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| author | dos-reis <gdr@axiomatics.org> | 2011-10-25 12:24:35 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-10-25 12:24:35 +0000 |
| commit | a0f5324aaab8bf19cad2dc6b80e9e026eea02854 (patch) | |
| tree | ea9eb2ce3396ce6f12e1c2d85c2f37d7a89120ee /src/algebra | |
| parent | 2092a554d70524bc90440d96367e32c9ede28ee8 (diff) | |
| download | open-axiom-a0f5324aaab8bf19cad2dc6b80e9e026eea02854.tar.gz | |
* algebra/modmon.spad.pamphlet (ModMonic): Rename second parameter
from Rep to P. Addd capsule-level definition for Rep.
[setPoly]: Adjust parameter type.
[coerce]: Likewise.
[UnVectorise]: Restrict reduction to %, then coerce to Rep.
[monomial]: Add appropriate coercion to Rep.
Diffstat (limited to 'src/algebra')
| -rw-r--r-- | src/algebra/modmon.spad.pamphlet | 32 |
1 files changed, 15 insertions, 17 deletions
diff --git a/src/algebra/modmon.spad.pamphlet b/src/algebra/modmon.spad.pamphlet index be0e86e3..e983e13d 100644 --- a/src/algebra/modmon.spad.pamphlet +++ b/src/algebra/modmon.spad.pamphlet @@ -15,19 +15,19 @@ ++ Description: ++ This package \undocumented -ModMonic(R,Rep): C == T +ModMonic(R,P): C == T where R: Ring - Rep: UnivariatePolynomialCategory(R) - C == Join(UnivariatePolynomialCategory(R),CoercibleFrom Rep) with + P: UnivariatePolynomialCategory(R) + C == Join(UnivariatePolynomialCategory(R),CoercibleFrom P) with --operations - setPoly : Rep -> Rep + setPoly : P -> P ++ setPoly(x) \undocumented - modulus : -> Rep + modulus : -> P ++ modulus() \undocumented - reduce: Rep -> % + reduce: P -> % ++ reduce(x) \undocumented - lift: % -> Rep --reduce lift = identity + lift: % -> P --reduce lift = identity ++ lift(x) \undocumented Vectorise: % -> Vector(R) ++ Vectorise(x) \undocumented @@ -46,6 +46,7 @@ ModMonic(R,Rep): C == T --assertions if R has Finite then Finite T == add + Rep := P --constants m:Rep := monomial(1,1)$Rep --| degree(m) > 0 and LeadingCoef(m) = R$1 d := degree(m)$Rep @@ -55,20 +56,17 @@ ModMonic(R,Rep): C == T --VectorRep:= DirectProduct(d:NonNegativeInteger,R) --declarations x,y: % - p: Rep d,n: Integer e,k1,k2: NonNegativeInteger c: R --vect: Vector(R) - power:PrimitiveArray(%) - frobeniusPower:PrimitiveArray(%) + power: PrimitiveArray(%) := new(0,0) + frobeniusPower: PrimitiveArray(%) := new(0,0) computeFrobeniusPowers : () -> PrimitiveArray(%) --representations --mutable m --take this out?? --define - power := new(0,0) - frobeniusPower := new(0,0) - setPoly (mon : Rep) == + setPoly (mon : P) == mon =$Rep m => mon oldm := m not one? leadingCoefficient mon => error "polynomial must be monic" @@ -104,7 +102,7 @@ ModMonic(R,Rep): C == T degree x == (degree x)$Rep lift(x) == x pretend Rep reduce(p) == (monicDivide(p,m)$Rep).remainder - coerce(p) == reduce(p) + coerce(p: P): % == reduce(p) x = y == x =$Rep y x + y == x +$Rep y - x == -$Rep x @@ -117,7 +115,7 @@ ModMonic(R,Rep): C == T ans+p Vectorise(x) == [coefficient(lift(x),i) for i in 0..d1] UnVectorise(vect) == - reduce(+/[monomial(vect.(i+1),i) for i in 0..d1]) + reduce(+/[monomial(vect.(i+1),i) for i in 0..d1]@%::Rep) computePowers == mat : PrimitiveArray(%):= new(d,0) mat.0:= reductum(-m)$Rep @@ -151,13 +149,13 @@ ModMonic(R,Rep): C == T else k1:=e quo twod k2 := (e-k1*twod)::NonNegativeInteger - reduce((power.d1 **k1)*monomial(c,k2)) + reduce(((power.d1 **k1)*monomial(c,k2))::Rep) if R has Field then (x:% exquo y:%):Union(%, "failed") == uv := extendedEuclidean(y, modulus(), x)$Rep uv case "failed" => "failed" - return reduce(uv.coef1) + return reduce(uv.coef1::Rep) recip(y:%):Union(%, "failed") == 1 exquo y divide(x:%, y:%) == |