1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
|
--- status: DRAFT
--- author(s): L.Gold, Josephine, Jonah
--- notes:
document {
Key => pdim,
Headline => "calculate the projective dimension",
Usage => "pdim M",
Caveat => { "For now, the method is to measure the length of a projective resolution."},
SeeAlso => {}
}
document {
Key => (pdim, Module),
Headline => "calculate the projective dimension of a module",
Usage => "pdim M",
Inputs => {
"M" => Module
},
Outputs => {
ZZ => "the projective dimension"
},
EXAMPLE {
"R = QQ[x,y,z];",
"I = ideal(x^2, x*y, y*z);",
"M = R^1/I",
"res M",
"pdim M"},
"Notice this is one more than the projective dimension of I as an R-module.",
EXAMPLE{
"res(module I)",
"pdim(module I)"
}
}
document {
Key => (pdim,CoherentSheaf),
Headline => "calculate the projective dimension",
Usage => "pdim S",
Inputs => {
"S" => CoherentSheaf
},
Outputs => {
ZZ => "the projective dimension"
},
EXAMPLE {
"V = Proj(ZZ/101[x_0..x_2]);",
"S = sheaf(image matrix {{x_0^3+x_1^3+x_2^3}})",
"pdim S"}
}
|
