Thu May 18 17:10:19 2023

chebyshev2_exactness_test:
  Python version: 3.8.10
  Test chebyshev2_exactness.

chebyshev2_exactness():
  Investigate the polynomial exactness of a Gauss-Chebyshev1
  type 2 quadrature rule by integrating all monomials up to a given
  degree over the [-1,+1] interval.

chebyshev2_exactness: User input:
  Quadrature rule X file = "cheby2_o4_x.txt".
  Quadrature rule W file = "cheby2_o4_w.txt".
  Quadrature rule R file = "cheby2_o4_r.txt".
  Maximum degree to check = 10

  Number of points  = 4

  The quadrature rule to be tested is
  a Gauss-Chebyshev type 2 rule
  ORDER =  4

  Standard rule:
    Integral ( -1 <= x <= +1 ) f(x) * ( 1 - x^2 ) dx
    is to be approximated by
    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).

  Weights W:

[0.21707871 0.56831945 0.56831945 0.21707871]

  Abscissas X:

[-0.80901699 -0.30901699  0.30901699  0.80901699]

  Region R:

[-1.  1.]

  A Gauss-Chebyshev type 2 rule would be able to exactly
  integrate monomials up to and including 
  degree =  7

      Error    Degree

        0.0000000000000001    0
        0.0000000000000000    1
        0.0000000000000000    2
        0.0000000000000000    3
        0.0000000000000003    4
        0.0000000000000000    5
        0.0000000000000001    6
        0.0000000000000000    7
        0.0714285714285713    8
        0.0000000000000000    9
        0.1904761904761904   10

chebyshev2_exactness_test:
  Normal end of execution.
Thu May 18 17:10:19 2023