-- -*- M2-comint -*- {* hash: 1270253531 *}

i1 : kk=ZZ/32003

o1 = kk

o1 : QuotientRing

i2 : S=kk[a..e]

o2 = S

o2 : PolynomialRing

i3 : i=ideal(a^2,b^3,c^4, d^5)

             2   3   4   5
o3 = ideal (a , b , c , d )

o3 : Ideal of S

i4 : F=res i

      1      4      6      4      1
o4 = S  <-- S  <-- S  <-- S  <-- S  <-- 0
                                         
     0      1      2      3      4      5

o4 : ChainComplex

i5 : f=F.dd_3

o5 = {5} | c4  d5  0   0   |
     {6} | -b3 0   d5  0   |
     {7} | a2  0   0   d5  |
     {7} | 0   -b3 -c4 0   |
     {8} | 0   a2  0   -c4 |
     {9} | 0   0   a2  b3  |

             6       4
o5 : Matrix S  <--- S

i6 : EG = evansGriffith(f,2)  -- notice that we have a matrix with one less row, as described in elementary, and the target module rank is one less.

o6 = {5} | c4  d5  0                                                   
     {6} | -b3 0   d5                                                  
     {7} | 0   -b3 7274a4-2219a3b+1698a2b2-3867a3c+15593a2bc+194a2c2-c4
     {7} | a2  0   2053a4+10346a3b+4507a2b2-11175a3c+13708a2bc+7857a2c2
     {8} | 0   a2  15111a3-7443a2b+6705a2c                             
     ------------------------------------------------------------------------
     0                                                       |
     0                                                       |
     7274a2b3-2219ab4+1698b5-3867ab3c+15593b4c+194b3c2       |
     2053a2b3+10346ab4+4507b5-11175ab3c+13708b4c+7857b3c2+d5 |
     15111ab3-7443b4+6705b3c-c4                              |

             5       4
o6 : Matrix S  <--- S

i7 : isSyzygy(coker EG,2)

o7 = true

i8 :