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, -1.3798e-17+1.28616e-15*ii}, {2.16645e-16-3.33476e-16*ii, 1},
     ------------------------------------------------------------------------
     {-2.49171e-16+4.80493e-16*ii, -1}, {1, 1.3798e-17-1.28616e-15*ii}}

o3 : List

Caveat

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