next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
GlicciPointsInP3 :: dimFormula

dimFormula -- return dimension of HC_hV

Synopsis

Description

The h-vector of a Gorenstein set of points in a possibly bi-dominant corrspondence have according to Proposition 4.1 of Twenty Points in P^3 one of the following two types

I) {1,3,...,binomial(s+1,2),binomial(s+1,2)+c,binomial(s+1,2),...,3,1}

II) {1,3,...,binomial(s+1,2),binomial(s+1,2)+c,binomial(s+1,2)+c,binomial(s+1,2),...,3,1}

with 0 ≤c ≤s+1. The function returns the dimension of HChV according to the formula of Proposition 4.2 of Twenty Points in P^3.
i1 : (L1,L2)=listhVectors 2

o1 = ({{1, 1, 1}, {1, 2, 1}, {1, 3, 1}, {1, 3, 3, 3, 1}, {1, 3, 4, 3, 1}, {1,
     ------------------------------------------------------------------------
     3, 5, 3, 1}, {1, 3, 6, 3, 1}}, {{1, 1}, {1, 1, 1, 1}, {1, 2, 2, 1}, {1,
     ------------------------------------------------------------------------
     3, 3, 1}, {1, 3, 3, 3, 3, 1}, {1, 3, 4, 4, 3, 1}, {1, 3, 5, 5, 3, 1},
     ------------------------------------------------------------------------
     {1, 3, 6, 6, 3, 1}})

o1 : Sequence
i2 : apply(L1,hV-> dimFormula hV)

o2 = {7, 11, 15, 23, 27, 31, 35}

o2 : List
i3 : apply(L2,hV->dimFormula hV)

o3 = {6, 8, 14, 21, 26, 31, 37, 44}

o3 : List

Ways to use dimFormula :