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
51
52
53
54
55
56
|
--- status: TODO
--- author(s):
--- notes:
document { Key => degrees,
Headline => "degrees of generators" }
document {
Key => {
(degrees, Ring),
(degrees, QuotientRing),
(degrees, FractionField),
(degrees, Module),
(degrees, Monoid),
(degrees, Ideal)},
Headline => "degrees of generators",
Usage => "degrees A",
Inputs => {"A" => { ofClass Ring, ", ", ofClass Ideal, ", ", ofClass Module, ", or ", ofClass Monoid }
},
Outputs => {
List => { "the list of multi-degrees for the generators of ", TT "A"}
},
EXAMPLE lines ///
R = ZZ/101[x,y,z];
degrees R
S = ZZ/101[x,y,z,Degrees => {{2,3},{1,2},{2,0}}];
degrees S
///,
"This function also applies to ideals, modules, and monoids.",
EXAMPLE lines ///
I = ideal"xy2,xyz,y3"
degrees I
///,
EXAMPLE lines ///
degrees R^5
degrees R^{1,2,3,4}
///,
SeeAlso => {degreeLength, degreesRing}
}
document {
Key => (degrees,Matrix),
Headline => "degrees of target and source",
Usage => "degrees f",
Inputs => {
"f"
},
Outputs => {
{ "a list ", TT "{x,y}", " where ", TT "x", " is the list
of degrees of the target of ", TT "f", " and ", TT "y", " is the
list of degrees of the source of ", TT "f", "." }
},
EXAMPLE lines ///
S = ZZ/101[x,y,z,Degrees => {{2,3},{1,2},{2,0}}];
degrees vars S
///,
SeeAlso => {degreeLength, degreesRing}
}
|
