-- -*- M2-comint -*- hash: 3005001746326012730

i1 : S = ZZ/101[x,y]

o1 = S

o1 : PolynomialRing

i2 : f1 = x^2

      2
o2 = x

o2 : S

i3 : f2 = (x+y)^2

      2           2
o3 = x  + 2x*y + y

o3 : S

i4 : betti res ideal fromDual f1

            0 1 2
o4 = total: 1 2 1
         0: 1 1 .
         1: . . .
         2: . 1 1

o4 : BettiTally

i5 : betti res ideal fromDual f2

            0 1 2
o5 = total: 1 2 1
         0: 1 . .
         1: . 2 .
         2: . . 1

o5 : BettiTally

i6 : betti res (I = ideal fromDual(f2, DividedPowers => false))

            0 1 2
o6 = total: 1 2 1
         0: 1 1 .
         1: . . .
         2: . 1 1

o6 : BettiTally

i7 : I == inverseSystem (f2, DividedPowers => false)

o7 = true

i8 : inverseSystem (f2, DividedPowers => true)

                    2   2    2
o8 = ideal (x*y - 2y , x  - y )

o8 : Ideal of S

i9 : ideal fromDual(f2, DividedPowers => false)

                    3   3
o9 = ideal (x - y, x , y )

o9 : Ideal of S

i10 : ideal fromDual(f2, DividedPowers => true)

                     2   2    2   3   3
o10 = ideal (x*y - 2y , x  - y , x , y )

o10 : Ideal of S

i11 : 
