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--- status: Draft
--- author(s): Gregory G. Smith
--- notes:
undocumented{(isField, InexactField)}
document {
Key => {
isField,
(isField, Ring),
(isField, EngineRing),
(isField, GaloisField),
},
Headline => "whether something is a field",
Usage => "isField R",
Inputs => {
"R" => Ring
},
Outputs => {
Boolean => {TO "true", " if ", TT "R",
" was explicitly constructed as a field (no computation is done) and ",
TO "false", " otherwise"}
},
"This function recognizes basic fields, ", TO2("GaloisField","Galois fields"),
" and ", TO2("FractionField","fraction fields"), ".",
EXAMPLE {
"isField QQ",
"isField CC_53",
"isField GF(2,3)",
"isField(frac(QQ[x,y]))"
},
"This function will not recognize other rings as fields.",
EXAMPLE {
"R = QQ[x]/(x^2+1)",
"isUnit x",
"isField R",
"F = toField R",
"isField F"
},
SeeAlso => {toField, FractionField, GaloisField, QuotientRing, isUnit}
}
doc ///
Node
Key
isFinitePrimeField
(isFinitePrimeField, Ring)
(isFinitePrimeField, GaloisField)
Headline
whether a ring is a finite prime field
Usage
isFinitePrimeField R
Inputs
R:Ring
Outputs
:Boolean
whether R is a finite prime field
Description
Example
isFinitePrimeField QQ
isFinitePrimeField (ZZ/101)
///
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