-- -*- M2-comint -*- {* hash: 1963160086 *}

i1 : R = QQ[a..d];

i2 : I = ideal(a^3+c^2*d, b^3-a*d^2);

o2 : Ideal of R

i3 : gin(I)

             3   2      3   5
o3 = ideal (a , a b, a*b , b )

o3 : Ideal of R

i4 : loadPackage "GenericInitialIdeal"

o4 = GenericInitialIdeal

o4 : Package

i5 : R = QQ[x0,x1,x2,x3,x4,x5]

o5 = R

o5 : PolynomialRing

i6 : M = matrix {{x1*x3*x4, x0*x3*x4, x1*x2*x4, x0*x2*x3, x0*x1*x2, x2*x4*x5, x0*x4*x5, x2*x3*x5, x1*x3*x5, x0*x1*x5}} --Stanley-Reisner ideal of RP^2

o6 = | x1x3x4 x0x3x4 x1x2x4 x0x2x3 x0x1x2 x2x4x5 x0x4x5 x2x3x5 x1x3x5 x0x1x5
     ------------------------------------------------------------------------
     |

             1       10
o6 : Matrix R  <--- R

i7 : I=ideal flatten entries M

o7 = ideal (x1*x3*x4, x0*x3*x4, x1*x2*x4, x0*x2*x3, x0*x1*x2, x2*x4*x5,
     ------------------------------------------------------------------------
     x0*x4*x5, x2*x3*x5, x1*x3*x5, x0*x1*x5)

o7 : Ideal of R

i8 : J=(ideal{x0,x1,x2})^3

              3    2      2         2                 2    3    2         2 
o8 = ideal (x0 , x0 x1, x0 x2, x0*x1 , x0*x1*x2, x0*x2 , x1 , x1 x2, x1*x2 ,
     ------------------------------------------------------------------------
       3
     x2 )

o8 : Ideal of R

i9 : assert(gin(I)==J)

i10 :