-- -*- M2-comint -*- {* hash: -102465891 *}

i1 : kk=ZZ/32003

o1 = kk

o1 : QuotientRing

i2 : S=kk[a..d]

o2 = S

o2 : PolynomialRing

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

             2   2   2   2
o3 = ideal (a , b , c , d )

o3 : Ideal of S

i4 : betti (F=res i)

            0 1 2 3 4
o4 = total: 1 4 6 4 1
         0: 1 . . . .
         1: . 4 . . .
         2: . . 6 . .
         3: . . . 4 .
         4: . . . . 1

o4 : BettiTally

i5 : M = image F.dd_3

o5 = image {4} | c2  d2  0   0   |
           {4} | -b2 0   d2  0   |
           {4} | a2  0   0   d2  |
           {4} | 0   -b2 -c2 0   |
           {4} | 0   a2  0   -c2 |
           {4} | 0   0   a2  b2  |

                             6
o5 : S-module, submodule of S

i6 : j1 = bruns M

                  4         2 2    2 2        2 2       4         2 2
o6 = ideal (-9350d , - 8444b c  - a d  + 7477b d , 8444b  + 15572b d )

o6 : Ideal of S

i7 : betti res j1

            0 1 2 3 4
o7 = total: 1 3 5 4 1
         0: 1 . . . .
         1: . . . . .
         2: . . . . .
         3: . 3 . . .
         4: . . . . .
         5: . . . . .
         6: . . 5 . .
         7: . . . 4 .
         8: . . . . 1

o7 : BettiTally

i8 : j2=brunsIdeal i

                  4         2 2    2 2        2 2       4        2 2
o8 = ideal (-9815d , - 5142b c  - a d  + 9132b d , 5142b  + 8380b d )

o8 : Ideal of S

i9 : betti res j2

            0 1 2 3 4
o9 = total: 1 3 5 4 1
         0: 1 . . . .
         1: . . . . .
         2: . . . . .
         3: . 3 . . .
         4: . . . . .
         5: . . . . .
         6: . . 5 . .
         7: . . . 4 .
         8: . . . . 1

o9 : BettiTally

i10 : (betti res j1) == (betti res j2)

o10 = true

i11 :