**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^e2where 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

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

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

circle_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2d.

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

disk01_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2d.

hexagon_integrals, a MATLAB code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2d.

hyperball_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in m dimensions.

hypercube_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in m dimensions.

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

line_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the length of the unit line in 1d.

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

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

simplex_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit simplex in m dimensions.

sphere_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3d.

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

square_felippa_rule, a MATLAB code which returns the points and weights of a felippa quadrature rule over the interior of a square in 2d.

square_grid, a MATLAB code which computes a grid of points over the interior of a square in 2d.

square_hex_grid, a MATLAB code which computes a hexagonal grid of points over the interior of a square in 2d.

square_minimal_rule, a MATLAB code which returns "almost minimal" quadrature rules, with exactness up to total degree 55, over the interior of the symmetric square in 2d, by mattia festa and alvise sommariva.

square_monte_carlo, a MATLAB code which uses the monte carlo method to estimate the integral of a function over the interior of the unit square in 2d.

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.

- i4vec_uniform_ab.m, returns a scaled pseudorandom I4VEC.
- monomial_value.m, evaluates a monomial.
- r8mat_uniform_ab.m, returns a scaled uniform pseudorandom R8MAT.
- square01_area.m, returns the area of the unit square in 2D.
- square01_monomial_integral.m, integrates a monomial in the unit square in 2D.
- square01_sample.m, samples points from the unit square in 2D.
- squaresym_area.m, returns the area of the symmetric unit square in 2D.
- squaresym_monomial_integral.m, integrates a monomial in the symmetric square in 2D.
- squaresym_sample.m, samples points from the symmetric unit square in 2D.