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CompleteIntersectionResolutions :: BRanks

BRanks -- ranks of the modules B_i(d) in a matrixFactorization

Synopsis

Description

i1 : c = 2

o1 = 2
i2 : S = ZZ/32003[x_0..x_(c-1),a_(0,0)..a_(c-1,c-1)];
i3 : A = genericMatrix(S,a_(0,0),c,c);

             2       2
o3 : Matrix S  <--- S
i4 : f = matrix{{x_0..x_(c-1)}}*map(S^{c:-1},S^{c:-2},A)

o4 = | x_0a_(0,0)+x_1a_(0,1) x_0a_(1,0)+x_1a_(1,1) |

             1       2
o4 : Matrix S  <--- S
i5 : R = S/ideal f;
i6 : kR = R^1/ideal(x_0..x_(c-1))

o6 = cokernel | x_0 x_1 |

                            1
o6 : R-module, quotient of R
i7 : MF = matrixFactorization(f,highSyzygy kR)

o7 = {{2} | a_(0,1) a_(0,0) a_(1,1) a_(1,0) |, {3} | x_1 -a_(0,0) 0  
      {2} | -x_0    x_1     0       0       |  {3} | x_0 a_(0,1)  0  
      {2} | 0       0       -x_0    x_1     |  {3} | 0   0        x_1
                                               {3} | 0   0        x_0
     ------------------------------------------------------------------------
     -a_(1,0) 0        |}
     a_(1,1)  0        |
     -a_(0,0) -a_(1,0) |
     a_(0,1)  a_(1,1)  |

o7 : List
i8 : netList BRanks MF

     +-+-+
o8 = |2|2|
     +-+-+
     |1|2|
     +-+-+
i9 : netList dMaps MF

     +---------------------------------------+
o9 = |{2} | a_(0,1) a_(0,0) |                |
     |{2} | -x_0    x_1     |                |
     +---------------------------------------+
     |{2} | a_(0,1) a_(0,0) a_(1,1) a_(1,0) ||
     |{2} | -x_0    x_1     0       0       ||
     |{2} | 0       0       -x_0    x_1     ||
     +---------------------------------------+
i10 : netList bMaps MF

      +-----------------------+
o10 = |{2} | a_(0,1) a_(0,0) ||
      |{2} | -x_0    x_1     ||
      +-----------------------+
      |{2} | -x_0 x_1 |       |
      +-----------------------+
i11 : netList psiMaps MF

      +-----------------------+
o11 = |{2} | a_(1,1) a_(1,0) ||
      |{2} | 0       0       ||
      +-----------------------+

See also

Ways to use BRanks :