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 = {{1.88243e-15+1.96659e-16*ii, -1}, {-1, -1.04025e-15-7.11635e-16*ii},
     ------------------------------------------------------------------------
     {1, 1.06107e-15+7.22043e-16*ii}, {-1.92796e-15-2.25281e-16*ii, 1}}

o3 : List

Caveat

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