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New options added and bugs fixed in ConwayPolynomials #1179

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merged 4 commits into from
May 22, 2020
Merged

New options added and bugs fixed in ConwayPolynomials #1179

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cff5328
Added new option 'Variable' to conwayPolynomial; map between GaloisFi…
zeromath May 20, 2020
6442b9f
updated as requested
zeromath May 21, 2020
0698551
extra test deleted
zeromath May 21, 2020
23d4c2e
removed getSymbol because monoid implicitly uses it
zeromath May 21, 2020
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34 changes: 20 additions & 14 deletions M2/Macaulay2/packages/ConwayPolynomials.m2
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Original file line number Diff line number Diff line change
Expand Up @@ -10,24 +10,28 @@ newPackage(
Headline => "a database of Conway polynomials"
)
-- the data comes libflint
export "conwayPolynomial"
export {
"conwayPolynomial",
-- options to set the variable to use
"Variable"
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"Variable" is a symbol in the Core package, so just use it -- don't export a new one with the same name.

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Gotcha! Just changed!

}
rawConwayPolynomial := value Core#"private dictionary"#"rawConwayPolynomial"
getCP := (p,n) -> rawConwayPolynomial (p,n,false)
Ap := memoize(p -> (ZZ/p)(monoid [getSymbol "a"]))
Ap := memoize((p, a) -> (ZZ/p)(monoid [a]))
fix := (p,n,co,a) -> sum(#co, i -> co#i * a^i)
conwayPolynomial = method()
conwayPolynomial(ZZ,ZZ) := (p,n) -> (
conwayPolynomial = method(Options=>{Variable=>getSymbol "a"})
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I think that if you run ' installPackage "ConwayPolynomials" ', this change will lead to a problem -- the error message will be something like " can't determine package of symbol a ". The solution will be to let the default value be the string "a", and run getSymbol later.

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I rewrite this part by following the code in galois.m2

conwayPolynomial(ZZ,ZZ) := opts -> (p,n) -> (
cp := getCP(p,n);
if cp != {} then fix(p,n,cp,(Ap p)_0))
conwayPolynomial ZZ := q -> (
if cp != {} then fix(p,n,cp,(Ap(p, opts.Variable))_0))
conwayPolynomial ZZ := opts -> q -> (
factors := factor q;
if #factors =!= 1 or factors#0#0 === -1
then error "expected a power of a prime";
conwayPolynomial(factors#0#0,factors#0#1))
conwayPolynomial(factors#0#0,factors#0#1,opts))
addHook(GaloisField,FindOne,(p,n,a) -> (
cp := getCP(p,n);
if cp != {} then break fix(p,n,cp,a)))
isConway := (F) -> (gens ideal ambient F)_(0,0) == sub(conwayPolynomial(F.char,F.degree),ambient ambient F)
isConway := (F) -> (gens ideal ambient F)_(0,0) == sub(conwayPolynomial(F.char,F.degree, Variable=>F_0),ambient ambient F)
map(GaloisField,GaloisField) := RingMap => o -> (K,F) -> (
p := char F;
n := K.degree;
Expand Down Expand Up @@ -71,9 +75,10 @@ document {
Key => {conwayPolynomial, (conwayPolynomial,ZZ,ZZ), (conwayPolynomial,ZZ)},
Headline => "provide a Conway polynomial",
SYNOPSIS (
Usage => "conwayPolynomial q",
Usage => "conwayPolynomial(q,Variable=>a)",
Inputs => {
"q" => ZZ => {"a power of a prime number"}
"q" => ZZ => {"a power of a prime number"},
"a" => Symbol => {"an optional input, the symbol served as variable, default a"}
},
Outputs => {
{"a Conway polynomial whose roots generate a field with q elements"}
Expand All @@ -83,16 +88,17 @@ document {
///
),
SYNOPSIS (
Usage => "conwayPolynomial(p,n)",
Usage => "conwayPolynomial(p,n,Variable=>a)",
Inputs => {
"p" => ZZ => {"a prime number"},
"n" => ZZ
"n" => ZZ,
"a" => Symbol => {"an optional input, the symbol served as variable, default a"}
},
Outputs => {
{"a Conway polynomial whose roots generate a field with p^n elements"}
{"a Conway polynomial whose roots generate a field with ", TEX "p^n", " elements"}
},
EXAMPLE lines ///
conwayPolynomial(2,20)
conwayPolynomial(2,20,Variable=>"b")
///
)
}
Expand Down