Math.Lattices.Fplll.LLL

Bindings to FPLLL's implementation of the LLL Algorithm.

Documentation

lllReduce :: LLLOptions -> [[Integer]] -> Either RedStatus [[Integer]]

Compute an LLL-reduced basis for the given lattice. Each item of the list is a basis vector. Returns a Left RedStatus on failure.

lllReduceTrack :: LLLOptions -> [[Integer]] -> Either RedStatus ([[Integer]], [[Integer]])

Similar to lllReduce, but additionally return (in the second output) the operations that were applied to the basis vectors. In other words, the second return value tracks the operations applied to the basis vectors by applying them to the identity matrix as well.

lllReduceTrackInv :: LLLOptions -> [[Integer]] -> Either RedStatus ([[Integer]], [[Integer]], [[Integer]])

Like lllReduceTrackInv, but return the inverse matrix of the applied operations in the third output.

data LLLOptions

Options to configure the LLL reduction algorithm.

Constructors

LLLOptions

Fields

• delta :: Double

  δ controls the Lovász condition, i.e. how much the length of consecutive Gram-Schmidt orthogonal basis vectors can decrease.

• eta :: Double

  η is an upper bound on the largest Gram-Schmidt coefficient, i.e. how far from orthogonal the reduced basis can be.

• method :: LLLMethod

  LLL reduction method.

• floatType :: FloatType

  What sort of floating point to use for orthogonalization.

• precision :: Int

  Bits of precision for floating point if ftMpfr is used. Chooses automatically if set to zero.

• flags :: LLLFlags

  Extra options for the LLL reduction.

Instances

Eq LLLOptions

Defined in Math.Lattices.Fplll.LLL

Methods

(==) :: LLLOptions -> LLLOptions -> Bool

(/=) :: LLLOptions -> LLLOptions -> Bool

Ord LLLOptions

Defined in Math.Lattices.Fplll.LLL

Methods

compare :: LLLOptions -> LLLOptions -> Ordering

(<) :: LLLOptions -> LLLOptions -> Bool

(<=) :: LLLOptions -> LLLOptions -> Bool

(>) :: LLLOptions -> LLLOptions -> Bool

(>=) :: LLLOptions -> LLLOptions -> Bool

max :: LLLOptions -> LLLOptions -> LLLOptions

min :: LLLOptions -> LLLOptions -> LLLOptions

Show LLLOptions

Defined in Math.Lattices.Fplll.LLL

Methods

showsPrec :: Int -> LLLOptions -> ShowS

show :: LLLOptions -> String

showList :: [LLLOptions] -> ShowS

defaultLLL :: LLLOptions