NumericalSchubertCalculus : Index
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bracket2partition -- dictionary between different notations for Schubert conditions.
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bracket2partition(List,ZZ) -- dictionary between different notations for Schubert conditions.
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changeFlags -- Parameter homotopies to move solutions of a Schubert problem from one instance to another
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changeFlags(...,oneHomotopy=>...) -- Strategy for moving solutions to a Schubert problem from one instance to another.
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changeFlags(List,Sequence) -- Parameter homotopies to move solutions of a Schubert problem from one instance to another
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changeFlags(Matrix,List,Sequence) -- Recursive call of change flags
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checkIncidenceSolution -- Check if a solution satisfies the incidence conditions of a Schubert problem
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checkIncidenceSolution(Matrix,List) -- Check if a solution satisfies the incidence conditions of a Schubert problem
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findGaloisElement (missing documentation)
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higherWorkingPrecision -- option to raise the working precision to double double or quad double.
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isFullSymmetric (missing documentation)
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isGaloisFullSymmetric (missing documentation)
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LRcheater -- A cheater's homotopy to a real Schubert triple intersection problem
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LRcheater(ZZ,Matrix,String) -- A cheater's homotopy to a real Schubert triple intersection problem
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LRhomotopies -- interface to the Littlewood-Richardson homotopies in PHCpack
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LRrule -- uses the geometric Littlewood-Richardson rule to resolve a Schubert intersection problem.
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LRrule(ZZ,Matrix) -- uses the geometric Littlewood-Richardson rule to resolve a Schubert intersection problem.
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LRtriple -- runs the Littlewood-Richardson homotopy to solve a generic Schubert problem.
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LRtriple(...,higherWorkingPrecision=>...) -- option to raise the working precision to double double or quad double.
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LRtriple(...,luckySeed=>...) -- option to set the seed of the random number generators.
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LRtriple(ZZ,Matrix) -- runs the Littlewood-Richardson homotopy to solve a generic Schubert problem.
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luckySeed -- seed for the random number generators.
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NumericalSchubertCalculus -- Numerical Algorithms for Schubert Calculus
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oneHomotopy -- Strategy for changing flags.
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parseTriplet -- Parses a flag, system, and solutions (the output from LRtriple) into Macaulay2 objects.
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parseTriplet(String,String,String) -- Parses a flag, system, and solutions (the output from LRtriple) into Macaulay2 objects.
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partition2bracket -- dictionary between different notations for Schubert conditions.
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partition2bracket(List,ZZ,ZZ) -- dictionary between different notations for Schubert conditions.
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PieriHomotopies -- runs the Pieri homotopies to solve a general hypersurface problem
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PieriHomotopies(ZZ,ZZ) -- runs the Pieri homotopies to solve a general hypersurface problem
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PieriRootCount -- the number of solutions to a generic Pieri problem
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PieriRootCount(ZZ,ZZ,ZZ) -- the number of solutions to a generic Pieri problem
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printStatistics (missing documentation)
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randomSchubertProblemInstance -- Returns a random instance of a given Schubert problem by computing random matrices representing flags
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randomSchubertProblemInstance(...,Strategy=>...) -- Strategy for creating a random matrix representing a random flag
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randomSchubertProblemInstance(List,ZZ,ZZ) -- Returns a random instance of a given Schubert problem by computing random matrices representing flags
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setVerboseLevel -- Set different levels of information printed on screen
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solutionsToAffineCoords -- writes solutions in global coords to affine coordinates.
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solutionsToAffineCoords(List) -- writes solutions in global coords to affine coordinates.
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solveSchubertProblem -- uses Littlewood-Richardson homotopy to solve Schubert problems on Grassmannians
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solveSchubertProblem(...,LinearAlgebra=>...) -- switch between Linear Algebra and Parameter Homotopy
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solveSchubertProblem(List,ZZ,ZZ) -- uses Littlewood-Richardson homotopy to solve Schubert problems on Grassmannians
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solveSimpleSchubert -- uses Pieri homotopy algorithm to solve simple Schubert problems on Grassmannians
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solveSimpleSchubert(List,ZZ,ZZ) -- uses Pieri homotopy algorithm to solve simple Schubert problems on Grassmannians
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wrapTriplet -- Wraps a flag, system, and solutions into one string for phc -e.
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wrapTriplet(String,String,String) -- Wraps a flag, system, and solutions into one string for phc -e.