-- -*- M2-comint -*- {* hash: -463732367 *}

i1 : T = ZZ/101[c,d];

i2 : D = 4;

i3 : P = product(D, i -> random(1,T))

          4      3       2 2       3      4
o3 = - 34c  + 41c d + 30c d  + 7c*d  - 36d

o3 : T

i4 : R = ZZ/101[a,b,c,d]

o4 = R

o4 : PolynomialRing

i5 : I = ideal(a^2, a*b*(substitute(P,R)), b^2)

             2           4          3           2 2           3          4 
o5 = ideal (a , - 34a*b*c  + 41a*b*c d + 30a*b*c d  + 7a*b*c*d  - 36a*b*d ,
     ------------------------------------------------------------------------
      2
     b )

o5 : Ideal of R

i6 : ass I

o6 = {ideal (b, a), ideal (c - 13d, b, a), ideal (c - 39d, b, a), ideal (c -
     ------------------------------------------------------------------------
     11d, b, a), ideal (c + 41d, b, a)}

o6 : List

i7 : primaryDecomposition I

              2        2                    2   2                    2   2  
o7 = {ideal (b , a*b, a ), ideal (c - 13d, b , a ), ideal (c + 41d, b , a ),
     ------------------------------------------------------------------------
                      2   2                    2   2
     ideal (c - 11d, b , a ), ideal (c - 39d, b , a )}

o7 : List

i8 : distinguished(I)

o8 = {ideal (b, a)}

o8 : List

i9 : K = distinguishedAndMult(I)

o9 = {{2, ideal (b, a)}}

o9 : List

i10 :