Wed Oct 8 07:27:43 2025 circle_integrals_test(): python version: 3.10.12 numpy version: 1.26.4 Test circle_integrals(). circle01_length_test Python version: 3.10.12 circle01_length returns the length of the unit circle. circle01_length() = 6.28319 circle01_monomial_integral_test(): circle01_monomial_integral() returns the value of the integral of a monomial over the unit circle in 2D. Compare with a Monte Carlo estimate. Number of sample points used is 4192 If any exponent is odd, the integral is zero. We restrict this test to randomly chosen even exponents. Ex Ey MC-Estimate Exact Error 2 2 0.791228 0.785398 0.0058 8 6 0.0154983 0.0153398 0.00016 8 10 0.00343939 0.00335558 8.4e-05 8 0 1.70295 1.71806 0.015 10 0 1.53516 1.54625 0.011 10 10 0.00154237 0.00151001 3.2e-05 8 10 0.00343939 0.00335558 8.4e-05 8 2 0.167798 0.171806 0.004 8 6 0.0154983 0.0153398 0.00016 0 0 6.28319 6.28319 8.9e-16 10 8 0.00340495 0.00335558 4.9e-05 2 6 0.250889 0.245437 0.0055 0 4 2.36502 2.35619 0.0088 4 8 0.0441594 0.0429515 0.0012 10 2 0.125089 0.128854 0.0038 0 0 6.28319 6.28319 8.9e-16 6 10 0.0088759 0.00862864 0.00025 4 2 0.391032 0.392699 0.0017 0 10 1.53842 1.54625 0.0078 8 4 0.0427097 0.0429515 0.00024 circle01_sample_test)_ circle01_sample() samples the unit circle. Sample points in the unit circle. Row: 0 1 Col 0 : 0.85699 -0.515333 1 : -0.266544 0.963823 2 : 0.394559 0.918871 3 : -0.613166 -0.789954 4 : -0.5651 0.825023 5 : -0.42254 0.906344 6 : -0.687917 -0.725789 7 : -0.998797 0.0490376 8 : 0.431411 0.902155 9 : -0.278067 -0.960562 circle_integrals_test(): Normal end of execution. Wed Oct 8 07:27:44 2025