Copyright	(c) Masahiro Sakai 2012-2013
License	BSD-style
Maintainer	masahiro.sakai@gmail.com
Stability	provisional
Portability	non-portable
Safe Haskell	Safe-Inferred
Language	Haskell2010
Extensions	ScopedTypeVariables ExplicitForAll

ToySolver.Data.Polynomial.GroebnerBasis

Contents

Options
Gröbner basis computation

Description

Gröbner basis

References:

Monomial order http://en.wikipedia.org/wiki/Monomial_order
Gröbner basis http://en.wikipedia.org/wiki/Gr%C3%B6bner_basis
グレブナー基底 http://d.hatena.ne.jp/keyword/%A5%B0%A5%EC%A5%D6%A5%CA%A1%BC%B4%F0%C4%EC
Gröbner Bases and Buchberger’s Algorithm http://math.rice.edu/~cbruun/vigre/vigreHW6.pdf
Docon http://www.haskell.org/docon/

Synopsis

data Options = Options {
- optStrategy :: Strategy
}
data Strategy
- = NormalStrategy
- | SugarStrategy
basis :: forall k v. (Eq k, Fractional k, Ord k, Ord v) => MonomialOrder v -> [Polynomial k v] -> [Polynomial k v]
basis' :: forall k v. (Eq k, Fractional k, Ord k, Ord v) => Options -> MonomialOrder v -> [Polynomial k v] -> [Polynomial k v]
spolynomial :: (Eq k, Fractional k, Ord v) => MonomialOrder v -> Polynomial k v -> Polynomial k v -> Polynomial k v
reduceGBasis :: forall k v. (Eq k, Ord k, Fractional k, Ord v) => MonomialOrder v -> [Polynomial k v] -> [Polynomial k v]

Options

data Options Source #

Options for Gröbner Basis computation.

The default option can be obtained by def.

Constructors

Options
Fields optStrategy :: Strategy

Instances

Instances details

Default Options Source #
Instance details Defined in ToySolver.Data.Polynomial.GroebnerBasis Methods def :: Options #

data Strategy Source #

Constructors

NormalStrategy
SugarStrategy	sugar strategy (not implemented yet)

Instances

Instances details

Bounded Strategy Source #
Instance details Defined in ToySolver.Data.Polynomial.GroebnerBasis Methods minBound :: Strategy # maxBound :: Strategy #
Enum Strategy Source #
Instance details Defined in ToySolver.Data.Polynomial.GroebnerBasis Methods succ :: Strategy -> Strategy # pred :: Strategy -> Strategy # toEnum :: Int -> Strategy # fromEnum :: Strategy -> Int # enumFrom :: Strategy -> [Strategy] # enumFromThen :: Strategy -> Strategy -> [Strategy] # enumFromTo :: Strategy -> Strategy -> [Strategy] # enumFromThenTo :: Strategy -> Strategy -> Strategy -> [Strategy] #
Read Strategy Source #
Instance details Defined in ToySolver.Data.Polynomial.GroebnerBasis Methods readsPrec :: Int -> ReadS Strategy # readList :: ReadS [Strategy] # readPrec :: ReadPrec Strategy # readListPrec :: ReadPrec [Strategy] #
Show Strategy Source #
Instance details Defined in ToySolver.Data.Polynomial.GroebnerBasis Methods showsPrec :: Int -> Strategy -> ShowS # show :: Strategy -> String # showList :: [Strategy] -> ShowS #
Eq Strategy Source #
Instance details Defined in ToySolver.Data.Polynomial.GroebnerBasis Methods (==) :: Strategy -> Strategy -> Bool # (/=) :: Strategy -> Strategy -> Bool #
Ord Strategy Source #
Instance details Defined in ToySolver.Data.Polynomial.GroebnerBasis Methods compare :: Strategy -> Strategy -> Ordering # (<) :: Strategy -> Strategy -> Bool # (<=) :: Strategy -> Strategy -> Bool # (>) :: Strategy -> Strategy -> Bool # (>=) :: Strategy -> Strategy -> Bool # max :: Strategy -> Strategy -> Strategy # min :: Strategy -> Strategy -> Strategy #

Gröbner basis computation

basis :: forall k v. (Eq k, Fractional k, Ord k, Ord v) => MonomialOrder v -> [Polynomial k v] -> [Polynomial k v] Source #

basis' :: forall k v. (Eq k, Fractional k, Ord k, Ord v) => Options -> MonomialOrder v -> [Polynomial k v] -> [Polynomial k v] Source #

spolynomial :: (Eq k, Fractional k, Ord v) => MonomialOrder v -> Polynomial k v -> Polynomial k v -> Polynomial k v Source #

reduceGBasis :: forall k v. (Eq k, Ord k, Fractional k, Ord v) => MonomialOrder v -> [Polynomial k v] -> [Polynomial k v] Source #