square_integrals, a Python 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.
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 python code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3d.
circle_integrals, a python code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2d.
cube_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.
disk01_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2d.
hyperball_integrals, a python 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 python 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 python 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 python code which returns the exact value of the integral of any monomial over the length of the unit line in 1d.
polygon_integrals, a python code which returns the exact value of the integral of any monomial over the interior of a polygon in 2d.
pyramid_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.
simplex_integrals, a python 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 python code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3d.
square_grid, a python code which computes a grid of points over the interior of a square in 2d.
square_minimal_rule, a python 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.
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.