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

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: 1: bertini: not found
true


o4 = need to install Bertini to run these lines

Caveat