module Factory.Data.MonicPolynomial(
MonicPolynomial(getPolynomial),
mkMonicPolynomial
) where
import qualified Control.Arrow
import qualified Factory.Data.Monomial as Data.Monomial
import Factory.Data.Polynomial((*=))
import qualified Factory.Data.Polynomial as Data.Polynomial
import qualified Factory.Data.QuotientRing as Data.QuotientRing
import Factory.Data.Ring((=*=), (=+=), (=-=))
import qualified Factory.Data.Ring as Data.Ring
import qualified ToolShed.Data.Pair
newtype MonicPolynomial c e = MkMonicPolynomial {
MonicPolynomial c e -> Polynomial c e
getPolynomial :: Data.Polynomial.Polynomial c e
} deriving (MonicPolynomial c e -> MonicPolynomial c e -> Bool
(MonicPolynomial c e -> MonicPolynomial c e -> Bool)
-> (MonicPolynomial c e -> MonicPolynomial c e -> Bool)
-> Eq (MonicPolynomial c e)
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
forall c e.
(Eq c, Eq e) =>
MonicPolynomial c e -> MonicPolynomial c e -> Bool
/= :: MonicPolynomial c e -> MonicPolynomial c e -> Bool
$c/= :: forall c e.
(Eq c, Eq e) =>
MonicPolynomial c e -> MonicPolynomial c e -> Bool
== :: MonicPolynomial c e -> MonicPolynomial c e -> Bool
$c== :: forall c e.
(Eq c, Eq e) =>
MonicPolynomial c e -> MonicPolynomial c e -> Bool
Eq, Int -> MonicPolynomial c e -> ShowS
[MonicPolynomial c e] -> ShowS
MonicPolynomial c e -> String
(Int -> MonicPolynomial c e -> ShowS)
-> (MonicPolynomial c e -> String)
-> ([MonicPolynomial c e] -> ShowS)
-> Show (MonicPolynomial c e)
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
forall c e. (Show c, Show e) => Int -> MonicPolynomial c e -> ShowS
forall c e. (Show c, Show e) => [MonicPolynomial c e] -> ShowS
forall c e. (Show c, Show e) => MonicPolynomial c e -> String
showList :: [MonicPolynomial c e] -> ShowS
$cshowList :: forall c e. (Show c, Show e) => [MonicPolynomial c e] -> ShowS
show :: MonicPolynomial c e -> String
$cshow :: forall c e. (Show c, Show e) => MonicPolynomial c e -> String
showsPrec :: Int -> MonicPolynomial c e -> ShowS
$cshowsPrec :: forall c e. (Show c, Show e) => Int -> MonicPolynomial c e -> ShowS
Show)
mkMonicPolynomial :: (
Eq c,
Num c,
Show c,
Show e
) => Data.Polynomial.Polynomial c e -> MonicPolynomial c e
mkMonicPolynomial :: Polynomial c e -> MonicPolynomial c e
mkMonicPolynomial Polynomial c e
polynomial
| Bool -> Bool
not (Bool -> Bool) -> Bool -> Bool
forall a b. (a -> b) -> a -> b
$ Polynomial c e -> Bool
forall c e. (Eq c, Num c) => Polynomial c e -> Bool
Data.Polynomial.isMonic Polynomial c e
polynomial = String -> MonicPolynomial c e
forall a. HasCallStack => String -> a
error (String -> MonicPolynomial c e) -> String -> MonicPolynomial c e
forall a b. (a -> b) -> a -> b
$ String
"Factory.Data.MonicPolynomial.mkMonicPolynomial:\tnot monic; " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Polynomial c e -> String
forall a. Show a => a -> String
show Polynomial c e
polynomial
| Bool
otherwise = Polynomial c e -> MonicPolynomial c e
forall c e. Polynomial c e -> MonicPolynomial c e
MkMonicPolynomial Polynomial c e
polynomial
instance (
Eq c,
Num c,
Num e,
Ord e,
Show c,
Show e
) => Data.Ring.Ring (MonicPolynomial c e) where
MkMonicPolynomial Polynomial c e
l =*= :: MonicPolynomial c e -> MonicPolynomial c e -> MonicPolynomial c e
=*= MkMonicPolynomial Polynomial c e
r = Polynomial c e -> MonicPolynomial c e
forall c e. Polynomial c e -> MonicPolynomial c e
MkMonicPolynomial (Polynomial c e -> MonicPolynomial c e)
-> Polynomial c e -> MonicPolynomial c e
forall a b. (a -> b) -> a -> b
$ Polynomial c e
l Polynomial c e -> Polynomial c e -> Polynomial c e
forall r. Ring r => r -> r -> r
=*= Polynomial c e
r
MkMonicPolynomial Polynomial c e
l =+= :: MonicPolynomial c e -> MonicPolynomial c e -> MonicPolynomial c e
=+= MkMonicPolynomial Polynomial c e
r = Polynomial c e -> MonicPolynomial c e
forall c e.
