# square_integrals

square_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit square or symmetric unit square in 2D.

The interior of the unit square in 2D is defined by

```        0 <= X <= 1,
0 <= Y <= 1.
```

The interior of the symmetric unit square in 2D is defined by

```        -1 <= X <= 1,
-1 <= Y <= 1.
```

The integrands are all of the form

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

### Languages:

square_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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square_symq_rule, a MATLAB code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2d, by hong xiao and zydrunas gimbutas.

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

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

wedge_integrals, a MATLAB 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 22 March 2019.