# parameterHomotopy(List,List,List) -- solve a parametric system of equations

## Synopsis

• Function: parameterHomotopy
• Usage:
sols = parameterHomotopy(F,varsP,valuesP)
• Inputs:
• F, a list, contains the polynomials in the system
• varsP, a list, names of the parameters
• valuesP, a list, contains (possibly several sets of) values of the parameters
• Optional inputs:
• Software => ..., default value null, specify internal or external software
• Outputs:
• sols, a list, lists of lists of solutions for each set of the parameters

## Description

Solves a parameteric polynomial system for several values of parameters.
 i1 : R = CC[u1,u2,u3,x,y] o1 = R o1 : PolynomialRing i2 : f1 = u1*(y-1)+u2*(y-2)+u3*(y-3) o2 = u1*y + u2*y + u3*y - u1 - 2u2 - 3u3 o2 : R i3 : f2 = (x-11)*(x-12)*(x-13) 3 2 o3 = x - 36x + 431x - 1716 o3 : R i4 : try parameterHomotopy({f1,f2},{u1,u2,u3},{{1,0,0},{0,1+2*ii,0}}, Software=>BERTINI) else "need to install Bertini to run these lines" sh: bertini: command not found true o4 = need to install Bertini to run these lines

## Caveat

Avalaible only with Software=>BERTINI at the moment...