Tue Oct 19 11:25:04 2021

cauchy_principal_value_test():
  Python version: 3.6.9
  Test cauchy_principal_value().

cauchy_principal_value_test01():
  Python version: 3.6.9
  cauchy_principal_value() for Integral ( -1 <= t <= 1 ) exp(t) / t dt

   N           Estimate             Error

   2         2.112977728449278      0.00152402
   4         2.114501718105385     3.26446e-08
   6         2.114501750751336     1.33626e-12
   8         2.114501750751458      1.4575e-12

cauchy_principal_value_test01():
  Normal end of execution.

cauchy_principal_value_test02():
  Python version: 3.6.9
  cauchy_principal_value ( Integral ( 1-delta <= t <= 1+delta ) 1/(1-t)^3 dt )
  Try this for delta = 1, 1/2, 1/4.

   N          Estimate                  Exact                  Error

   2       -0.7397260273972603       -0.7363873204868445     0.00333871
   4       -0.7364116807468272       -0.7363873204868445    2.43603e-05
   6       -0.7363867923558026       -0.7363873204868445    5.28131e-07
   8       -0.7363873252791506       -0.7363873204868445    4.79231e-09

   2       -0.3425852498017447       -0.3425632583544805    2.19914e-05
   4       -0.3425633493215302       -0.3425632583544805     9.0967e-08
   6        -0.342563258302464       -0.3425632583544805    5.20165e-11
   8        -0.342563258354488       -0.3425632583544805    7.54952e-15

   2       -0.1678240178701501       -0.1678238552950642    1.62575e-07
   4       -0.1678238554770549       -0.1678238552950642    1.81991e-10
   6       -0.1678238552950588       -0.1678238552950642    5.38458e-15
   8       -0.1678238552950641       -0.1678238552950642    1.38778e-16

cauchy_principal_value_test02():
  Normal end of execution.

legendre_set_test01():
  Python version: 3.6.9
  legendre_set() returns points and weights of a Gauss-Legendre quadrature rule.

  Gauss-Legendre rule of order 3:

        X            W

       -0.7745966692414834        0.5555555555555556
        0.0000000000000000        0.8888888888888888
        0.7745966692414834        0.5555555555555556

  Gauss-Legendre rule of order 6:

        X            W

       -0.9324695142031521        0.1713244923791704
       -0.6612093864662645        0.3607615730481386
       -0.2386191860831969        0.4679139345726910
        0.2386191860831969        0.4679139345726910
        0.6612093864662645        0.3607615730481386
        0.9324695142031521        0.1713244923791704

  Gauss-Legendre rule of order 11:

        X            W

       -0.9782286581460570        0.0556685671161737
       -0.8870625997680953        0.1255803694649046
       -0.7301520055740494        0.1862902109277343
       -0.5190961292068118        0.2331937645919905
       -0.2695431559523450        0.2628045445102467
        0.0000000000000000        0.2729250867779006
        0.2695431559523450        0.2628045445102467
        0.5190961292068118        0.2331937645919905
        0.7301520055740494        0.1862902109277343
        0.8870625997680953        0.1255803694649046
        0.9782286581460570        0.0556685671161737

legendre_set_test01():
  Normal end of execution.

cauchy_principal_value_test():
  Normal end of execution.
Tue Oct 19 11:25:04 2021