Safe Haskell	None
Language	Haskell2010

Algebra.Ring.Polynomial.Monomial

Contents

Orphan instances

Synopsis

type Monomial n = USized n Int
newtype OrderedMonomial ordering n = OrderedMonomial (Monomial n)
getMonomial :: OrderedMonomial ordering n -> Monomial n
class IsOrder (n :: Nat) (ordering :: Type) where
- cmpMonomial :: Proxy ordering -> MonomialOrder n
class IsOrder n name => IsMonomialOrder n name
type MonomialOrder n = Monomial n -> Monomial n -> Ordering
type IsStrongMonomialOrder ord = Forall (IsMonomialOrder' ord)
isRelativelyPrime :: KnownNat n => OrderedMonomial ord n -> OrderedMonomial ord n -> Bool
totalDegree :: OrderedMonomial ord n -> Int
data ProductOrder (n :: Nat) (m :: Nat) (a :: Type) (b :: Type) where
- ProductOrder :: SNat n -> SNat m -> ord -> ord' -> ProductOrder n m ord ord'
productOrder :: forall ord ord' n m. (IsOrder n ord, IsOrder m ord', KnownNat n, KnownNat m) => Proxy (ProductOrder n m ord ord') -> MonomialOrder (n + m)
productOrder' :: forall n ord ord' m. (IsOrder n ord, IsOrder m ord') => SNat n -> SNat m -> ord -> ord' -> MonomialOrder (n + m)
type WeightProxy (v :: [Nat]) = SList v
data WeightOrder (v :: [Nat]) (ord :: Type) where
- WeightOrder :: SList (v :: [Nat]) -> Proxy ord -> WeightOrder v ord
gcdMonomial :: KnownNat n => OrderedMonomial ord n -> OrderedMonomial ord n -> OrderedMonomial ord n
divs :: KnownNat n => OrderedMonomial ord n -> OrderedMonomial ord n -> Bool
isPowerOf :: KnownNat n => OrderedMonomial ord n -> OrderedMonomial ord n -> Bool
tryDiv :: (KnownNat n, Field r) => (r, OrderedMonomial ord n) -> (r, OrderedMonomial ord n) -> (r, OrderedMonomial ord n)
lcmMonomial :: KnownNat n => OrderedMonomial ord n -> OrderedMonomial ord n -> OrderedMonomial ord n
data Lex = Lex
class (IsMonomialOrder n ord, KnownNat n) => EliminationType n m ord
type EliminationOrder n m = ProductOrder n m Grevlex Grevlex
type WeightedEliminationOrder (n :: Nat) (ord :: Type) = WeightOrder (Replicate n 1) ord
eliminationOrder :: SNat n -> SNat m -> EliminationOrder n m
weightedEliminationOrder :: SNat n -> WeightedEliminationOrder n Grevlex
lex :: KnownNat n => MonomialOrder n
revlex :: KnownNat n => MonomialOrder n
graded :: MonomialOrder n -> MonomialOrder n
grlex :: KnownNat n => MonomialOrder n
grevlex :: MonomialOrder n
weightOrder :: forall n ns ord. (KnownNat n, IsOrder n ord, SingI ns) => Proxy (WeightOrder ns ord) -> MonomialOrder n
data Grevlex = Grevlex
fromList :: SNat n -> [Int] -> Monomial n
data Revlex = Revlex
data Grlex = Grlex
newtype Graded ord = Graded ord
castMonomial :: KnownNat m => OrderedMonomial o n -> OrderedMonomial o' m
scastMonomial :: SNat m -> OrderedMonomial o n -> OrderedMonomial o m
varMonom :: SNat n -> Ordinal n -> Monomial n
changeMonomialOrder :: o' -> OrderedMonomial ord n -> OrderedMonomial o' n
changeMonomialOrderProxy :: Proxy o' -> OrderedMonomial ord n -> OrderedMonomial o' n
sOnes :: SNat n -> SList (Replicate n 1)
withStrongMonomialOrder :: forall ord n r proxy (proxy' :: Nat -> Type). IsStrongMonomialOrder ord => proxy ord -> proxy' n -> (IsMonomialOrder n ord => r) -> r
cmpAnyMonomial :: (IsStrongMonomialOrder ord, KnownNat n, KnownNat m) => Proxy ord -> Monomial n -> Monomial m -> Ordering
orderMonomial :: proxy ord -> Monomial n -> OrderedMonomial ord n
ifoldMapMonom :: (KnownNat n, Monoid m) => (Ordinal n -> Int -> m) -> Monomial n -> m

Documentation

type Monomial n = USized n Int Source #

newtype OrderedMonomial ordering n Source #

A wrapper for monomials with a certain (monomial) order.

