parameter_homotopy: Parameter Homotopies

In dkahle/bertini: Interface to 'Bertini'

Parameter Homotopies

Description

Parameter Homotopies

Usage

parameter_homotopy(
  input,
  parameters,
  varorder,
  precomputed_solutions = NULL,
  dir = tempdir(),
  definitions = list(),
  configurations = list(),
  subfunctions = list()
)

Arguments

input	system of polynomials as either a character vector, mpolyList, or bertini_input object
parameters	the parameters that define the family as a character vector
varorder	(optional) order of variables in string
precomputed_solutions	an optional list that contains the pertinent results of an ab initio run (start and start_parameters files) for the system. Supplying these files can greatly decrease the computation time.
dir	directory to place the files in, without an ending /
definitions	an optional named list of the definitions to be given to Bertini. The definitions name all arguments used in the polynomial and tell Bertini what type of homotopy to use. Defaults to a total-degree homotopy.
configurations	an optional named list of configurations to be given to Bertini. Names will be changed to lower case.
subfunctions	an optional named list that contains subfunctions and other equations needed in the input file but do not need to be named in the definitions block.

Value

a closure that accepts specific values for the parameters and computes the solutions for those specific values

Examples

# a sextic in one variable (from Bertini)
polys <- c("a0 + x*(a1 + x*(a2 + x*(a3 + x*(a4 + x*(a5 + x*a6)))))")

generator <- parameter_homotopy(polys, parameters = c("a0","a1","a2","a3","a4","a5","a6"))
generator(c(1.1, 2.4, 0.8, 3.6, -0.52, -1.8, 4.4))

dkahle/bertini documentation built on July 16, 2022, 9:26 a.m.