-- -*- M2-comint -*- hash: 258372902079327300

i1 : kk=QQ;

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

i3 : P4=ideal(y0,y1,y2);--a P4

o3 : Ideal of U

i4 : P5=ideal(y1,y2);--a P5

o4 : Ideal of U

i5 : X2=P4+ideal(random(2,U));--a quadric 3-fold in P4

o5 : Ideal of U

i6 : CI1223=ideal(y0)+ideal(random(2,P4),random(2,P4),random(3,X2)); --a complete intersection (1,2,2,3) that intersects  P4 in X2 and X1, a P3.

o6 : Ideal of U

i7 : X10=CI1223:X2;  --a reducible 3-fold X10 of degree 10 linked to the quadric threefold X2.  X10 is the union of X1 and  3-fold X9 of degree 9.

o7 : Ideal of U

i8 : Z6=X10+X2;----a complete intersection (1,1,1,2,3) surface  contained in X10

o8 : Ideal of U

i9 : X6=P5+ideal(random(2,Z6),random(3,Z6));-- X6 is a complete intersection (1,1,2,3) that intersects s10 in a hyperplane section of X6

o9 : Ideal of U

i10 : X16=intersect(X6,X10);--a 3-fold of degree 16 in P7 with betti table of type 430.  X16 is the union of X6, X1 and X9

o10 : Ideal of U

i11 : betti res X16

             0 1  2 3 4
o11 = total: 1 7 12 7 1
          0: 1 .  . . .
          1: . 4  3 . .
          2: . 3  6 3 .
          3: . .  3 4 .
          4: . .  . . 1

o11 : BettiTally

i12 : 
