Safe Haskell	None
Language	Haskell2010

Algebra.Algorithms.Groebner.SelectionStrategy

Synopsis

class SelectionStrategy n s where
- type Weight n s ord :: Type
- calcWeight :: (IsOrderedPolynomial poly, n ~ Arity poly) => Proxy s -> poly -> poly -> Weight n s (MOrder poly)
calcWeight' :: (SelectionStrategy (Arity poly) s, IsOrderedPolynomial poly) => s -> poly -> poly -> Weight (Arity poly) s (MOrder poly)
data GrevlexStrategy = GrevlexStrategy
data NormalStrategy = NormalStrategy
newtype SugarStrategy s = SugarStrategy s
data GradedStrategy = GradedStrategy

Documentation

class SelectionStrategy n s where Source #

Type-class for selection strategies in Buchberger's algorithm.

Associated Types

type Weight n s ord :: Type Source #

Methods

calcWeight :: (IsOrderedPolynomial poly, n ~ Arity poly) => Proxy s -> poly -> poly -> Weight n s (MOrder poly) Source #

Calculates the weight for the given pair of polynomial used for selection strategy.

Instances

Instances details

SelectionStrategy n GradedStrategy Source #	Choose the pair with the least LCM(LT(f), LT(g)) w.r.t. graded current ordering.
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Associated Types type Weight n GradedStrategy ord Source # Methods calcWeight :: (IsOrderedPolynomial poly, n ~ Arity poly) => Proxy GradedStrategy -> poly -> poly -> Weight n GradedStrategy (MOrder poly) Source #
SelectionStrategy n GrevlexStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Associated Types type Weight n GrevlexStrategy ord Source # Methods calcWeight :: (IsOrderedPolynomial poly, n ~ Arity poly) => Proxy GrevlexStrategy -> poly -> poly -> Weight n GrevlexStrategy (MOrder poly) Source #
SelectionStrategy n NormalStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Associated Types type Weight n NormalStrategy ord Source # Methods calcWeight :: (IsOrderedPolynomial poly, n ~ Arity poly) => Proxy NormalStrategy -> poly -> poly -> Weight n NormalStrategy (MOrder poly) Source #
SelectionStrategy n s => SelectionStrategy n (SugarStrategy s :: Type) Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Associated Types type Weight n (SugarStrategy s) ord Source # Methods calcWeight :: (IsOrderedPolynomial poly, n ~ Arity poly) => Proxy (SugarStrategy s) -> poly -> poly -> Weight n (SugarStrategy s) (MOrder poly) Source #

calcWeight' :: (SelectionStrategy (Arity poly) s, IsOrderedPolynomial poly) => s -> poly -> poly -> Weight (Arity poly) s (MOrder poly) Source #

Calculate the weight of given polynomials w.r.t. the given strategy. Buchberger's algorithm proccesses the pair with the most least weight first. This function requires the Ord instance for the weight; this constraint is not required in the calcWeight because of the ease of implementation. So use this function.

data GrevlexStrategy Source #

Choose the pair with the least LCM(LT(f), LT(g)) w.r.t. Grevlex order.

Constructors

GrevlexStrategy

Instances

Instances details

Eq GrevlexStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods (==) :: GrevlexStrategy -> GrevlexStrategy -> Bool # (/=) :: GrevlexStrategy -> GrevlexStrategy -> Bool #
Ord GrevlexStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods compare :: GrevlexStrategy -> GrevlexStrategy -> Ordering # (<) :: GrevlexStrategy -> GrevlexStrategy -> Bool # (<=) :: GrevlexStrategy -> GrevlexStrategy -> Bool # (>) :: GrevlexStrategy -> GrevlexStrategy -> Bool # (>=) :: GrevlexStrategy -> GrevlexStrategy -> Bool # max :: GrevlexStrategy -> GrevlexStrategy -> GrevlexStrategy # min :: GrevlexStrategy -> GrevlexStrategy -> GrevlexStrategy #
Read GrevlexStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods readsPrec :: Int -> ReadS GrevlexStrategy # readList :: ReadS [GrevlexStrategy] # readPrec :: ReadPrec GrevlexStrategy # readListPrec :: ReadPrec [GrevlexStrategy] #
Show GrevlexStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods showsPrec :: Int -> GrevlexStrategy -> ShowS # show :: GrevlexStrategy -> String # showList :: [GrevlexStrategy] -> ShowS #
SelectionStrategy n GrevlexStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Associated Types type Weight n GrevlexStrategy ord Source # Methods calcWeight :: (IsOrderedPolynomial poly, n ~ Arity poly) => Proxy GrevlexStrategy -> poly -> poly -> Weight n GrevlexStrategy (MOrder poly) Source #
type Weight n GrevlexStrategy ord Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy type Weight n GrevlexStrategy ord = OrderedMonomial Grevlex n

data NormalStrategy Source #

Buchberger's normal selection strategy. This selects the pair with the least LCM(LT(f), LT(g)) w.r.t. current monomial ordering.