Constructors

OrderedMonomial (Monomial n)

Instances

Instances details

Eq (OrderedMonomial ordering n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: OrderedMonomial ordering n -> OrderedMonomial ordering n -> Bool # (/=) :: OrderedMonomial ordering n -> OrderedMonomial ordering n -> Bool #
(Eq (Monomial n), IsOrder n name) => Ord (OrderedMonomial name n) Source #	Special ordering for ordered-monomials.
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: OrderedMonomial name n -> OrderedMonomial name n -> Ordering # (<) :: OrderedMonomial name n -> OrderedMonomial name n -> Bool # (<=) :: OrderedMonomial name n -> OrderedMonomial name n -> Bool # (>) :: OrderedMonomial name n -> OrderedMonomial name n -> Bool # (>=) :: OrderedMonomial name n -> OrderedMonomial name n -> Bool # max :: OrderedMonomial name n -> OrderedMonomial name n -> OrderedMonomial name n # min :: OrderedMonomial name n -> OrderedMonomial name n -> OrderedMonomial name n #
KnownNat n => Show (OrderedMonomial ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> OrderedMonomial ord n -> ShowS # show :: OrderedMonomial ord n -> String # showList :: [OrderedMonomial ord n] -> ShowS #
KnownNat n => Unital (OrderedMonomial ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods one :: OrderedMonomial ord n # pow :: OrderedMonomial ord n -> Natural -> OrderedMonomial ord n # productWith :: Foldable f => (a -> OrderedMonomial ord n) -> f a -> OrderedMonomial ord n #
KnownNat n => Division (OrderedMonomial ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods recip :: OrderedMonomial ord n -> OrderedMonomial ord n # (/) :: OrderedMonomial ord n -> OrderedMonomial ord n -> OrderedMonomial ord n # (\\) :: OrderedMonomial ord n -> OrderedMonomial ord n -> OrderedMonomial ord n # (^) :: Integral n0 => OrderedMonomial ord n -> n0 -> OrderedMonomial ord n
KnownNat n => Multiplicative (OrderedMonomial ord n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (*) :: OrderedMonomial ord n -> OrderedMonomial ord n -> OrderedMonomial ord n # pow1p :: OrderedMonomial ord n -> Natural -> OrderedMonomial ord n # productWith1 :: Foldable1 f => (a -> OrderedMonomial ord n) -> f a -> OrderedMonomial ord n #
Hashable (OrderedMonomial ordering n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods hashWithSalt :: Int -> OrderedMonomial ordering n -> Int # hash :: OrderedMonomial ordering n -> Int #
NFData (OrderedMonomial ordering n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods rnf :: OrderedMonomial ordering n -> () #
Wrapped (OrderedMonomial ordering n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Associated Types type Unwrapped (OrderedMonomial ordering n) Methods _Wrapped' :: Iso' (OrderedMonomial ordering n) (Unwrapped (OrderedMonomial ordering n))
OrderedMonomial ordering1 n1 ~ t => Rewrapped (OrderedMonomial ordering2 n2) t Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
type Unwrapped (OrderedMonomial ordering n) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial type Unwrapped (OrderedMonomial ordering n) = Monomial n

getMonomial :: OrderedMonomial ordering n -> Monomial n Source #

class IsOrder (n :: Nat) (ordering :: Type) where Source #

Class to lookup ordering from its (type-level) name.

Methods

cmpMonomial :: Proxy ordering -> MonomialOrder n Source #

Instances

Instances details

KnownNat n => IsOrder n Grlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Grlex -> MonomialOrder n Source #
KnownNat n => IsOrder n Lex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Lex -> MonomialOrder n Source #
KnownNat n => IsOrder n Revlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Revlex -> MonomialOrder n Source #
KnownNat n => IsOrder n Grevlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Grevlex -> MonomialOrder n Source #
IsOrder n ord => IsOrder n (Graded ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy (Graded ord) -> MonomialOrder n Source #
(KnownNat n, IsOrder n ord, SingI ws) => IsOrder n (WeightOrder ws ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy (WeightOrder ws ord) -> MonomialOrder n Source #
(IsOrder n ord, IsOrder m ord', KnownNat m, KnownNat n, k ~ (n + m)) => IsOrder k (ProductOrder n m ord ord') Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy (ProductOrder n m ord ord') -> MonomialOrder k Source #

class IsOrder n name => IsMonomialOrder n name Source #

Class for Monomial' orders.

