i1 : kk= ZZ/101
o1 = kk
o1 : QuotientRing
|
i2 : S = kk[x,y,z]
o2 = S
o2 : PolynomialRing
|
i3 : I1 = ideal "x3y"
3
o3 = ideal(x y)
o3 : Ideal of S
|
i4 : R1 = S/I1
o4 = R1
o4 : QuotientRing
|
i5 : M1 = R1^1/ideal(x^2)
o5 = cokernel | x2 |
1
o5 : R1-module, quotient of R1
|
i6 : betti res (M1, LengthLimit =>5)
0 1 2 3 4 5
o6 = total: 1 1 1 1 1 1
0: 1 . . . . .
1: . 1 . . . .
2: . . 1 . . .
3: . . . 1 . .
4: . . . . 1 .
5: . . . . . 1
o6 : BettiTally
|
i7 : E = ExtModule M1
2
o7 = (kk[X ])
0
o7 : kk[X ]-module, free, degrees {0..1}
0
|
i8 : apply(toList(0..10), i->hilbertFunction(i, E))
o8 = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
o8 : List
|
i9 : Eeven = evenExtModule(M1)
1
o9 = (kk[X ])
0
o9 : kk[X ]-module, free
0
|
i10 : apply(toList(0..5), i->hilbertFunction(i, Eeven))
o10 = {1, 1, 1, 1, 1, 1}
o10 : List
|
i11 : Eodd = oddExtModule(M1)
1
o11 = (kk[X ])
0
o11 : kk[X ]-module, free
0
|
i12 : apply(toList(0..5), i->hilbertFunction(i, Eodd))
o12 = {1, 1, 1, 1, 1, 1}
o12 : List
|
i13 : use S
o13 = S
o13 : PolynomialRing
|
i14 : I2 = ideal"x3,yz"
3
o14 = ideal (x , y*z)
o14 : Ideal of S
|
i15 : R2 = S/I2
o15 = R2
o15 : QuotientRing
|
i16 : M2 = R2^1/ideal"x2,y,z"
o16 = cokernel | x2 y z |
1
o16 : R2-module, quotient of R2
|
i17 : betti res (M2, LengthLimit =>10)
0 1 2 3 4 5 6 7 8 9 10
o17 = total: 1 3 5 7 9 11 13 15 17 19 21
0: 1 2 2 2 2 2 2 2 2 2 2
1: . 1 3 4 4 4 4 4 4 4 4
2: . . . 1 3 4 4 4 4 4 4
3: . . . . . 1 3 4 4 4 4
4: . . . . . . . 1 3 4 4
5: . . . . . . . . . 1 3
o17 : BettiTally
|
i18 : E = ExtModule M2
8
o18 = (kk[X ..X ])
0 1
o18 : kk[X ..X ]-module, free, degrees {0..1, 2:1, 3:2, 3}
0 1
|
i19 : apply(toList(0..10), i->hilbertFunction(i, E))
o19 = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21}
o19 : List
|
i20 : Eeven = evenExtModule M2
4
o20 = (kk[X ..X ])
0 1
o20 : kk[X ..X ]-module, free, degrees {0..1, 2:1}
0 1
|
i21 : apply(toList(0..5), i->hilbertFunction(i, Eeven))
o21 = {1, 5, 9, 13, 17, 21}
o21 : List
|
i22 : Eodd = oddExtModule M2
4
o22 = (kk[X ..X ])
0 1
o22 : kk[X ..X ]-module, free, degrees {3:0, 1}
0 1
|
i23 : apply(toList(0..5), i->hilbertFunction(i, Eodd))
o23 = {3, 7, 11, 15, 19, 23}
o23 : List
|