Algebra.Ring.Polynomial

Synopsis

• type Polynomial r = OrderedPolynomial r Grevlex
• type Monomial n = Vector Int n
• type MonomialOrder n = Monomial n -> Monomial n -> Ordering
• class Order a
• lex :: MonomialOrder n
• revlex :: Monomial n -> Monomial n -> Ordering
• graded :: (Monomial n -> Monomial n -> Ordering) -> Monomial n -> Monomial n -> Ordering
• grlex :: MonomialOrder n
• grevlex :: MonomialOrder n
• transformMonomial :: (IsOrder o, IsPolynomial k n, IsPolynomial k m) => (Monomial n -> Monomial m) -> OrderedPolynomial k o n -> OrderedPolynomial k o m
• type IsPolynomial r n = (NoetherianRing r, Sing n, Eq r)
• coeff :: (IsOrder order, IsPolynomial r n) => Monomial n -> OrderedPolynomial r order n -> r
• lcmMonomial :: Monomial n -> Monomial n -> Monomial n
• sPolynomial :: (IsPolynomial k n, Field k, IsOrder order) => OrderedPolynomial k order n -> OrderedPolynomial k order n -> OrderedPolynomial k order n
• polynomial :: (Sing n, Eq r, NoetherianRing r, IsOrder order) => Map (OrderedMonomial order n) r -> OrderedPolynomial r order n
• castMonomial :: (IsOrder o, IsOrder o', Sing m, n :<= m) => OrderedMonomial o n -> OrderedMonomial o' m
• castPolynomial :: (IsPolynomial r n, IsPolynomial r m, Sing m, IsOrder o, IsOrder o', n :<= m) => OrderedPolynomial r o n -> OrderedPolynomial r o' m
• toPolynomial :: (IsOrder order, IsPolynomial r n) => (r, Monomial n) -> OrderedPolynomial r order n
• changeOrder :: (Eq (Monomial n), IsOrder o, IsOrder o', Sing n) => o' -> OrderedPolynomial k o n -> OrderedPolynomial k o' n
• scastMonomial :: n :<= m => SNat m -> OrderedMonomial o n -> OrderedMonomial o m
• scastPolynomial :: (IsOrder o, IsOrder o', IsPolynomial r n, IsPolynomial r m, n :<= m, Sing m) => SNat m -> OrderedPolynomial r o n -> OrderedPolynomial r o' m
• data OrderedPolynomial r order n
• showPolynomialWithVars :: (Eq a, Show a, Sing n, NoetherianRing a, IsOrder ordering) => [(Int, String)] -> OrderedPolynomial a ordering n -> String
• normalize :: (Eq r, IsOrder order, IsPolynomial r n) => OrderedPolynomial r order n -> OrderedPolynomial r order n
• injectCoeff :: IsPolynomial r n => r -> OrderedPolynomial r order n
• varX :: (NoetherianRing r, Sing n, One :<= n) => OrderedPolynomial r order n
• var :: (NoetherianRing r, Sing m, S n :<= m) => SNat (S n) -> OrderedPolynomial r order m
• getTerms :: OrderedPolynomial k order n -> [(k, Monomial n)]
• shiftR :: forall k r n ord. (Field r, IsPolynomial r n, IsPolynomial r (k :+: n), IsOrder ord) => SNat k -> OrderedPolynomial r ord n -> OrderedPolynomial r ord (k :+: n)
• orderedBy :: IsOrder o => OrderedPolynomial k o n -> o -> OrderedPolynomial k o n
• divs :: Monomial n -> Monomial n -> Bool
• tryDiv :: Field r => (r, Monomial n) -> (r, Monomial n) -> (r, Monomial n)
• fromList :: SNat n -> [Int] -> Monomial n
• leadingTerm :: (IsOrder order, IsPolynomial r n) => OrderedPolynomial r order n -> (r, Monomial n)
• leadingMonomial :: (IsOrder order, IsPolynomial r n) => OrderedPolynomial r order n -> Monomial n
• leadingCoeff :: (IsOrder order, IsPolynomial r n) => OrderedPolynomial r order n -> r
• genVars :: forall k o n. (IsPolynomial k (S n), IsOrder o) => SNat (S n) -> [OrderedPolynomial k o (S n)]
• sDegree :: OrderedPolynomial k ord n -> SNat n
• newtype OrderedMonomial ordering n = OrderedMonomial {
  • getMonomial :: Monomial n
  }
• data Grevlex = Grevlex
• data Revlex = Revlex
• data Lex = Lex
• data Grlex = Grlex
• class IsOrder ordering
• class IsOrder name => IsMonomialOrder name

Documentation