Instances

Instances details

KnownNat n => IsMonomialOrder n Lex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
KnownNat n => IsMonomialOrder n Grevlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
KnownNat n => IsMonomialOrder n Grlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
IsMonomialOrder n ord => IsMonomialOrder n (Graded ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
(KnownNat k, SingI ws, IsMonomialOrder k ord) => IsMonomialOrder k (WeightOrder ws ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
(KnownNat n, KnownNat m, IsMonomialOrder n o, IsMonomialOrder m o', k ~ (n + m)) => IsMonomialOrder k (ProductOrder n m o o') Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial

type MonomialOrder n = Monomial n -> Monomial n -> Ordering Source #

Monomial' order (of degree n). This should satisfy following laws: (1) Totality: forall a, b (a < b || a == b || b < a) (2) Additivity: a b == a + c <= b + c (3) Non-negative: forall a, 0 <= a

type IsStrongMonomialOrder ord = Forall (IsMonomialOrder' ord) Source #

Monomial' ordering which can do with monomials of arbitrary large arity.

isRelativelyPrime :: KnownNat n => OrderedMonomial ord n -> OrderedMonomial ord n -> Bool Source #

totalDegree :: OrderedMonomial ord n -> Int Source #

data ProductOrder (n :: Nat) (m :: Nat) (a :: Type) (b :: Type) where Source #

Constructors

ProductOrder :: SNat n -> SNat m -> ord -> ord' -> ProductOrder n m ord ord'

Instances

Instances details

(KnownNat n, KnownNat m, IsMonomialOrder n ord, IsMonomialOrder m ord', k ~ (n + m), KnownNat k) => EliminationType k (n :: Nat) (ProductOrder n m ord ord') Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
(KnownNat n, KnownNat m, IsMonomialOrder n o, IsMonomialOrder m o', k ~ (n + m)) => IsMonomialOrder k (ProductOrder n m o o') Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
(IsOrder n ord, IsOrder m ord', KnownNat m, KnownNat n, k ~ (n + m)) => IsOrder k (ProductOrder n m ord ord') Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy (ProductOrder n m ord ord') -> MonomialOrder k Source #

productOrder :: forall ord ord' n m. (IsOrder n ord, IsOrder m ord', KnownNat n, KnownNat m) => Proxy (ProductOrder n m ord ord') -> MonomialOrder (n + m) Source #

productOrder' :: forall n ord ord' m. (IsOrder n ord, IsOrder m ord') => SNat n -> SNat m -> ord -> ord' -> MonomialOrder (n + m) Source #

type WeightProxy (v :: [Nat]) = SList v Source #

data WeightOrder (v :: [Nat]) (ord :: Type) where Source #

Constructors

WeightOrder :: SList (v :: [Nat]) -> Proxy ord -> WeightOrder v ord

Instances

Instances details

(IsMonomialOrder k ord, ones ~ Replicate n 1, SingI ones, Length ones <= k, KnownNat k) => EliminationType k (n :: Nat) (WeightOrder ones ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
(KnownNat k, SingI ws, IsMonomialOrder k ord) => IsMonomialOrder k (WeightOrder ws ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
(KnownNat n, IsOrder n ord, SingI ws) => IsOrder n (WeightOrder ws ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy (WeightOrder ws ord) -> MonomialOrder n Source #

gcdMonomial :: KnownNat n => OrderedMonomial ord n -> OrderedMonomial ord n -> OrderedMonomial ord n Source #

divs :: KnownNat n => OrderedMonomial ord n -> OrderedMonomial ord n -> Bool Source #

isPowerOf :: KnownNat n => OrderedMonomial ord n -> OrderedMonomial ord n -> Bool Source #

tryDiv :: (KnownNat n, Field r) => (r, OrderedMonomial ord n) -> (r, OrderedMonomial ord n) -> (r, OrderedMonomial ord n) Source #

lcmMonomial :: KnownNat n => OrderedMonomial ord n -> OrderedMonomial ord n -> OrderedMonomial ord n Source #