(Eq c, Num c, Show c, Show e) =>
Polynomial c e -> MonicPolynomial c e
mkMonicPolynomial (Polynomial c e -> MonicPolynomial c e)
-> Polynomial c e -> MonicPolynomial c e
forall a b. (a -> b) -> a -> b
$ Polynomial c e
l Polynomial c e -> Polynomial c e -> Polynomial c e
forall r. Ring r => r -> r -> r
=+= Polynomial c e
r
additiveInverse :: MonicPolynomial c e -> MonicPolynomial c e
additiveInverse MonicPolynomial c e
_ = String -> MonicPolynomial c e
forall a. HasCallStack => String -> a
error String
"Factory.Data.MonicPolynomial.additiveInverse:\tresult isn't monic"
multiplicativeIdentity :: MonicPolynomial c e
multiplicativeIdentity = Polynomial c e -> MonicPolynomial c e
forall c e. Polynomial c e -> MonicPolynomial c e
MkMonicPolynomial Polynomial c e
forall r. Ring r => r
Data.Ring.multiplicativeIdentity
additiveIdentity :: MonicPolynomial c e
additiveIdentity = Polynomial c e -> MonicPolynomial c e
forall c e. Polynomial c e -> MonicPolynomial c e
MkMonicPolynomial Polynomial c e
forall r. Ring r => r
Data.Ring.additiveIdentity
instance (
Eq c,
Num c,
Num e,
Ord e,
Show c,
Show e
) => Data.QuotientRing.QuotientRing (MonicPolynomial c e) where
MkMonicPolynomial Polynomial c e
polynomialN quotRem' :: MonicPolynomial c e
-> MonicPolynomial c e
-> (MonicPolynomial c e, MonicPolynomial c e)
`quotRem'` MkMonicPolynomial Polynomial c e
polynomialD = (Polynomial c e -> MonicPolynomial c e)
-> (Polynomial c e, Polynomial c e)
-> (MonicPolynomial c e, MonicPolynomial c e)
forall a b. (a -> b) -> (a, a) -> (b, b)
ToolShed.Data.Pair.mirror Polynomial c e -> MonicPolynomial c e
forall c e. Polynomial c e -> MonicPolynomial c e
MkMonicPolynomial ((Polynomial c e, Polynomial c e)
-> (MonicPolynomial c e, MonicPolynomial c e))
-> (Polynomial c e, Polynomial c e)
-> (MonicPolynomial c e, MonicPolynomial c e)
forall a b. (a -> b) -> a -> b
$ Polynomial c e -> (Polynomial c e, Polynomial c e)
longDivide Polynomial c e
polynomialN where
longDivide :: Polynomial c e -> (Polynomial c e, Polynomial c e)
longDivide Polynomial c e
numerator
| Polynomial c e -> Bool
forall c e. Polynomial c e -> Bool
Data.Polynomial.isZero Polynomial c e
numerator Bool -> Bool -> Bool
|| Monomial c e -> e
forall c e. Monomial c e -> e
Data.Monomial.getExponent Monomial c e
quotient e -> e -> Bool
forall a. Ord a => a -> a -> Bool
< e
0 = (Polynomial c e
forall c e. Polynomial c e
Data.Polynomial.zero, Polynomial c e
numerator)
| Bool
otherwise = (Polynomial c e -> Polynomial c e)
-> (Polynomial c e, Polynomial c e)
-> (Polynomial c e, Polynomial c e)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (b, d) (c, d)
Control.Arrow.first ((MonomialList c e -> MonomialList c e)
-> Polynomial c e -> Polynomial c e
forall c1 e1 c2 e2.
(MonomialList c1 e1 -> MonomialList c2 e2)
-> Polynomial c1 e1 -> Polynomial c2 e2
Data.Polynomial.lift (Monomial c e
quotient Monomial c e -> MonomialList c e -> MonomialList c e
forall a. a -> [a] -> [a]
:)) ((Polynomial c e, Polynomial c e)
-> (Polynomial c e, Polynomial c e))
-> (Polynomial c e, Polynomial c e)
-> (Polynomial c e, Polynomial c e)
forall a b. (a -> b) -> a -> b
$ Polynomial c e -> (Polynomial c e, Polynomial c e)
longDivide (Polynomial c e
numerator Polynomial c e -> Polynomial c e -> Polynomial c e
forall r. Ring r => r -> r -> r
=-= Polynomial c e
polynomialD Polynomial c e -> Monomial c e -> Polynomial c e
forall c e.
(Eq c, Num c, Num e) =>
Polynomial c e -> Monomial c e -> Polynomial c e
*= Monomial c e
quotient)
where
quotient :: Monomial c e
quotient = Polynomial c e -> Monomial c e
forall c e. Polynomial c e -> Monomial c e
Data.Polynomial.getLeadingTerm Polynomial c e
numerator Monomial c e -> e -> Monomial c e
forall e c. Num e => Monomial c e -> e -> Monomial c e
`Data.Monomial.shiftExponent` e -> e
forall a. Num a => a -> a
negate (Monomial c e -> e
forall c e. Monomial c e -> e
Data.Monomial.getExponent (Monomial c e -> e) -> Monomial c e -> e
forall a b. (a -> b) -> a -> b
$ Polynomial c e -> Monomial c e
forall c e. Polynomial c e -> Monomial c e
Data.Polynomial.getLeadingTerm Polynomial c e
polynomialD)