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|
data FieldElement =
FieldElement
{ number :: Int
, prime :: Int
}
deriving (Eq)
instance Show FieldElement where
show a = "FieldElement_" ++ show (prime a) ++ " " ++ show (number a)
assert :: Bool -> Bool
assert False = error "WRONG"
assert x = x
instance Num FieldElement where
(FieldElement a b) + (FieldElement c d)
| b /= d = error "Distinct Fields"
| otherwise = FieldElement (mod (a + c) b) b
(FieldElement a b) * (FieldElement c d)
| b /= d = error "Distinct Fields"
| otherwise = FieldElement (mod (a * c) b) b
abs a = a
signum _ = 1
negate (FieldElement a b) = FieldElement (mod (b - a) b) b
fromInteger _ = error "can't transform"
instance Fractional FieldElement where
recip a = a ^ (prime a - 2)
fromRational _ = error "can't transform"
aa =
let a = FieldElement 2 31
b = FieldElement 15 31
in assert
(and
[ a + b == FieldElement 17 31
, a /= b
, a - b == FieldElement 18 31
])
bb =
let a = FieldElement 19 31
b = FieldElement 24 31
in a * b
|
