We determine for which pairs of integers (d,e) there exist a direct Gorenstein link from the generic set of d points in P^3 to a generic set of e points in P^3. Our method of proving existence is computational: we choose examples of Gorenstein linkages using a probabilstic method, and show by a tangent space computation that the incidence correspondence are bidominant. Our paper Twenty Points in P^3 shows that no further bidominant correspondences can occur, and explains how the routines in this package establish the existence.## Splitting and Factoring

## Degrees and h-Vectors

## Tangent Space Computations

## Building the Bidominance Graph

## Univariate Polynomial Statistics

## Verification

- hasFactor -- check for a factor of desired degree
- pickGorensteinIdeal -- select a codimension 3 Gorenstein ideal
- findSplittingExample -- find an example of a Gorenstein ideal of points with a subset of degree n
- testSplitting -- test a random Gorenstein set of points in P^3 for a factor

- hVector -- compute the h-vector
- BEdegrees -- compute the degrees of the Buchsbaum-Eisenbud skew matrix

- tangentDimension -- compute the dimension of tangentspaces
- dimFormula -- return dimension of HC_hV
- checkDimensionsHCG -- check that the dimension formula gives the dimension of the tangentspace at HC_G for a random choice of G

- listhVectors -- list all admissible h-vectors of Gorenstein points up to b
- createCandidates -- create numerical candidates for bi-dominant Gorenstein linkage correspondences
- checkCandidates -- check which numerical candidates lead to a bi-dominant Gorenstein linkage correspondence
- getGraph -- compute the graph of the bi-dominant Gorenstein linkage correspondences.
- graphvizFile -- builds an input file for graphviz

- isEven -- Is L the class of an even permutation?
- sizeConjClass -- number of permutations with given cycle decomposition
- probOfFactor -- probability that a polynomial of degree n is square free AND has a factor of degree k over the same finite ground field
- primeDivisors -- compute List of prime factors of an integer
- numOfIrreducible -- the number of irreducible polynomials
- numOfSquareFree -- the number of irreducible polynomials
- polynomialsWithFactor -- number of monic square-free polynomials of degree n with factor of degree degree k over F_q

- verifyAllAssertionsOfThePaper -- print commands to verfy the assertions of the paper
- verifyGraphInSmallCharacteristic -- print commands to verfy the assertions of the paper

- Functions and commands
- BEdegrees -- compute the degrees of the Buchsbaum-Eisenbud skew matrix
- checkCandidates -- check which numerical candidates lead to a bi-dominant Gorenstein linkage correspondence
- checkDimensionsHCG -- check that the dimension formula gives the dimension of the tangentspace at HC_G for a random choice of G
- createCandidates -- create numerical candidates for bi-dominant Gorenstein linkage correspondences
- dimFormula -- return dimension of HC_hV
- findSplittingExample -- find an example of a Gorenstein ideal of points with a subset of degree n
- getGraph -- compute the graph of the bi-dominant Gorenstein linkage correspondences.
- graphvizFile -- builds an input file for graphviz
- hasFactor -- check for a factor of desired degree
- hVector -- compute the h-vector
- isEven -- Is L the class of an even permutation?
- listhVectors -- list all admissible h-vectors of Gorenstein points up to b
- numOfIrreducible -- the number of irreducible polynomials
- numOfSquareFree -- the number of irreducible polynomials
- pickGorensteinIdeal -- select a codimension 3 Gorenstein ideal
- polynomialsWithFactor -- number of monic square-free polynomials of degree n with factor of degree degree k over F_q
- primeDivisors -- compute List of prime factors of an integer
- probOfFactor -- probability that a polynomial of degree n is square free AND has a factor of degree k over the same finite ground field
- sizeConjClass -- number of permutations with given cycle decomposition
- tangentDimension -- compute the dimension of tangentspaces
- testSplitting -- test a random Gorenstein set of points in P^3 for a factor
- verifyAllAssertionsOfThePaper -- print commands to verfy the assertions of the paper
- verifyGraphInSmallCharacteristic -- print commands to verfy the assertions of the paper