-- -*- M2-comint -*- hash: 11138851303613009281

i1 : kk=QQ;

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

i3 : P5c=ideal(y0,y1);  -- a P5

o3 : Ideal of U

i4 : P5a=ideal(y2,y3);  --P5 of S8

o4 : Ideal of U

i5 : P5b=ideal(y4,y5);   --P5 of S7

o5 : Ideal of U

i6 : P3ac=P5a+P5c;-- P3 intersection of P5a and P5c

o6 : Ideal of U

i7 : P3bc=P5b+P5c;

o7 : Ideal of U

i8 : P1=P5a+P5b+P5c; --a line L, the intersection of all three P5s

o8 : Ideal of U

i9 : F=matrix{{y0,random(2,U),random(2,P1)},{y1,random(2,U),random(2,P1)}};

             2      3
o9 : Matrix U  <-- U

i10 : X8=P5a+minors(2,F);-- a 3-fold of degree 8 in P5a

o10 : Ideal of U

i11 : Z4=P5c+X8; -- a quartic surface in P3ac that contains L

o11 : Ideal of U

i12 : XY=P5c+ideal(random(2,intersect(P5a,P5b)),random(4,intersect(Z4,P5b)));

o12 : Ideal of U

i13 : X7=XY:P3bc;--a 3-fold of degree 7 in P5b

o13 : Ideal of U

i14 : (dim X7, degree X7)

o14 = (4, 7)

o14 : Sequence

i15 : betti res X7

             0 1 2 3 4
o15 = total: 1 5 9 7 2
          0: 1 2 1 . .
          1: . 1 2 1 .
          2: . . . . .
          3: . 2 6 6 2

o15 : BettiTally

i16 : X15=intersect(X7,X8);--a 3-fold of degree 15 in P7 with betti table of type [562],  the union of X7 and X8.

o16 : Ideal of U

i17 : (dim X15, degree X15)

o17 = (4, 15)

o17 : Sequence

i18 : betti res X15

             0 1  2 3 4
o18 = total: 1 9 16 9 1
          0: 1 .  . . .
          1: . 5  6 2 .
          2: . 2  4 2 .
          3: . 2  6 5 .
          4: . .  . . 1

o18 : BettiTally

i19 : 
