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MatFac15 :: BSCandidates

BSCandidates -- compute Boij-Soederberg points in the cone of resolution which could lead to the given a matrix factorization

Synopsis

Description

Given the shape of the desired matrix facorization, we compute a list of hypothetical resolutions, which could lead to such a matrix factorization, as all integral points in the Boij-Soederberg cone.

i1 : kk=ZZ/10007;S=kk[x_0..x_4];
i3 : beta=betti random(S^3,S^{3:-1})

            0 1
o3 = total: 3 3
         0: 3 3

o3 : BettiTally
i4 : BSCandidates(beta,3)

             0 1 2 3         0 1 2         0 1
o4 = {total: 1 2 2 1, total: 2 3 1, total: 3 3}
          0: 1 2 . .      0: 2 3 .      0: 3 3
          1: . . 2 1      1: . . 1

o4 : List
i5 : beta=betti random(S^9,S^{9:-1})

            0 1
o5 = total: 9 9
         0: 9 9

o5 : BettiTally
i6 : cands=BSCandidates(beta,3)

             0 1 2 3         0 1 2 3         0 1 2 3         0 1         0 1
o6 = {total: 3 6 6 3, total: 4 7 5 2, total: 5 7 4 2, total: 9 9, total: 7 9
          0: 3 6 . .      0: 4 7 . .      0: 5 7 . .      0: 9 9      0: 7 9
          1: . . 6 3      1: . . 5 2      1: . . 4 2                  1: . .
     ------------------------------------------------------------------------
     2         0 1 2         0 1 2         0 1 2 3         0 1 2 3         0
     2, total: 6 9 3, total: 8 9 1, total: 7 8 2 1, total: 5 8 4 1, total: 6
     .      0: 6 9 .      0: 8 9 .      0: 7 8 . .      0: 5 8 . .      0: 6
     2      1: . . 3      1: . . 1      1: . . 2 1      1: . . 4 1      1: .
     ------------------------------------------------------------------------
     1 2 3
     8 3 1}
     8 . .
     . 3 1

o6 : List
i7 : apply(select(cands,b->codim b>2),b->(codim b,degree b, betti b))

                    0 1 2 3
o7 = {(3, 6, total: 3 6 6 3)}
                 0: 3 6 . .
                 1: . . 6 3

o7 : List

Ways to use BSCandidates :

  • BSCandidates(BettiTally,ZZ)