data Lex Source #

Lexicographical order

Constructors

Lex

Instances

Instances details

Eq Lex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: Lex -> Lex -> Bool # (/=) :: Lex -> Lex -> Bool #
Ord Lex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: Lex -> Lex -> Ordering # (<) :: Lex -> Lex -> Bool # (<=) :: Lex -> Lex -> Bool # (>) :: Lex -> Lex -> Bool # (>=) :: Lex -> Lex -> Bool # max :: Lex -> Lex -> Lex # min :: Lex -> Lex -> Lex #
Show Lex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> Lex -> ShowS # show :: Lex -> String # showList :: [Lex] -> ShowS #
KnownNat n => IsMonomialOrder n Lex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
KnownNat n => IsOrder n Lex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Lex -> MonomialOrder n Source #
KnownNat n => EliminationType n (m :: k) Lex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial

class (IsMonomialOrder n ord, KnownNat n) => EliminationType n m ord Source #

Monomial' order which can be use to calculate n-th elimination ideal of m-ary polynomial. This should judge monomial to be bigger if it contains variables to eliminate.

Instances

Instances details

KnownNat n => EliminationType n (m :: k) Lex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
(IsMonomialOrder k ord, ones ~ Replicate n 1, SingI ones, Length ones <= k, KnownNat k) => EliminationType k (n :: Nat) (WeightOrder ones ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
(KnownNat n, KnownNat m, IsMonomialOrder n ord, IsMonomialOrder m ord', k ~ (n + m), KnownNat k) => EliminationType k (n :: Nat) (ProductOrder n m ord ord') Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial

type EliminationOrder n m = ProductOrder n m Grevlex Grevlex Source #

type WeightedEliminationOrder (n :: Nat) (ord :: Type) = WeightOrder (Replicate n 1) ord Source #

eliminationOrder :: SNat n -> SNat m -> EliminationOrder n m Source #

weightedEliminationOrder :: SNat n -> WeightedEliminationOrder n Grevlex Source #

lex :: KnownNat n => MonomialOrder n Source #

Lexicographical order. This *is* a monomial order.

revlex :: KnownNat n => MonomialOrder n Source #

Reversed lexicographical order. This is *not* a monomial order.

graded :: MonomialOrder n -> MonomialOrder n Source #

Convert ordering into graded one.

grlex :: KnownNat n => MonomialOrder n Source #

Graded lexicographical order. This *is* a monomial order.

grevlex :: MonomialOrder n Source #

Graded reversed lexicographical order. This *is* a monomial order.

weightOrder :: forall n ns ord. (KnownNat n, IsOrder n ord, SingI ns) => Proxy (WeightOrder ns ord) -> MonomialOrder n Source #

data Grevlex Source #

Graded reversed lexicographical order. Same as Graded Revlex.

Constructors

Grevlex

Instances

Instances details

Eq Grevlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: Grevlex -> Grevlex -> Bool # (/=) :: Grevlex -> Grevlex -> Bool #
Ord Grevlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: Grevlex -> Grevlex -> Ordering # (<) :: Grevlex -> Grevlex -> Bool # (<=) :: Grevlex -> Grevlex -> Bool # (>) :: Grevlex -> Grevlex -> Bool # (>=) :: Grevlex -> Grevlex -> Bool # max :: Grevlex -> Grevlex -> Grevlex # min :: Grevlex -> Grevlex -> Grevlex #
Show Grevlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> Grevlex -> ShowS # show :: Grevlex -> String # showList :: [Grevlex] -> ShowS #
KnownNat n => IsMonomialOrder n Grevlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
KnownNat n => IsOrder n Grevlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Grevlex -> MonomialOrder n Source #

fromList :: SNat n -> [Int] -> Monomial n Source #

convert NAry list into Monomial'.

data Revlex Source #

Reversed lexicographical order

Constructors

Revlex

Instances

Instances details

Eq Revlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: Revlex -> Revlex -> Bool # (/=) :: Revlex -> Revlex -> Bool #
Ord Revlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: Revlex -> Revlex -> Ordering # (<) :: Revlex -> Revlex -> Bool # (<=) :: Revlex -> Revlex -> Bool # (>) :: Revlex -> Revlex -> Bool # (>=) :: Revlex -> Revlex -> Bool # max :: Revlex -> Revlex -> Revlex # min :: Revlex -> Revlex -> Revlex #
Show Revlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> Revlex -> ShowS # show :: Revlex -> String # showList :: [Revlex] -> ShowS #
KnownNat n => IsOrder n Revlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Revlex -> MonomialOrder n Source #

data Grlex Source #

Graded lexicographical order. Same as Graded Lex.

