solveSystem(List) -- solve a square system of polynomial equations

Synopsis

Usage:
s = solveSystem F
Function: solveSystem
Inputs:
- a list, F, polynomials with complex coefficients
Outputs:
- a list, s, all complex solutions to the system F=0
Optional inputs:
- Software => ..., -- specify software for the solver

Description

Solve a system of polynomial equations using homotopy continuation methods.

i1 : R = CC[x,y];

i2 : F = {x^2+y^2-1, x*y};

i3 : solveSystem F / first                                

o3 = {{-1, 9.08193e-16-9.27546e-16*ii}, {-1.13298e-16+3.72186e-16*ii, 1},
     ------------------------------------------------------------------------
     {1.43006e-16-4.45045e-16*ii, -1}, {1, -8.87376e-16+8.65096e-16*ii}}

o3 : List

Caveat

The system is assumed to be square (#equations = #variables) and have finitely many solutions.