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
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
|
-- -*- coding: utf-8 -*-
--- status: DRAFT
--- author(s): MES
--- notes:
-- in Classic: (monomialIdeal, String)
document {
Key => monomialIdeal,
Headline => "make a monomial ideal"
}
document {
Key => {
(monomialIdeal,Matrix),
(monomialIdeal,RingElement),
(monomialIdeal,List),
(monomialIdeal,Sequence)},
Headline => "monomial ideal of lead monomials",
Usage => "monomialIdeal L",
Inputs => {
"L" => Nothing => {ofClass Matrix, ", ",
ofClass RingElement, ", ",
ofClass List, ", or ",
ofClass Sequence}
},
Outputs => {
MonomialIdeal => "the monomial ideal of lead monomials of the elements of L",
},
"If L is a matrix, then it must have only one row. For all of these types,
the result is generated by only the lead monomials given: no Gröbner bases are computed.
See ", TO (monomialIdeal,Ideal), " if the lead monomials of a Gröbner basis is desired.",
EXAMPLE lines ///
R = ZZ/101[a,b,c];
I = monomialIdeal(a^3,b^3,c^3, a^2-b^2)
M = monomialIdeal vars R
J = monomialIdeal 0_R
///,
"If the coefficient ring is ZZ, lead coefficients of the monomials are ignored.",
EXAMPLE lines ///
R = ZZ[x,y]
monomialIdeal(2*x,3*y)
///,
SeeAlso => {MonomialIdeal}
}
document {
Key => {
(monomialIdeal, Ideal),
(monomialIdeal, Module),
(monomialIdeal, MonomialIdeal)},
Headline => "monomial ideal of lead monomials of a Gröbner basis",
Usage => "monomialIdeal J",
Inputs => {
"J"
},
Outputs => {
MonomialIdeal => {"the monomial ideal generated by the lead monomials of a Gröbner basis of ",
TT "J" } },
"J may also be a submodule of R^1, for R the ring of J.",
EXAMPLE lines ///
R = ZZ/101[a,b,c];
I = ideal(a^3,b^3,c^3, a^2-b^2)
monomialIdeal I
monomialSubideal I
///,
"If the coefficient ring is ZZ, lead coefficients of the monomials are ignored.",
EXAMPLE lines ///
R = ZZ[x,y]
monomialIdeal ideal(2*x,3*y)
///,
SeeAlso => {MonomialIdeal,monomialSubideal}
}
|
