hypercube_integrals, an Octave 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 MIT license
hypercube_integrals is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
ball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.
circle_integrals, an Octave code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.
cube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.
disk01_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.
hexagon_integrals, an Octave code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2D.
hyperball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.
line_integrals, an Octave code which returns the exact value of the integral of any monomial over the length of the unit line in 1D.
simplex_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.