-- -*- M2-comint -*- {* hash: 14173195 *}

i1 : kk = ZZ/101;

i2 : S = kk[a..c];

i3 : m = ideal vars S;

o3 : Ideal of S

i4 : i = (ideal"a,b")*m+ideal"c3"

             2                  2        3
o4 = ideal (a , a*b, a*c, a*b, b , b*c, c )

o4 : Ideal of S

i5 : analyticSpread i

o5 = 3

i6 : minimalReduction i

                 3      2              2                   3      2          
o6 = ideal (- 30c  + 50a  - 49a*b + 44b  + 45a*c + b*c, 13c  + 39a  - 15a*b -
     ------------------------------------------------------------------------
        2                      3     2              2
     18b  - 20a*c + 4b*c, - 16c  - 3a  - 34a*b - 38b  + 2a*c + 24b*c)

o6 : Ideal of S

i7 : f = gens i

o7 = | a2 ab ac ab b2 bc c3 |

             1       7
o7 : Matrix S  <--- S

i8 : for a from 0 to 3 do(jhom=ideal (f*random(source f, S^{3-a:-2,a:-3})); print(i^6 == (i^5)*jhom))
false
false
false
false

i9 :