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NumericalComputationOptions -- define homotopy options and configurations

Description

This object stores all the options needed compute an ED degree using homotopy continuation with Bertini. It is created using the newNumericalComputationOptions method.

Keys available to customize the homotopy include: "Directory" to change the directory Bertini is run from, the directory need not exist initially. "StartData" and "TargetData" if executing a Data homotopy, defaults to random complex data. "StartWeight" and "TargetWeight" if executing a Weight homotopy, defaults to random complex and unit weights respectively. "Infinity" to add a hyperplane at infinity for homogenization, one is created by default in homotopyEDDegree if not present. "PrimalCoordinates" to add additional variables to the ambient space. By default this field will already contain the variables of `ring F`, thus it is safer to append extra variables rather than overwriting the less, otherwise subsequent methods may fail.

Keys are also available to customize the Bertini run: "FinerRestriction" a list of polynomials to filter down critical points. Critical points will only be kept if they vanish for every polynomial in this list. "BertiniStartFiberSolveConfiguration" a list of options (e.g. `FinalTol -> 1e-8`) that will be passed into the Berni inputs file. By default, the options `{"TrackType"=>0, "PrintPathProgress"=>1000}` are included.

Methods that use an object of class NumericalComputationOptions:

  • homotopyEDDegree(NumericalComputationOptions,String,Boolean,Boolean) -- see homotopyEDDegree -- numerically compute ED degrees of affine cones using homotopy continuation

For the programmer

The object NumericalComputationOptions is a type, with ancestor classes MutableHashTable < HashTable < Thing.


The source of this document is in /build/reproducible-path/macaulay2-1.26.06+ds/M2/Macaulay2/packages/EuclideanDistanceDegree.m2:364:0.