Polynom-0.1: A commutative algebra packageContentsIndex
Algebra.Elimination
Description
The Elimination module defines elimination orders and the functions needed to perform elimination of variables.
Synopsis
newtype EliminationMonoid a b = ElimPair (a, b)
elim_fst :: EliminationMonoid a b -> a
elim_snd :: EliminationMonoid a b -> b
elim_map :: (a -> a -> a) -> (b -> b -> b) -> EliminationMonoid a b -> EliminationMonoid a b -> EliminationMonoid a b
separate_pols :: (Num r, VarList v) => [v] -> Polynom r v -> MonoidRing r (EliminationMonoid (Monom v) (Monom v))
eliminate :: (Fractional r, VarList v) => [v] -> Ideal (Polynom r v) -> GroebnerIdeal r (Monom v)
step_eliminate :: (Fractional r, VarList v) => [v] -> Ideal (Polynom r v) -> GroebnerIdeal r (Monom v)
Documentation
newtype EliminationMonoid a b
We define a tuple type which inherits a product structure. The elimination order is the reverse lexicographic order on pairs.
Constructors
ElimPair (a, b)
show/hide Instances
elim_fst :: EliminationMonoid a b -> a
elim_snd :: EliminationMonoid a b -> b
elim_map :: (a -> a -> a) -> (b -> b -> b) -> EliminationMonoid a b -> EliminationMonoid a b -> EliminationMonoid a b
A helper function
separate_pols :: (Num r, VarList v) => [v] -> Polynom r v -> MonoidRing r (EliminationMonoid (Monom v) (Monom v))
Convert to monomial order according to a list of variables
eliminate :: (Fractional r, VarList v) => [v] -> Ideal (Polynom r v) -> GroebnerIdeal r (Monom v)
Given a list of variables and an ideal, eliminate these variables.
step_eliminate :: (Fractional r, VarList v) => [v] -> Ideal (Polynom r v) -> GroebnerIdeal r (Monom v)
Eliminate variables one at a time
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