ideal: Create a new ideal in Macaulay2
In musicman3320/m2r: Interface to 'Macaulay2'
Description
Usage
Arguments
Value
Examples
Description
Create a new ideal in Macaulay2
Usage
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
ideal(..., raw_chars = FALSE, code = FALSE)
ideal.(..., raw_chars = FALSE, code = FALSE)
ideal_(x, raw_chars = FALSE, code = FALSE, ...)
ideal_.(x, raw_chars = FALSE, code = FALSE, ...)
## S3 method for class 'm2_ideal'
print(x, ...)
## S3 method for class 'm2_ideal_list'
print(x, ...)
radical(ideal, ring, code = FALSE, ...)
radical.(ideal, ring, code = FALSE, ...)
saturate(I, J, code = FALSE, ...)
saturate.(I, J, code = FALSE, ...)
quotient(I, J, code = FALSE, ...)
quotient.(I, J, code = FALSE, ...)
primary_decomposition(ideal, code = FALSE, ...)
primary_decomposition.(ideal, code = FALSE, ...)
dimension(ideal, code = FALSE, ...)
## S3 method for class 'm2_ideal'
e1 + e2
## S3 method for class 'm2_ideal'
e1 * e2
## S3 method for class 'm2_ideal'
e1 == e2
## S3 method for class 'm2_ideal'
e1 ^ e2
Arguments
...
...
raw_chars
if TRUE, the character vector will not be parsed by
mp(), saving time (default: FALSE). the down-side is that the
strings must be formated for M2 use directly, as opposed to for mp().
(e.g. "x*y+3" instead of "x y + 3")
code
return only the M2 code? (default: FALSE)
x
a listing of polynomials. several formats are accepted, see
examples.
ideal
an ideal object of class m2_ideal or
m2_ideal_pointer
ring
the referent ring in Macaulay2
I, J
ideals or objects parsable into ideals
e1, e2
ideals for arithmetic
Value
a reference to a Macaulay2 ideal
Examples
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
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
## Not run: requires Macaulay2
##### basic usage
########################################
ring("x", "y", coefring = "QQ")
ideal("x + y", "x^2 + y^2")
##### different versions of gb
########################################
# standard evaluation version
poly_chars <- c("x + y", "x^2 + y^2")
ideal_(poly_chars)
# reference nonstandard evaluation version
ideal.("x + y", "x^2 + y^2")
# reference standard evaluation version
ideal_.(poly_chars)
##### different inputs to gb
########################################
ideal_( c("x + y", "x^2 + y^2") )
ideal_(mp(c("x + y", "x^2 + y^2")))
ideal_(list("x + y", "x^2 + y^2") )
##### predicate functions
########################################
I <- ideal ("x + y", "x^2 + y^2")
I. <- ideal.("x + y", "x^2 + y^2")
is.m2_ideal(I)
is.m2_ideal(I.)
is.m2_ideal_pointer(I)
is.m2_ideal_pointer(I.)
##### ideal radical
########################################
I <- ideal("(x^2 + 1)^2 y", "y + 1")
radical(I)
radical.(I)
##### ideal dimension
########################################
I <- ideal_(c("(x^2 + 1)^2 y", "y + 1"))
dimension(I)
# dimension of a line
ring("x", "y", coefring = "QQ")
I <- ideal("y - (x+1)")
dimension(I)
# dimension of a plane
ring("x", "y", "z", coefring = "QQ")
I <- ideal("z - (x+y+1)")
dimension(I)
##### ideal quotients and saturation
########################################
ring("x", "y", "z", coefring = "QQ")
(I <- ideal("x^2", "y^4", "z + 1"))
(J <- ideal("x^6"))
quotient(I, J)
quotient.(I, J)
saturate(I)
saturate.(I)
saturate(I, J)
saturate(I, mp("x"))
saturate(I, "x")
ring("x", "y", coefring = "QQ")
saturate(ideal("x y"), "x^2")
# saturation removes parts of varieties
# solution over R is x = -1, 0, 1
ring("x", coefring = "QQ")
I <- ideal("(x-1) x (x+1)")
saturate(I, "x") # remove x = 0 from solution
ideal("(x-1) (x+1)")
##### primary decomposition
########################################
ring("x", "y", "z", coefring = "QQ")
I <- ideal("(x^2 + 1) (x^2 + 2)", "y + 1")
primary_decomposition(I)
primary_decomposition.(I)
I <- ideal("x (x + 1)", "y")
primary_decomposition(I)
# variety = z axis union x-y plane
(I <- ideal("x z", "y z"))
dimension(I) # = max dimension of irreducible components
(Is <- primary_decomposition(I))
dimension(Is)
##### ideal arithmetic
########################################
ring("x", "y", "z", coefring = "RR")
# sums (cox et al., 184)
(I <- ideal("x^2 + y"))
(J <- ideal("z"))
I + J
# products (cox et al., 185)
(I <- ideal("x", "y"))
(J <- ideal("z"))
I * J
# equality
(I <- ideal("x", "y"))
(J <- ideal("z"))
I == J
I == I
# powers
(I <- ideal("x", "y"))
I^3
## End(Not run)
musicman3320/m2r documentation built on May 31, 2020, 11:16 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Value Examples
Description
Create a new ideal in Macaulay2
Usage
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 | ideal(..., raw_chars = FALSE, code = FALSE)
ideal.(..., raw_chars = FALSE, code = FALSE)
ideal_(x, raw_chars = FALSE, code = FALSE, ...)
ideal_.(x, raw_chars = FALSE, code = FALSE, ...)
