# tetrahedron_integrals

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.

The interior of the unit tetrahedron in 3D is defined by

```        0 <= x
0 <= y
0 <= z
x + y + z <= 1
```

The integrands are all of the form

```        f(x,y,z) = x^e1 * y^e2 * z^e3
```
where the exponents are nonnegative integers.

### Languages:

tetrahedron_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:

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TETRAHEDRON_MONTE_CARLO, a Python code which uses the Monte Carlo method to estimate integrals 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.

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### Reference:

• Jean Lasserre, Konstantin Avrachenkov,
The multidimensional version of the integral from A to B of X to the P,
American Mathematics Monthly,
Volume 108, Number 2, 2001, pages 151-154.

### Source Code:

Last revised on 03 February 2020.