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
|
--- status: Draft
--- author(s): Gregory G. Smith
--- notes:
document {
Key => {isAffineRing, (isAffineRing,QuotientRing), (isAffineRing,PolynomialRing), (isAffineRing,Ring)},
Headline => "whether something is an affine ring",
Usage => "isAffineRing R",
Inputs => {
"R" => Ring
},
Outputs => {
Boolean =>
{TO "true", " if ", TT "R", " is an affine ring and ", TO "false", " otherwise"}
},
"For our purposes, an affine ring is a quotient of a (not necessarily commutative) ", TO2("PolynomialRing","polynomial ring"),
" over a field.",
EXAMPLE {
"isAffineRing (ZZ[a,b,c,d])",
"isAffineRing (ZZ/101[a,b,c,d])",
"isAffineRing (ZZ/2[x,y,z]/(x^2-y*z))",
"isAffineRing (QQ[x,dx, WeylAlgebra => {x => dx}])"
},
SeeAlso => {coefficientRing, isField, ambient}
}
|
