Sat Feb  7 15:51:17 2026

root_test():
  python version: 3.10.12
  numpy version:  1.26.4
  root() seeks a solution x of one or more nonlinear
  equations f(x)=0.

root_test01
  Use root_scalar() to solve 1 equation in 1 unknown.
    Initial X0 =  0.0   f(x0) =  -5.0
    Final X =  4.275232621860821   f(x) =  -4.440892098500626e-16

root_test02
  Use root() to solve 1 nonlinear equation.

  Initial X and F(X)

       0:              0            -5

  Final X and F(X)

       0:        4.27523  -4.44089e-16

root_test03():
  Use root() to solve 2 nonlinear equations in 2 variables.

  Initial X and F(X)

       0:              3           -13
       1:              0            11

  Final X and F(X)

       0:              1  -1.77636e-15
       1:              1  -1.27898e-13

root_test04
  Use root() to solve 4 nonlinear equations in 4 variables.

  Initial X and F(X)

       0:              0             1
       1:              0             4
       2:              0             9
       3:              0            16

  Final X and F(X)

       0:              1    1.2326e-32
       1:              2   4.43734e-31
       2:              3   3.15544e-30
       3:              4   1.77494e-30

root_test05():
  Use root() to solve 8 nonlinear equations in 8 variables.

  Initial X and F(X)

       0:              0             1
       1:              0             1
       2:              0             1
       3:              0             1
       4:              0             1
       5:              0             1
       6:              0             1
       7:              0             1

  Final X and F(X)

       0:       -0.57047      1.28e-11
       1:      -0.681141   -3.0721e-11
       2:      -0.700428   4.27283e-11
       3:      -0.700672  -2.40672e-11
       4:      -0.691736   1.62188e-11
       5:      -0.665767  -4.45932e-12
       6:      -0.596029  -1.06826e-11
       7:      -0.416411   1.17305e-11

root_test06():
  Use root() to minimize 1 function in 3 unknowns.

  Initial X and F(X)

       0:              0             0