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Bertini :: bertiniZeroDimSolve

bertiniZeroDimSolve -- solve zero-dimensional system of equations

Synopsis

Description

Finds solutions to the zero-dimensional system F via numerical polynomial homotopy continuation. This function builds a Bertini input file from the system F and calls Bertini on this input file. Solutions are pulled from machine readable file finitesolutions and returned as a list.
i1 : R = CC[x,y];
i2 : F = {x^2-1,y^2-1};
i3 : S = bertiniZeroDimSolve F
Temporary directory for input and output files:/tmp/M2-14863-0/0

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.


o3 = {{1, 1}, {1, -1}, {-1, 1}, {-1, -1}}

o3 : List
Each solution is of type Point. Additional information about the solution can be accessed by using peek.
i4 : peek S_0

o4 = Point{ConditionNumber => 1.87793     }
           Coordinates => {1, 1}
           CycleNumber => 1
           FunctionResidual => 2.28878e-16
           LastT => .0015625
           MaximumPrecision => 52
           NewtonResidual => 5.81262e-17
           SolutionNumber => 1

Caveat

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

Ways to use bertiniZeroDimSolve :

  • bertiniZeroDimSolve(List)