-- -*- M2-comint -*- {* hash: 1291941303 *}

i1 : R = ZZ/32003[vars(0..17)];

i2 : M = coker genericMatrix(R,a,3,6)

o2 = cokernel | a d g j m p |
              | b e h k n q |
              | c f i l o r |

                            3
o2 : R-module, quotient of R

i3 : isHomogeneous M

o3 = true

i4 : codim M

o4 = 4

i5 : degree M

o5 = 15

i6 : genera M

o6 = {-2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, 4, 14}

o6 : List

i7 : poincare M

                 4      5     6
o7 = 3 - 6T + 15T  - 18T  + 6T

o7 : ZZ[T]

i8 : hf = hilbertSeries M

                 4      5     6
     3 - 6T + 15T  - 18T  + 6T
o8 = --------------------------
                     18
              (1 - T)

o8 : Expression of class Divide

i9 : reduceHilbert hf

                2
     3 + 6T + 6T
o9 = ------------
              14
       (1 - T)

o9 : Expression of class Divide

i10 : poincare' = (M) -> (
              H := poincare M;
              t := (ring H)_0;  -- The variable t above
              while H % (1-t) == 0 do H = H // (1-t);
              H)

o10 = poincare'

o10 : FunctionClosure

i11 : poincare' M

                 2
o11 = 3 + 6T + 6T

o11 : ZZ[T]

i12 : C = resolution M

       3      6      15      18      6
o12 = R  <-- R  <-- R   <-- R   <-- R  <-- 0
                                            
      0      1      2       3       4      5

o12 : ChainComplex

i13 : C.dd_3

o13 = {4} | m  -n o  p  -q r  0  0  0  0  0  0  0  0  0  0  0  0  |
      {4} | -j k  -l 0  0  0  p  0  0  0  -q r  0  0  0  0  0  0  |
      {4} | g  -h i  0  0  0  0  p  0  0  0  0  -q 0  0  r  0  0  |
      {4} | -d e  -f 0  0  0  0  0  p  0  0  0  0  -q 0  0  r  0  |
      {4} | a  -b c  0  0  0  0  0  0  p  0  0  0  0  -q 0  0  r  |
      {4} | 0  0  0  -j k  -l -m 0  0  0  n  -o 0  0  0  0  0  0  |
      {4} | 0  0  0  g  -h i  0  -m 0  0  0  0  n  0  0  -o 0  0  |
      {4} | 0  0  0  -d e  -f 0  0  -m 0  0  0  0  n  0  0  -o 0  |
      {4} | 0  0  0  a  -b c  0  0  0  -m 0  0  0  0  n  0  0  -o |
      {4} | 0  0  0  0  0  0  g  j  0  0  -h i  -k 0  0  l  0  0  |
      {4} | 0  0  0  0  0  0  -d 0  j  0  e  -f 0  -k 0  0  l  0  |
      {4} | 0  0  0  0  0  0  a  0  0  j  -b c  0  0  -k 0  0  l  |
      {4} | 0  0  0  0  0  0  0  -d -g 0  0  0  e  h  0  -f -i 0  |
      {4} | 0  0  0  0  0  0  0  a  0  -g 0  0  -b 0  h  c  0  -i |
      {4} | 0  0  0  0  0  0  0  0  a  d  0  0  0  -b -e 0  c  f  |

              15       18
o13 : Matrix R   <--- R

i14 : betti C

             0 1  2  3 4
o14 = total: 3 6 15 18 6
          0: 3 6  .  . .
          1: . .  .  . .
          2: . . 15 18 6

o14 : BettiTally

i15 :