Portability | non-portable (Rank2Types) |
---|---|
Stability | provisional |
Maintainer | masahiro.sakai@gmail.com |
Safe Haskell | None |
Algebraic reals
Reference:
- Why the concept of a field extension is a natural one http://www.dpmms.cam.ac.uk/~wtg10/galois.html
- data AReal
- realRoots :: UPolynomial Rational -> [AReal]
- realRootsEx :: UPolynomial AReal -> [AReal]
- minimalPolynomial :: AReal -> UPolynomial Rational
- deg :: Degree t => t -> Integer
- isRational :: AReal -> Bool
- isAlgebraicInteger :: AReal -> Bool
- height :: AReal -> Integer
- rootIndex :: AReal -> Int
- nthRoot :: Integer -> AReal -> AReal
- approx :: AReal -> Rational -> Rational
- approxInterval :: AReal -> Rational -> Interval Rational
- simpARealPoly :: UPolynomial AReal -> UPolynomial Rational
- goldenRatio :: AReal
Algebraic real type
Algebraic real numbers.
Construction
realRoots :: UPolynomial Rational -> [AReal]Source
Real roots of the polynomial in ascending order.
realRootsEx :: UPolynomial AReal -> [AReal]Source
Real roots of the polynomial in ascending order.
Properties
minimalPolynomial :: AReal -> UPolynomial RationalSource
The polynomial of which the algebraic number is root.
isRational :: AReal -> BoolSource
Whether the algebraic number is a rational.
isAlgebraicInteger :: AReal -> BoolSource
Whether the algebraic number is a root of a polynomial with integer
coefficients with leading coefficient 1
(a monic polynomial).
rootIndex :: AReal -> IntSource
root index, satisfying
realRoots
(minimalPolynomial
a) !! rootIndex a == a
Operations
Approximation
Returns approximate rational value such that abs (a - approx a epsilon) <= epsilon
.
Returns approximate interval such that width (approxInterval a epsilon) <= epsilon
.
Misc
Golden ratio