-- -*- M2-comint -*- hash: 6395961873740048903

i1 : needsPackage "LocalRings";

i2 : R = ZZ/32003[vars(0..5)];

i3 : I = ideal"abc-def,ab2-cd2-c,-b3+acd";

o3 : Ideal of R

i4 : C = freeResolution I;

i5 : M = ideal gens R;

o5 : Ideal of R

i6 : RM = localRing(R, M);

i7 : F = C.dd_2;

             4      6
o7 : Matrix R  <-- R

i8 : FM = F ** RM

o8 = {3} | 0    0    -b3+acd   -abc+def  0       a2c2-b2ef  |
     {3} | cef  ac2  ab2-cd2-c 0         abc-def -ac2d+abef |
     {3} | -ac2 -b2c 0         ab2-cd2-c -b3+acd -a2bc+b2cd |
     {5} | b    d    0         0         0       1          |

              4       6
o8 : Matrix RM  <-- RM

i9 : f = liftUp FM;

             4      6
o9 : Matrix R  <-- R

i10 : g = syz f;

              6      5
o10 : Matrix R  <-- R

i11 : h = syz g;

              5      2
o11 : Matrix R  <-- R

i12 : C = {g ** RM, h ** RM}/mutableMatrix;

i13 : C = pruneDiff(C, 1, PruningMap => false)

o13 = {| -d d2+1 0   |, 0}
       | b  -bd  -1  |
       | 0  ef   -ac |
       | 0  -ac  b2  |
       | -c 0    ab  |
       | 0  -b   d   |

o13 : List

i14 : g' = C#0;

i15 : N = transpose entries FM;

i16 : for i from 0 to numcols FM - 1 do
        rowMult(g', i, N_i/denominator//lcm);

i17 : GM = map(source FM, , matrix g')

o17 = {6} | -d d2+1 0   |
      {6} | b  -bd  -1  |
      {6} | 0  ef   -ac |
      {6} | 0  -ac  b2  |
      {6} | -c 0    ab  |
      {7} | 0  -b   d   |

               6       3
o17 : Matrix RM  <-- RM

i18 : kernel FM == image GM

o18 = true

i19 : 
