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MatFacCurvesP4 :: listOfPossibleMatFac

listOfPossibleMatFac -- different shapes of the same matrix factorization

Synopsis

Description

If (phi,psi) is a matrix factorization, then also (dual psi, dual phi), (psi, syz psi), and (dual phi, syz dual phi) are. This function provides a list of the shapes of the above matrix factorizations, including the original one

i1 : p=32009;
i2 : Fp=ZZ/p;
i3 : S=Fp[x_0..x_4];
i4 : beta=betti map(S^{9:0,1:-1},S^{1:-1,9:-2},0)

             0  1
o4 = total: 10 10
         0:  9  1
         1:  1  9

o4 : BettiTally
i5 : listOfPossibleMatFac(beta,3)

              0  1          0  1
o5 = {total: 10 10, total: 10 10}
          0:  9  1      0:  1  .
          1:  1  9      1:  9  9
                        2:  .  1

o5 : List
i6 : listOfPossibleMatFac(beta,4)

              0  1          0  1
o6 = {total: 10 10, total: 10 10}
          0:  9  1      0:  1  .
          1:  1  9      1:  9  .
                        2:  .  9
                        3:  .  1

o6 : List
i7 : beta=betti map(S^{9:0,1:-1},S^{0:-1,10:-2},0)

             0  1
o7 = total: 10 10
         0:  9  .
         1:  1 10

o7 : BettiTally
i8 : listOfPossibleMatFac(beta,3)

              0  1          0  1          0  1          0  1
o8 = {total: 10 10, total: 10 10, total: 10 10, total: 10 10}
          0:  9  .      0: 10  1      0: 10  9      0:  1  .
          1:  1 10      1:  .  9      1:  .  1      1:  9 10

o8 : List

Ways to use listOfPossibleMatFac :