-- -*- M2-comint -*- {* hash: 2133672428 *}

i1 : S = QQ[a,b,c,d,e];

i2 : I1 = ideal(a,b,c);

o2 : Ideal of S

i3 : I2 = ideal(a,b,d);

o3 : Ideal of S

i4 : I3 = ideal(a,e);

o4 : Ideal of S

i5 : P = I1*I2*I3

             3   2    2           2           2             2   2         
o5 = ideal (a , a e, a b, a*b*e, a d, a*d*e, a b, a*b*e, a*b , b e, a*b*d,
     ------------------------------------------------------------------------
             2
     b*d*e, a c, a*c*e, a*b*c, b*c*e, a*c*d, c*d*e)

o5 : Ideal of S

i6 : L1 = associatedPrimes P

o6 = {ideal (e, a), ideal (d, b, a), ideal (c, b, a), ideal (d, c, b, a),
     ------------------------------------------------------------------------
     ideal (e, c, b, a), ideal (e, d, b, a), ideal (e, d, c, b, a)}

o6 : List

i7 : L2 = apply(associatedPrimes monomialIdeal P, J -> ideal J)

o7 = {ideal (a, e), ideal (a, b, c), ideal (a, b, d), ideal (a, b, c, d),
     ------------------------------------------------------------------------
     ideal (a, b, c, e), ideal (a, b, d, e), ideal (a, b, c, d, e)}

o7 : List

i8 : M1 = set apply(L1, I -> sort flatten entries gens I)

o8 = set {{c, b, a}, {d, b, a}, {d, c, b, a}, {e, a}, {e, c, b, a}, {e, d, b,
     ------------------------------------------------------------------------
     a}, {e, d, c, b, a}}

o8 : Set

i9 : M2 = set apply(L2, I -> sort flatten entries gens I)

o9 = set {{c, b, a}, {d, b, a}, {d, c, b, a}, {e, a}, {e, c, b, a}, {e, d, b,
     ------------------------------------------------------------------------
     a}, {e, d, c, b, a}}

o9 : Set

i10 : assert(M1 === M2)

i11 :