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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
~/bertini

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{AccuracyEst => 3.09883e-16     }
           AccuracyEstInternal => 0
           ConditionNumber => 2.80882
           Coordinates => {1, 1}
           CycleNumber => 1
           FinalTValue => .0015625
           FunctionResidual => 5.55112e-17
           MaxPrecisionUtilized => 52
           Multiplicity => 1
           NewtonResidual => 3.58271e-17
           PathNumber => 0
           PathsWithSameEndpoint => {}
           PrecisionIncreased => 0
           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 :