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Bertini :: bertiniTrackHomotopy

bertiniTrackHomotopy -- track a user-defined homotopy

Synopsis

Description

This method calls Bertini to track a user-defined homotopy. The user needs to specify the homotopy H, the path variable t, and a list of start solutions S1. In the following example, we solve x2-2 by moving from x2-1 with a linear homotopy. Bertini tracks homotopies starting at t=1 and ending at t=0. Final solutions are of type Point.

i1 : R = CC[x,t]; -- include the path variable in the ring
i2 : H = { (x^2-1)*t + (x^2-2)*(1-t)};
i3 : sol1 = point {{1}};
i4 : sol2 = point {{-1}};
i5 : S1= { sol1, sol2  };--solutions to H when t=1
i6 : S0 = bertiniTrackHomotopy (t, H, S1) --solutions to H when t=0
Temporary directory for input and output files:/var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-74655-0/1

The version of Bertini 
            you have installed on your computer 
            was used for this run. 
Bertini is under ongoing development by 
            D. Bates, J. Hauenstein, A. Sommese, and C. Wampler.


o6 = {{-1.41421}, {1.41421}}

o6 : List
i7 : peek S0_0

o7 = Point{ConditionNumber => 1           }
           Coordinates => {-1.41421}
           CycleNumber => 1
           FunctionResidual => 4.44089e-16
           LastT => .0015625
           MaximumPrecision => 52
           Multiplicity => 1
           NewtonResidual => 0
           SolutionNumber => -1
           SolutionStatus => Regular
i8 : R=CC[x,y,t]; -- include the path variable in the ring
i9 : f1=(x^2-y^2);
i10 : f2=(2*x^2-3*x*y+5*y^2);
i11 : H = { f1*t + f2*(1-t)}; --H is a list of polynomials in x,y,t
i12 : sol1=    point{{1,1}}--{{x,y}} coordinates

o12 = sol1

o12 : Point
i13 : sol2=    point{{ -1,1}}

o13 = sol2

o13 : Point
i14 : S1={sol1,sol2}--solutions to H when t=1

o14 = {sol1, sol2}

o14 : List
i15 : S0=bertiniTrackHomotopy(t, H, S1, IsProjective=>1) --solutions to H when t=0
Temporary directory for input and output files:/var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-74655-0/2

The version of Bertini 
            you have installed on your computer 
            was used for this run. 
Bertini is under ongoing development by 
            D. Bates, J. Hauenstein, A. Sommese, and C. Wampler.


o15 = {{.720337-.299683*ii, .382957+.311162*ii}, {.982183-1.46707*ii,
      -----------------------------------------------------------------------
      -.522176-.986978*ii}}

o15 : List

Caveat

Variables must begin with a letter (lowercase or capital) and can only contain letters, numbers, underscores, and square brackets.

Ways to use bertiniTrackHomotopy :