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bracket2partition
-- dictionary between different notations for Schubert conditions.
bracket2partition(List,ZZ)
-- dictionary between different notations for Schubert conditions.
changeFlags
-- continue solutions of a Schubert problem to another instance
changeFlags(...,OneHomotopy=>...)
-- strategy for moving solutions to a Schubert problem
changeFlags(List,Sequence)
-- continue solutions of a Schubert problem to another instance
changeFlags(Matrix,List,Sequence)
-- recursive call of change flags
checkIncidenceSolution
-- check if a solution satisfies an instance of a Schubert problem
checkIncidenceSolution(Matrix,List)
-- check if a solution satisfies an instance of a Schubert problem
LRcheater
-- A cheater's homotopy to a real Schubert triple intersection problem
LRcheater(...,Verbose=>...)
-- request verbose feedback
LRcheater(ZZ,Matrix,String)
-- A cheater's homotopy to a real Schubert triple intersection problem
LRhomotopies
-- interface to the Littlewood-Richardson homotopies in PHCpack
LRnumber
-- returns the number of solutions to the given Schubert problem
LRnumber(...,Strategy=>...)
-- strategy for computing the number of solutions to a Schubert problem
LRnumber(List,ZZ,ZZ)
-- returns the number of solutions to the given Schubert problem
LRrule
-- computes the product of Schubert classes using geometric Littlewood-Richardson rule
LRrule(...,Verbose=>...)
-- request verbose feedback
LRrule(ZZ,Matrix)
-- computes the product of Schubert classes using geometric Littlewood-Richardson rule
LRtriple
-- uses Littlewood-Richardson homotopy algorithm to solve a Schubert problem
LRtriple(...,RandomSeed=>...)
-- option to set the seed of the random number generators.
LRtriple(...,Verbose=>...)
-- request verbose feedback
LRtriple(...,WorkingPrecision=>...)
-- option to raise the working precision to double double or quad double.
LRtriple(ZZ,Matrix)
-- uses Littlewood-Richardson homotopy algorithm to solve a Schubert problem
NSC2phc
-- dictionary between different notations for Schubert problems.
NSC2phc(List,ZZ,ZZ)
-- dictionary between different notations for Schubert problems.
NumericalSchubertCalculus
-- Numerical Algorithms for Schubert Calculus
OneHomotopy
-- strategy for changing flags.
parseTriplet
-- Parses the output from LRtriple into Macaulay2 objects.
parseTriplet(...,Verbose=>...)
-- request verbose feedback
parseTriplet(String,String,String)
-- Parses the output from LRtriple into Macaulay2 objects.
partition2bracket
-- dictionary between different notations for Schubert conditions.
partition2bracket(List,ZZ,ZZ)
-- dictionary between different notations for Schubert conditions.
PieriHomotopies
-- runs the Pieri homotopies to solve a general hypersurface problem
PieriHomotopies(...,Verbose=>...)
-- request verbose feedback
PieriHomotopies(ZZ,ZZ)
-- runs the Pieri homotopies to solve a general hypersurface problem
PieriRootCount
-- the number of solutions to a generic Pieri problem
PieriRootCount(...,Verbose=>...)
-- request verbose feedback
PieriRootCount(ZZ,ZZ,ZZ)
-- the number of solutions to a generic Pieri problem
printStatistics
-- summary statistics (used by developers)
randomSchubertProblemInstance
-- returns a random instance of a given Schubert problem
randomSchubertProblemInstance(...,Strategy=>...)
-- strategy for creating a random matrix representing a flag
randomSchubertProblemInstance(List,ZZ,ZZ)
-- returns a random instance of a given Schubert problem
RandomSeed
-- seed for the random number generators.
resetStatistics
-- summary statistics (used by developers)
setVerboseLevel
-- set different levels of information printed on screen
setVerboseLevel(ZZ)
-- set different levels of information printed on screen
solutionsToAffineCoords
-- writes solutions in global coords to affine coordinates.
solutionsToAffineCoords(List)
-- writes solutions in global coords to affine coordinates.
solveSchubertProblem
-- uses Littlewood-Richardson homotopy algorithm to solve a Schubert problem
solveSchubertProblem(...,LinearAlgebra=>...)
-- switch between Linear Algebra and Parameter Homotopy
solveSchubertProblem(List,ZZ,ZZ)
-- uses Littlewood-Richardson homotopy algorithm to solve a Schubert problem
solveSimpleSchubert
-- uses Pieri homotopy algorithm to solve a simple Schubert problem
solveSimpleSchubert(List,ZZ,ZZ)
-- uses Pieri homotopy algorithm to solve a simple Schubert problem
WorkingPrecision
-- option to raise the working precision to double double or quad double.
wrapTriplet
-- Wraps a flag, system, and solutions into one string for phc -e.
wrapTriplet(String,String,String)
-- Wraps a flag, system, and solutions into one string for phc -e.