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
|
--- status: TODO
--- author(s):
--- notes:
document {
Key => {index,(index,RingElement)},
Headline => "numeric index of a ring variable",
Usage => "index v",
Inputs => {
"v" => RingElement
},
Outputs => {
ZZ => {"the integer index, starting at 0, of v, if it is a variable.
If v is not a variable, then ", TO null, " is returned"}
},
"Variables are indexed in the following way: the first variable has index 0,
the second index 1, and so on, until n-1, where n is the number of generators of R,
the ring of v. Then, if the coefficient ring is a polynomial ring, those variables
are numbered starting at n, and so on.",
EXAMPLE {
"R = ZZ/101[a..d,t]",
"index a",
"index t",
},
EXAMPLE {
"A = ZZ[a..d]; B = A[r,s,t]; C = B[x,y,z]",
"index x",
"index z",
"index r"
},
"Notice that r is an element of B, and so indices are taken from that ring.
If we consider r as an element of C, we get a different answer. Variables
of coefficient rings of coefficient rings have an index too.",
EXAMPLE {
"index(r*1_C)",
"index(b*1_C)"
},
PARA{},
"The symbol ", TT "index", " is also as a key used in
", TO {"Monoid", "s"}, " to store a table that is used to
map generator names to the position of the generator in the list of generators.",
SeeAlso => {indices, support, (symbol_,Ring,ZZ)}
}
|
