| Safe Haskell | Safe-Infered |
|---|
Algebra.Algorithms.Groebner.Monomorphic
Description
Monomorphic interface for Groenber basis.
- class (Eq r, Field r, NoetherianRing r) => Groebnerable r
- divModPolynomial :: Groebnerable r => Polynomial r -> [Polynomial r] -> ([(Polynomial r, Polynomial r)], Polynomial r)
- divPolynomial :: Groebnerable r => Polynomial r -> [Polynomial r] -> [(Polynomial r, Polynomial r)]
- modPolynomial :: Groebnerable r => Polynomial r -> [Polynomial r] -> Polynomial r
- divModPolynomialWith :: forall ord r. (IsMonomialOrder ord, Groebnerable r) => ord -> Polynomial r -> [Polynomial r] -> ([(Polynomial r, Polynomial r)], Polynomial r)
- divPolynomialWith :: Groebnerable r => IsMonomialOrder ord => ord -> Polynomial r -> [Polynomial r] -> [(Polynomial r, Polynomial r)]
- modPolynomialWith :: (Groebnerable r, IsMonomialOrder ord) => ord -> Polynomial r -> [Polynomial r] -> Polynomial r
- calcGroebnerBasis :: Groebnerable r => [Polynomial r] -> [Polynomial r]
- calcGroebnerBasisWith :: forall ord r. (Groebnerable r, IsMonomialOrder ord) => ord -> [Polynomial r] -> [Polynomial r]
- isIdealMember :: forall r. Groebnerable r => Polynomial r -> [Polynomial r] -> Bool
- intersection :: forall r. Groebnerable r => [[Polynomial r]] -> [Polynomial r]
- thEliminationIdeal :: Groebnerable r => Int -> [Polynomial r] -> [Polynomial r]
- eliminate :: forall r. Groebnerable r => [Variable] -> [Polynomial r] -> [Polynomial r]
- quotIdeal :: Groebnerable r => [Polynomial r] -> [Polynomial r] -> [Polynomial r]
- quotByPrincipalIdeal :: Groebnerable r => [Polynomial r] -> Polynomial r -> [Polynomial r]
- saturationIdeal :: Groebnerable r => [Polynomial r] -> [Polynomial r] -> [Polynomial r]
- saturationByPrincipalIdeal :: Groebnerable r => [Polynomial r] -> Polynomial r -> [Polynomial r]
- data Lex = Lex
- data Revlex = Revlex
- data Grlex = Grlex
- data Grevlex = Grevlex
- class IsOrder ordering
- class IsOrder name => IsMonomialOrder name
Documentation
class (Eq r, Field r, NoetherianRing r) => Groebnerable r
Synonym
Instances
| (Eq r, Field r, NoetherianRing r) => Groebnerable r |
Polynomial division
divModPolynomial :: Groebnerable r => Polynomial r -> [Polynomial r] -> ([(Polynomial r, Polynomial r)], Polynomial r)
divPolynomial :: Groebnerable r => Polynomial r -> [Polynomial r] -> [(Polynomial r, Polynomial r)]
modPolynomial :: Groebnerable r => Polynomial r -> [Polynomial r] -> Polynomial r
divModPolynomialWith :: forall ord r. (IsMonomialOrder ord, Groebnerable r) => ord -> Polynomial r -> [Polynomial r] -> ([(Polynomial r, Polynomial r)], Polynomial r)
divPolynomialWith :: Groebnerable r => IsMonomialOrder ord => ord -> Polynomial r -> [Polynomial r] -> [(Polynomial r, Polynomial r)]
modPolynomialWith :: (Groebnerable r, IsMonomialOrder ord) => ord -> Polynomial r -> [Polynomial r] -> Polynomial r
Groebner basis
calcGroebnerBasis :: Groebnerable r => [Polynomial r] -> [Polynomial r]
calcGroebnerBasisWith :: forall ord r. (Groebnerable r, IsMonomialOrder ord) => ord -> [Polynomial r] -> [Polynomial r]
Ideal operations
isIdealMember :: forall r. Groebnerable r => Polynomial r -> [Polynomial r] -> Bool
intersection :: forall r. Groebnerable r => [[Polynomial r]] -> [Polynomial r]
Calculate a intersection of given ideals.
thEliminationIdeal :: Groebnerable r => Int -> [Polynomial r] -> [Polynomial r]
Computes nth elimination ideal.
eliminate :: forall r. Groebnerable r => [Variable] -> [Polynomial r] -> [Polynomial r]
Computes the ideal with specified variables eliminated.
quotIdeal :: Groebnerable r => [Polynomial r] -> [Polynomial r] -> [Polynomial r]
Calculate the ideal quotient of I of J.
quotByPrincipalIdeal :: Groebnerable r => [Polynomial r] -> Polynomial r -> [Polynomial r]
Calculate ideal quotient of I by principal ideal
saturationIdeal :: Groebnerable r => [Polynomial r] -> [Polynomial r] -> [Polynomial r]
Calculate saturation ideal.
saturationByPrincipalIdeal :: Groebnerable r => [Polynomial r] -> Polynomial r -> [Polynomial r]
Calculate saturation ideal by the principal ideal generated by the second argument.
Re-exports
class IsOrder ordering
Class to lookup ordering from its (type-level) name.
class IsOrder name => IsMonomialOrder name
Class for Monomial orders.