some interesting examples and families ====================================== PHCpack has been tested on many examples of polynomial systems taken from the research literature. The module examples exports some of those examples. Running **python examples.py** at the command prompt performs a regression test, solving all examples. Polynomial systems often occur in families and are defined for any number of equations and variables. interactive regression testing ------------------------------ An interactive use of examples.py at the Python prompt can go as follows: :: >>> from phcpy.examples import noon3 >>> f = noon3() >>> for p in f: print(p) ... x1*x2^2 + x1*x3^2 - 1.1*x1 + 1; x2*x1^2 + x2*x3^2 - 1.1*x2 + 1; x3*x1^2 + x3*x2^2 - 1.1*x3 + 1; The functions in examples.py returns the polynomials as lists of strings. If we want to solve the system defined by f, we continue the above session as :: >>> from phcpy.solver import solve >>> s = solve(f,silent=True) >>> len(s) 21 >>> print(s[0]) t : 1.00000000000000E+00 0.00000000000000E+00 m : 1 the solution for t : x1 : -1.65123467890611E-01 -7.61734168646636E-01 x2 : 8.98653694263692E-01 -3.48820047576431E-01 x3 : 8.98653694263692E-01 -3.48820047576431E-01 == err : 3.034E-16 = rco : 2.761E-01 = res : 5.974E-16 = The example session continues in the description of the module solutions. the cyclic n-roots problem -------------------------- One such noteworthy family is the cyclic n-roots problem: :: >>> from phcpy.families import cyclic >>> c4 = cyclic(4) >>> for p in c4: print(p) ... x0 + x1 + x2 + x3; x0*x1 + x1*x2 + x2*x3 + x3*x0; x0*x1*x2 + x1*x2*x3 + x2*x3*x0 + x3*x0*x1; x0*x1*x2*x3 - 1;