-- -*- M2-comint -*- {* hash: -281568638 *}

i1 : QQ[a,b,c,d];

i2 : I = monomialIdeal(a*b, b*c, c*d)

o2 = monomialIdeal (a*b, b*c, c*d)

o2 : MonomialIdeal of QQ[a, b, c, d]

i3 : dual I

o3 = monomialIdeal (a*c, b*c, b*d)

o3 : MonomialIdeal of QQ[a, b, c, d]

i4 : intersect(monomialIdeal(a,b), 
                    monomialIdeal(b,c),
                    monomialIdeal(c,d))

o4 = monomialIdeal (a*c, b*c, b*d)

o4 : MonomialIdeal of QQ[a, b, c, d]

i5 : dual dual I

o5 = monomialIdeal (a*b, b*c, c*d)

o5 : MonomialIdeal of QQ[a, b, c, d]

i6 : QQ[x,y,z];

i7 : I = monomialIdeal(x^3, x*y, y*z^2)

                     3          2
o7 = monomialIdeal (x , x*y, y*z )

o7 : MonomialIdeal of QQ[x, y, z]

i8 : dual(I, {4,4,4})

                     2 4   4 3
o8 = monomialIdeal (x y , x z )

o8 : MonomialIdeal of QQ[x, y, z]

i9 : intersect( monomialIdeal(x^2),
                    monomialIdeal(x^4, y^4),
                    monomialIdeal(y^4, z^3))

                     2 4   4 3
o9 = monomialIdeal (x y , x z )

o9 : MonomialIdeal of QQ[x, y, z]

i10 : QQ[x,y,z];

i11 : J = monomialIdeal( x^3*y^2, x*y^4, x*z, y^2*z)

                      3 2     4        2
o11 = monomialIdeal (x y , x*y , x*z, y z)

o11 : MonomialIdeal of QQ[x, y, z]

i12 : dual dual J

                      3      3
o12 = monomialIdeal (x y, x*y , x*z, y*z)

o12 : MonomialIdeal of QQ[x, y, z]

i13 : dual( dual(J, {3,4,1}), {3,4,1})

                      3 2     4        2
o13 = monomialIdeal (x y , x*y , x*z, y z)

o13 : MonomialIdeal of QQ[x, y, z]

i14 :