# pyramid_integrals

pyramid_integrals, a Python 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.

### Languages:

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

### Related Data and Programs:

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.

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pyramid_grid, a python code which computes a grid of points over the interior of the unit pyramid in 3d;

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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.

### Source Code:

Last revised on 30 January 2020.