-- -*- M2-comint -*- {* hash: -1651133978 *}

i1 : R = ZZ/32003[x_1..x_3];

i2 : g = random(R^1, R^{-4})

o2 = | -13746x_1^4+11433x_1^3x_2-14908x_1^2x_2^2+10772x_1x_2^3-7400x_2^4+
     ------------------------------------------------------------------------
     5145x_1^3x_3+4181x_1^2x_2x_3-11130x_1x_2^2x_3+11719x_2^3x_3-4723x_1^2x_3
     ------------------------------------------------------------------------
     ^2-5777x_1x_2x_3^2+7518x_2^2x_3^2+12574x_1x_3^3-10597x_2x_3^3+13744x_3^4
     ------------------------------------------------------------------------
     |

             1       1
o2 : Matrix R  <--- R

i3 : f = fromDual g

o3 = | x_2^2x_3+13223x_1x_3^2-10668x_2x_3^2-14800x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-11297x_1x_3^2+9797x_2x_3^2+12655x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-6702x_1x_3^2+8756x_2x_3^2-15937x_3^3
     ------------------------------------------------------------------------
     x_2^3-3378x_1x_3^2+4419x_2x_3^2-13724x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-13565x_1x_3^2-1900x_2x_3^2-8306x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+10557x_1x_3^2-4629x_2x_3^2+5093x_3^3
     ------------------------------------------------------------------------
     x_1^3+9285x_1x_3^2+5412x_2x_3^2-13727x_3^3 |

             1       7
o3 : Matrix R  <--- R

i4 : res ideal f

      1      7      7      1
o4 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o4 : ChainComplex

i5 : betti oo

            0 1 2 3
o5 = total: 1 7 7 1
         0: 1 . . .
         1: . . . .
         2: . 7 7 .
         3: . . . .
         4: . . . 1

o5 : BettiTally

i6 :