Constructors

Grlex

Instances

Instances details

Eq Grlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: Grlex -> Grlex -> Bool # (/=) :: Grlex -> Grlex -> Bool #
Ord Grlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: Grlex -> Grlex -> Ordering # (<) :: Grlex -> Grlex -> Bool # (<=) :: Grlex -> Grlex -> Bool # (>) :: Grlex -> Grlex -> Bool # (>=) :: Grlex -> Grlex -> Bool # max :: Grlex -> Grlex -> Grlex # min :: Grlex -> Grlex -> Grlex #
Show Grlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> Grlex -> ShowS # show :: Grlex -> String # showList :: [Grlex] -> ShowS #
KnownNat n => IsMonomialOrder n Grlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
KnownNat n => IsOrder n Grlex Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy Grlex -> MonomialOrder n Source #

newtype Graded ord Source #

Graded order from another monomial order.

Constructors

Graded ord

Instances

Instances details

IsMonomialOrder n ord => IsMonomialOrder n (Graded ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial
IsOrder n ord => IsOrder n (Graded ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods cmpMonomial :: Proxy (Graded ord) -> MonomialOrder n Source #
Eq ord => Eq (Graded ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods (==) :: Graded ord -> Graded ord -> Bool # (/=) :: Graded ord -> Graded ord -> Bool #
Ord ord => Ord (Graded ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods compare :: Graded ord -> Graded ord -> Ordering # (<) :: Graded ord -> Graded ord -> Bool # (<=) :: Graded ord -> Graded ord -> Bool # (>) :: Graded ord -> Graded ord -> Bool # (>=) :: Graded ord -> Graded ord -> Bool # max :: Graded ord -> Graded ord -> Graded ord # min :: Graded ord -> Graded ord -> Graded ord #
Read ord => Read (Graded ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods readsPrec :: Int -> ReadS (Graded ord) # readList :: ReadS [Graded ord] # readPrec :: ReadPrec (Graded ord) # readListPrec :: ReadPrec [Graded ord] #
Show ord => Show (Graded ord) Source #
Instance details Defined in Algebra.Ring.Polynomial.Monomial Methods showsPrec :: Int -> Graded ord -> ShowS # show :: Graded ord -> String # showList :: [Graded ord] -> ShowS #

castMonomial :: KnownNat m => OrderedMonomial o n -> OrderedMonomial o' m Source #

scastMonomial :: SNat m -> OrderedMonomial o n -> OrderedMonomial o m Source #

varMonom :: SNat n -> Ordinal n -> Monomial n Source #

changeMonomialOrder :: o' -> OrderedMonomial ord n -> OrderedMonomial o' n Source #

changeMonomialOrderProxy :: Proxy o' -> OrderedMonomial ord n -> OrderedMonomial o' n Source #

sOnes :: SNat n -> SList (Replicate n 1) Source #

withStrongMonomialOrder :: forall ord n r proxy (proxy' :: Nat -> Type). IsStrongMonomialOrder ord => proxy ord -> proxy' n -> (IsMonomialOrder n ord => r) -> r Source #

cmpAnyMonomial :: (IsStrongMonomialOrder ord, KnownNat n, KnownNat m) => Proxy ord -> Monomial n -> Monomial m -> Ordering Source #

Comparing monomials with different arity, padding with 0 at bottom of the shorter monomial to make the length equal.

orderMonomial :: proxy ord -> Monomial n -> OrderedMonomial ord n Source #

ifoldMapMonom :: (KnownNat n, Monoid m) => (Ordinal n -> Int -> m) -> Monomial n -> m Source #

Orphan instances

KnownNat n => Unital (Monomial n) Source #
Instance details Methods one :: Monomial n # pow :: Monomial n -> Natural -> Monomial n # productWith :: Foldable f => (a -> Monomial n) -> f a -> Monomial n #
KnownNat n => Multiplicative (Monomial n) Source #
Instance details Methods (*) :: Monomial n -> Monomial n -> Monomial n # pow1p :: Monomial n -> Natural -> Monomial n # productWith1 :: Foldable1 f => (a -> Monomial n) -> f a -> Monomial n #