Extracts the odd degree part from ExtModule M. If the optional argument OutRing => T is given, and class T === PolynomialRing, then the output will be a module over T.
i1 : kk= ZZ/101
o1 = kk
o1 : QuotientRing
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i2 : S = kk[x,y,z]
o2 = S
o2 : PolynomialRing
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i3 : I2 = ideal"x3,yz"
3
o3 = ideal (x , y*z)
o3 : Ideal of S
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i4 : R2 = S/I2
o4 = R2
o4 : QuotientRing
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i5 : M2 = R2^1/ideal"x2,y,z"
o5 = cokernel | x2 y z |
1
o5 : R2-module, quotient of R2
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i6 : betti res (M2, LengthLimit =>10)
0 1 2 3 4 5 6 7 8 9 10
o6 = 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
o6 : BettiTally
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i7 : E = ExtModule M2
8
o7 = (kk[X ..X ])
0 1
o7 : kk[X ..X ]-module, free, degrees {0..1, 2:1, 3:2, 3}
0 1
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i8 : apply(toList(0..10), i->hilbertFunction(i, E))
o8 = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21}
o8 : List
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i9 : Eodd = oddExtModule M2
4
o9 = (kk[X ..X ])
0 1
o9 : kk[X ..X ]-module, free, degrees {3:0, 1}
0 1
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i10 : apply(toList(0..5), i->hilbertFunction(i, Eodd))
o10 = {3, 7, 11, 15, 19, 23}
o10 : List
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