| Safe Haskell | None |
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Algebra.Algorithms.Groebner
- divModPolynomial :: (IsMonomialOrder order, IsPolynomial r n, Field r) => OrderedPolynomial r order n -> [OrderedPolynomial r order n] -> ([(OrderedPolynomial r order n, OrderedPolynomial r order n)], OrderedPolynomial r order n)
- modPolynomial :: (IsPolynomial r n, Field r, IsMonomialOrder order) => OrderedPolynomial r order n -> [OrderedPolynomial r order n] -> OrderedPolynomial r order n
- divPolynomial :: (IsPolynomial r n, Field r, IsMonomialOrder order) => OrderedPolynomial r order n -> [OrderedPolynomial r order n] -> [(OrderedPolynomial r order n, OrderedPolynomial r order n)]
- simpleBuchberger :: (Field k, IsPolynomial k n, IsMonomialOrder order) => Ideal (OrderedPolynomial k order n) -> [OrderedPolynomial k order n]
- minimizeGroebnerBasis :: (Field k, IsPolynomial k n, IsMonomialOrder order) => [OrderedPolynomial k order n] -> [OrderedPolynomial k order n]
- reduceMinimalGroebnerBasis :: (Field k, IsPolynomial k n, IsMonomialOrder order) => [OrderedPolynomial k order n] -> [OrderedPolynomial k order n]
- calcGroebnerBasisWith :: (Field k, IsPolynomial k n, IsMonomialOrder order, IsMonomialOrder order') => order -> Ideal (OrderedPolynomial k order' n) -> [OrderedPolynomial k order n]
- calcGroebnerBasis :: (Field k, IsPolynomial k n, IsMonomialOrder order) => Ideal (OrderedPolynomial k order n) -> [OrderedPolynomial k order n]
- isIdealMember :: (IsPolynomial k n, Field k, IsMonomialOrder o) => OrderedPolynomial k o n -> Ideal (OrderedPolynomial k o n) -> Bool
- groebnerTest :: (IsPolynomial k n, Field k, IsMonomialOrder order) => OrderedPolynomial k order n -> [OrderedPolynomial k order n] -> Bool
- thEliminationIdeal :: (IsMonomialOrder ord, Field k, IsPolynomial k m, IsPolynomial k (n :+: m)) => SNat n -> Ideal (OrderedPolynomial k ord (n :+: m)) -> Ideal (OrderedPolynomial k Lex m)
- intersection :: forall r k n ord. (IsMonomialOrder ord, Field r, IsPolynomial r k, IsPolynomial r n, IsPolynomial r (k :+: n)) => Vector (Ideal (OrderedPolynomial r ord n)) k -> Ideal (OrderedPolynomial r Lex n)
- quotByPrincipalIdeal :: (Field k, IsPolynomial k n, IsMonomialOrder ord) => Ideal (OrderedPolynomial k ord n) -> OrderedPolynomial k ord n -> Ideal (OrderedPolynomial k Lex n)
- quotIdeal :: forall k ord n. (IsPolynomial k n, Field k, IsMonomialOrder ord) => Ideal (OrderedPolynomial k ord n) -> Ideal (OrderedPolynomial k ord n) -> Ideal (OrderedPolynomial k Lex n)
- saturationByPrincipalIdeal :: (Field k, IsPolynomial k n, IsMonomialOrder ord) => Ideal (OrderedPolynomial k ord n) -> OrderedPolynomial k ord n -> Ideal (OrderedPolynomial k Lex n)
- saturationIdeal :: forall k ord n. (IsPolynomial k n, Field k, IsMonomialOrder ord) => Ideal (OrderedPolynomial k ord n) -> Ideal (OrderedPolynomial k ord n) -> Ideal (OrderedPolynomial k Lex n)
Documentation
divModPolynomial :: (IsMonomialOrder order, IsPolynomial r n, Field r) => OrderedPolynomial r order n -> [OrderedPolynomial r order n] -> ([(OrderedPolynomial r order n, OrderedPolynomial r order n)], OrderedPolynomial r order n)Source
modPolynomial :: (IsPolynomial r n, Field r, IsMonomialOrder order) => OrderedPolynomial r order n -> [OrderedPolynomial r order n] -> OrderedPolynomial r order nSource
divPolynomial :: (IsPolynomial r n, Field r, IsMonomialOrder order) => OrderedPolynomial r order n -> [OrderedPolynomial r order n] -> [(OrderedPolynomial r order n, OrderedPolynomial r order n)]Source
simpleBuchberger :: (Field k, IsPolynomial k n, IsMonomialOrder order) => Ideal (OrderedPolynomial k order n) -> [OrderedPolynomial k order n]Source
minimizeGroebnerBasis :: (Field k, IsPolynomial k n, IsMonomialOrder order) => [OrderedPolynomial k order n] -> [OrderedPolynomial k order n]Source
reduceMinimalGroebnerBasis :: (Field k, IsPolynomial k n, IsMonomialOrder order) => [OrderedPolynomial k order n] -> [OrderedPolynomial k order n]Source
calcGroebnerBasisWith :: (Field k, IsPolynomial k n, IsMonomialOrder order, IsMonomialOrder order') => order -> Ideal (OrderedPolynomial k order' n) -> [OrderedPolynomial k order n]Source
calcGroebnerBasis :: (Field k, IsPolynomial k n, IsMonomialOrder order) => Ideal (OrderedPolynomial k order n) -> [OrderedPolynomial k order n]Source
isIdealMember :: (IsPolynomial k n, Field k, IsMonomialOrder o) => OrderedPolynomial k o n -> Ideal (OrderedPolynomial k o n) -> BoolSource
groebnerTest :: (IsPolynomial k n, Field k, IsMonomialOrder order) => OrderedPolynomial k order n -> [OrderedPolynomial k order n] -> BoolSource
thEliminationIdeal :: (IsMonomialOrder ord, Field k, IsPolynomial k m, IsPolynomial k (n :+: m)) => SNat n -> Ideal (OrderedPolynomial k ord (n :+: m)) -> Ideal (OrderedPolynomial k Lex m)Source
intersection :: forall r k n ord. (IsMonomialOrder ord, Field r, IsPolynomial r k, IsPolynomial r n, IsPolynomial r (k :+: n)) => Vector (Ideal (OrderedPolynomial r ord n)) k -> Ideal (OrderedPolynomial r Lex n)Source
An intersection ideal of given ideals.
quotByPrincipalIdeal :: (Field k, IsPolynomial k n, IsMonomialOrder ord) => Ideal (OrderedPolynomial k ord n) -> OrderedPolynomial k ord n -> Ideal (OrderedPolynomial k Lex n)Source
Ideal quotient by a principal ideals.
quotIdeal :: forall k ord n. (IsPolynomial k n, Field k, IsMonomialOrder ord) => Ideal (OrderedPolynomial k ord n) -> Ideal (OrderedPolynomial k ord n) -> Ideal (OrderedPolynomial k Lex n)Source
saturationByPrincipalIdeal :: (Field k, IsPolynomial k n, IsMonomialOrder ord) => Ideal (OrderedPolynomial k ord n) -> OrderedPolynomial k ord n -> Ideal (OrderedPolynomial k Lex n)Source
Saturation by a principal ideal.
saturationIdeal :: forall k ord n. (IsPolynomial k n, Field k, IsMonomialOrder ord) => Ideal (OrderedPolynomial k ord n) -> Ideal (OrderedPolynomial k ord n) -> Ideal (OrderedPolynomial k Lex n)Source