Constructors

NormalStrategy

Instances

Instances details

Eq NormalStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods (==) :: NormalStrategy -> NormalStrategy -> Bool # (/=) :: NormalStrategy -> NormalStrategy -> Bool #
Ord NormalStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods compare :: NormalStrategy -> NormalStrategy -> Ordering # (<) :: NormalStrategy -> NormalStrategy -> Bool # (<=) :: NormalStrategy -> NormalStrategy -> Bool # (>) :: NormalStrategy -> NormalStrategy -> Bool # (>=) :: NormalStrategy -> NormalStrategy -> Bool # max :: NormalStrategy -> NormalStrategy -> NormalStrategy # min :: NormalStrategy -> NormalStrategy -> NormalStrategy #
Read NormalStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods readsPrec :: Int -> ReadS NormalStrategy # readList :: ReadS [NormalStrategy] # readPrec :: ReadPrec NormalStrategy # readListPrec :: ReadPrec [NormalStrategy] #
Show NormalStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods showsPrec :: Int -> NormalStrategy -> ShowS # show :: NormalStrategy -> String # showList :: [NormalStrategy] -> ShowS #
SelectionStrategy n NormalStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Associated Types type Weight n NormalStrategy ord Source # Methods calcWeight :: (IsOrderedPolynomial poly, n ~ Arity poly) => Proxy NormalStrategy -> poly -> poly -> Weight n NormalStrategy (MOrder poly) Source #
type Weight n NormalStrategy ord Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy type Weight n NormalStrategy ord = OrderedMonomial ord n

newtype SugarStrategy s Source #

Sugar strategy. This chooses the pair with the least phantom homogenized degree and then break the tie with the given strategy (say s).

Constructors

SugarStrategy s

Instances

Instances details

Eq s => Eq (SugarStrategy s) Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods (==) :: SugarStrategy s -> SugarStrategy s -> Bool # (/=) :: SugarStrategy s -> SugarStrategy s -> Bool #
Ord s => Ord (SugarStrategy s) Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods compare :: SugarStrategy s -> SugarStrategy s -> Ordering # (<) :: SugarStrategy s -> SugarStrategy s -> Bool # (<=) :: SugarStrategy s -> SugarStrategy s -> Bool # (>) :: SugarStrategy s -> SugarStrategy s -> Bool # (>=) :: SugarStrategy s -> SugarStrategy s -> Bool # max :: SugarStrategy s -> SugarStrategy s -> SugarStrategy s # min :: SugarStrategy s -> SugarStrategy s -> SugarStrategy s #
Read s => Read (SugarStrategy s) Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods readsPrec :: Int -> ReadS (SugarStrategy s) # readList :: ReadS [SugarStrategy s] # readPrec :: ReadPrec (SugarStrategy s) # readListPrec :: ReadPrec [SugarStrategy s] #
Show s => Show (SugarStrategy s) Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods showsPrec :: Int -> SugarStrategy s -> ShowS # show :: SugarStrategy s -> String # showList :: [SugarStrategy s] -> ShowS #
SelectionStrategy n s => SelectionStrategy n (SugarStrategy s :: Type) Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Associated Types type Weight n (SugarStrategy s) ord Source # Methods calcWeight :: (IsOrderedPolynomial poly, n ~ Arity poly) => Proxy (SugarStrategy s) -> poly -> poly -> Weight n (SugarStrategy s) (MOrder poly) Source #
type Weight n (SugarStrategy s :: Type) ord Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy type Weight n (SugarStrategy s :: Type) ord = (Int, Weight n s ord)

data GradedStrategy Source #

Constructors

GradedStrategy

Instances

Instances details

Eq GradedStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods (==) :: GradedStrategy -> GradedStrategy -> Bool # (/=) :: GradedStrategy -> GradedStrategy -> Bool #
Ord GradedStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods compare :: GradedStrategy -> GradedStrategy -> Ordering # (<) :: GradedStrategy -> GradedStrategy -> Bool # (<=) :: GradedStrategy -> GradedStrategy -> Bool # (>) :: GradedStrategy -> GradedStrategy -> Bool # (>=) :: GradedStrategy -> GradedStrategy -> Bool # max :: GradedStrategy -> GradedStrategy -> GradedStrategy # min :: GradedStrategy -> GradedStrategy -> GradedStrategy #
Read GradedStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods readsPrec :: Int -> ReadS GradedStrategy # readList :: ReadS [GradedStrategy] # readPrec :: ReadPrec GradedStrategy # readListPrec :: ReadPrec [GradedStrategy] #
Show GradedStrategy Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Methods showsPrec :: Int -> GradedStrategy -> ShowS # show :: GradedStrategy -> String # showList :: [GradedStrategy] -> ShowS #
SelectionStrategy n GradedStrategy Source #	Choose the pair with the least LCM(LT(f), LT(g)) w.r.t. graded current ordering.
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy Associated Types type Weight n GradedStrategy ord Source # Methods calcWeight :: (IsOrderedPolynomial poly, n ~ Arity poly) => Proxy GradedStrategy -> poly -> poly -> Weight n GradedStrategy (MOrder poly) Source #
type Weight n GradedStrategy ord Source #
Instance details Defined in Algebra.Algorithms.Groebner.SelectionStrategy type Weight n GradedStrategy ord = OrderedMonomial (Graded ord) n