square_integrals


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.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

square_integrals is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

python_integrals, a Python code which returns the exact value of the integral of any monomial over the surface or interior of some geometric object, including a line, quadrilateral, box, circle, disk, sphere, ball and others.

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.

Source Code:


Last revised on 02 February 2020.