makeFiniteResolutionCodim2 -- Maps associated to the finite resolution of a high syzygy module in codim 2

i1 : kk=ZZ/101

o1 = kk

o1 : QuotientRing

i2 : S = kk[a,b]

o2 = S

o2 : PolynomialRing

i3 : ff = matrix"a4,b4"

o3 = | a4 b4 |

             1      2
o3 : Matrix S  <-- S

i4 : R = S/ideal ff

o4 = R

o4 : QuotientRing

i5 : N = R^1/ideal"a2, ab, b3"

o5 = cokernel | a2 ab b3 |

                            1
o5 : R-module, quotient of R

i6 : N = coker vars R

o6 = cokernel | a b |

                            1
o6 : R-module, quotient of R

i7 : M = highSyzygy N

o7 = cokernel {2} | 0 -b3 a3 0 |
              {4} | b a   0  0 |
              {4} | 0 0   b  a |

                            3
o7 : R-module, quotient of R

i8 : MS = pushForward(map(R,S),M)

o8 = cokernel {2} | 0 b3 a3 0 0  |
              {4} | b -a 0  0 0  |
              {4} | 0 0  b  a b4 |

                            3
o8 : S-module, quotient of S

i9 : mf = matrixFactorization(ff, M)

o9 = {{4} | a -b 0 0  |, {5} | a3 b 0   0  0  |, {2} | 0 -1 0 |}
      {2} | 0 a3 0 b3 |  {5} | 0  a -b3 0  0  |  {4} | 0 0  1 |
      {4} | 0 0  b a  |  {5} | 0  0 0   -a b3 |  {4} | 1 0  0 |
                         {5} | 0  0 a3  b  0  |

o9 : List

i10 : G = makeFiniteResolutionCodim2(ff,mf)

o10 = HashTable{"alpha" => {5} | 0   0 |              }
                           {5} | -b3 0 |
                "b" => {4} | b a |
                "h1'" => {5} | 0   0  0  |
                         {5} | -b3 0  0  |
                         {5} | 0   -a b3 |
                         {5} | a3  b  0  |
                "h1" => {5} | 0   0  0  |
                        {5} | -b3 0  0  |
                        {5} | 0   -a b3 |
                        {5} | a3  b  0  |
                "mu" => {5} | a3 b |
                        {5} | 0  a |
                "partial" => {4} | a -b |
                             {2} | 0 a3 |
                "psi" => {4} | 0 0  |
                         {2} | 0 b3 |
                                 3      5      2
                "resolution" => S  <-- S  <-- S  <-- 0
                                                      
                                0      1      2      3
                "sigma" => {5} | b3 |
                           {5} | 0  |
                "tau" => 0
                "u" => {8} | 1 0 |
                "v" => {9} | 0 -1 |
                       {9} | 1 0  |
                "X" => 0
                "Y" => 0

o10 : HashTable

i11 : F = G#"resolution"

       3      5      2
o11 = S  <-- S  <-- S  <-- 0
                            
      0      1      2      3

o11 : Complex