**pyramid_integrals**,
an Octave code which
returns the exact value of the integral of any monomial x^i y^j z^k
over the interior of the unit pyramid in 3D.

The unit pyramid has a square base of area 4, and a height of 1. Specifically, the integration region is:

- ( 1 - Z ) <= X <= 1 - Z - ( 1 - Z ) <= Y <= 1 - Z 0 <= Z <= 1.The volume of the unit pyramid is 4/3.

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

**pyramid_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.

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.

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

line_integrals, an Octave code which returns the exact value of the integral of any monomial over the unit line segment in 1d.

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

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.

- monomial_value.m, evaluates a monomial.
- pyramid01_monomial_integral.m, monomial integral in a unit pyramid.
- pyramid01_sample.m, sample the unit pyramid.
- pyramid01_volume.m, volume of a unit pyramid with square base.
- r8_mop.m, returns the I-th power of -1 as an R8.