Bertini examples from
Numerically solving polynomial systems with Bertini
by D.J. Bates, J.D. Hauenstein, A.J. Sommese, and C.W. Wampler

Download a .tar.gz file with all examples here.

Chapter Example name Files (click to download)
1 Polynomial Systems input input
CircleAndYaxisC0 CircleAndYaxisC0.input
CircleAndYaxisC1.input
degree10 degree10.input
degree10eval.input
degree10eval.points
subfunctions subfunctions.input
2 Basic Polynomial Continuation AroundTheUnitCircle AroundTheUnitCircle.input
AroundTheUnitCircle.start
AroundTheUnitCircleAlt.input
4 Projective Space Eigenvalue2x2 Eigenvalue2x2.input
GeneralizedEigenvalue GeneralizedEigenvalue.input
TwoCircles TwoCircles.input
5 Types of Homotopies TwoHyperbolas TwoHyperbolas_1Hom.input
TwoHyperbolas_2Hom.input
6R SixR_2hom.input
SixR_4hom.input
TwoQuadrics TwoQuadrics_2hom.input
TwoQuadrics_1hom.input
TwoSpheres_OneCone TwoSpheres_OneCone.input
LagrangePoints LagrangePoints.input
LagrangePoints_regen.input
ninepoint ninepoint_regen1group.input
ninepoint_regen2groups.input
ninepoint_regen4groups.input
6 Parameter Homotopies sextic sextic.input
StewartGough StewartGough.input
6R (parameter) SixR_parameter.input
LagrangePoints (parameter) LagrangePoints.input
LagrangePoints_parameter.input
ninepoint (parameter) ninepoint_parameter.input
7 Advanced Topics about
Isolated Solutions 		SharpenDigits SharpenDigits.input
HighCondNum HighCondNum.input
HighCondNum_sharpen.input
HyperbolaParabola HyperbolaParabola.input
HyperbolaParabola_sharpen.input
CircleParabola CircleParabola_eval.input
CircleParabola_newton.input
FixedPoint FixedPoint.input
NewtonHomotopy NewtonHomotopy.input
FunctionEval FunctionEval.input
FunctionEval.start
UserDefined_NewtonHomotopy UserDefined_NewtonHomotopy.input
UserDefined_ProductSpace UserDefined_ProductSpace.input
UserDefined_ProductSpace.start
CondNumCalc CondNumCalc.input
CondNumCalc.start
ScaledSystem ScaledSystem.input
Unscale.input
RoundingError RoundingError.input
8 Positive-Dimensional Components Illustrative Illustrative.input
ThreeLines ThreeLines.input
BricardSixR BricardSixR.input
GriffisDuffy GriffisDuffy.input
GriffisDuffyI.input
GriffisDuffyILegs.input
GriffisDuffyII.input
GriffisDuffyFoldable.input
SmallConstant SmallConstant.input
9 Computing Witness Supersets AdjacentMinors AdjacentMinors_DimByDim.input
AdjacentMinors_classical.input
AdjacentMinors_regenCascade.input
11 Advanced Topics about
Positive-Dimensional Solution Sets 		LineCircle LineCircle.input
LineCircle.print
MaxCodimension MaxCodimension.input
SpecificCodimension SpecificCodimension.input
Deflation Deflation.input
12 Intersection DiagonalIntersection DiagonalIntersection.input
DiagonalIntersection.start
IntersectComponents IntersectComponents.input
14 Real Solutions FritzJohn FritzJohnInitial.input
FritzJohnHomotopy.input
16 Projections of Algebraic Sets Enneper Enneper.input
Discriminant Discriminant.input
Appendix A: Bertini Quick Start Guide FirstRun FirstRun.input
Sqrt1 Sqrt1.input
MoreAccuracy MoreAccuracy.input
Homogeneous Homogeneous.input
TwoGroups TwoGroups.input
Subfunctions Subfunctions.input
TwistedCubic TwistedCubic.input
UserHomotopy UserHomotopy_Affine.input
UserHomotopy_Projective.input
UserHomotopy.start
ParameterHomotopy ParameterHomotopy.input
final_parameters

One additional example: As indicated in Section 3.2.4, if coefficients cannot be provided exactly, then it is essential to use very high precision approximations.

Here is an input file for the IPP system with all coefficients approximated to 300 digits.

Here is the same system, but with all coefficients truncated.

The latter input file yields a cluster of finite, nonsingular isolated solutions that are at infinity in the exact problem and are not found with the former input file.