-- -*- M2-comint -*- hash: 3984116672509181488

i1 : kk=QQ;

i2 : U=kk[y0,y1,y2,y3,y4,y5,y6,y7];

i3 : P3=ideal(y0,y1,y2,y3);--a P3

o3 : Ideal of U

i4 : P4=ideal(y1,y2,y3);--a P4

o4 : Ideal of U

i5 : P6=ideal(y0);--a P6

o5 : Ideal of U

i6 : M24=matrix{{y1,y2,random(2,U),random(2,U)},{y2,y3,random(2,U),random(2,U)}};--a 2x4 matrix with two columns of linear and two of quadratic forms

             2      4
o6 : Matrix U  <-- U

i7 : X12=P6+minors(2,M24);--a 3-fold of degree 12 in P6

o7 : Ideal of U

i8 : Z4=P3+X12;--a quartic surface in X12

o8 : Ideal of U

i9 : X4=P4+ideal(random(4,Z4));--a quartic 3-fold

o9 : Ideal of U

i10 : X16=intersect(X12,X4);-- a 3-fold of degree 16 in P7 with betti table of type 441

o10 : Ideal of U

i11 : betti res X16

             0 1  2 3 4
o11 = total: 1 9 16 9 1
          0: 1 .  . . .
          1: . 4  4 1 .
          2: . 4  8 4 .
          3: . 1  4 4 .
          4: . .  . . 1

o11 : BettiTally

i12 : 
