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