## S3 method for class 'm2_ideal'
print(x, ...)
## S3 method for class 'm2_ideal_list'
print(x, ...)
radical(ideal, ring, code = FALSE, ...)
radical.(ideal, ring, code = FALSE, ...)
saturate(I, J, code = FALSE, ...)
saturate.(I, J, code = FALSE, ...)
quotient(I, J, code = FALSE, ...)
quotient.(I, J, code = FALSE, ...)
primary_decomposition(ideal, code = FALSE, ...)
primary_decomposition.(ideal, code = FALSE, ...)
dimension(ideal, code = FALSE, ...)
## S3 method for class 'm2_ideal'
e1 + e2
## S3 method for class 'm2_ideal'
e1 * e2
## S3 method for class 'm2_ideal'
e1 == e2
## S3 method for class 'm2_ideal'
e1 ^ e2
|
Arguments
... |
... |
raw_chars |
if |
code |
return only the M2 code? (default: |
x |
a listing of polynomials. several formats are accepted, see examples. |
ideal |
an ideal object of class |
ring |
the referent ring in Macaulay2 |
I, J |
ideals or objects parsable into ideals |
e1, e2 |
ideals for arithmetic |
Value
a reference to a Macaulay2 ideal
Examples
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 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 | ## Not run: requires Macaulay2
##### basic usage
########################################
ring("x", "y", coefring = "QQ")
ideal("x + y", "x^2 + y^2")
##### different versions of gb
########################################
# standard evaluation version
poly_chars <- c("x + y", "x^2 + y^2")
ideal_(poly_chars)
# reference nonstandard evaluation version
ideal.("x + y", "x^2 + y^2")
# reference standard evaluation version
ideal_.(poly_chars)
##### different inputs to gb
########################################
ideal_( c("x + y", "x^2 + y^2") )
ideal_(mp(c("x + y", "x^2 + y^2")))
ideal_(list("x + y", "x^2 + y^2") )
##### predicate functions
########################################
I <- ideal ("x + y", "x^2 + y^2")
I. <- ideal.("x + y", "x^2 + y^2")
is.m2_ideal(I)
is.m2_ideal(I.)
is.m2_ideal_pointer(I)
is.m2_ideal_pointer(I.)
##### ideal radical
########################################
I <- ideal("(x^2 + 1)^2 y", "y + 1")
radical(I)
radical.(I)
##### ideal dimension
########################################
I <- ideal_(c("(x^2 + 1)^2 y", "y + 1"))
dimension(I)
# dimension of a line
ring("x", "y", coefring = "QQ")
I <- ideal("y - (x+1)")
dimension(I)
# dimension of a plane
ring("x", "y", "z", coefring = "QQ")
I <- ideal("z - (x+y+1)")
dimension(I)
##### ideal quotients and saturation
########################################
ring("x", "y", "z", coefring = "QQ")
(I <- ideal("x^2", "y^4", "z + 1"))
(J <- ideal("x^6"))
quotient(I, J)
quotient.(I, J)
saturate(I)
saturate.(I)
saturate(I, J)
saturate(I, mp("x"))
saturate(I, "x")
ring("x", "y", coefring = "QQ")
saturate(ideal("x y"), "x^2")
# saturation removes parts of varieties
# solution over R is x = -1, 0, 1
ring("x", coefring = "QQ")
I <- ideal("(x-1) x (x+1)")
saturate(I, "x") # remove x = 0 from solution
ideal("(x-1) (x+1)")
##### primary decomposition
########################################
ring("x", "y", "z", coefring = "QQ")
I <- ideal("(x^2 + 1) (x^2 + 2)", "y + 1")
primary_decomposition(I)
primary_decomposition.(I)
I <- ideal("x (x + 1)", "y")
primary_decomposition(I)
# variety = z axis union x-y plane
(I <- ideal("x z", "y z"))
dimension(I) # = max dimension of irreducible components
(Is <- primary_decomposition(I))
dimension(Is)
##### ideal arithmetic
########################################
ring("x", "y", "z", coefring = "RR")
# sums (cox et al., 184)
(I <- ideal("x^2 + y"))
(J <- ideal("z"))
I + J
# products (cox et al., 185)
(I <- ideal("x", "y"))
(J <- ideal("z"))
I * J
# equality
(I <- ideal("x", "y"))
(J <- ideal("z"))
I == J
I == I
# powers
(I <- ideal("x", "y"))
I^3
## End(Not run)
|
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.