code.
- hypercube_integrals.sh, runs all the tests.
- hypercube_integrals.txt, the output file.