LLLBases : Table of Contents

• LLLBases -- lattice reduction (Lenstra-Lenstra-Lovasz bases)
  • LLL -- compute an LLL basis
  • kernelLLL -- compute the kernel of an integer matrix using LLL bases
  • gcdLLL -- compute the gcd of integers, and small multipliers
  • hermite -- compute the Hermite normal form and small multiplier matrix using LLL bases
  • gram
  • isLLL -- is a basis an LLL basis?
• BKZ -- compute BKZ reduced basis instead of an LLL reduced basis
• CohenEngine -- use the original Macaulay2 LLL algorithm
• CohenTopLevel -- use the Macaulay2 language LLL algorithm
• gcdLLL(..., Strategy => ...)
• gcdLLL(..., Threshold => ...)
• Givens -- use Givens rotations instead of Gram-Schmidt during LLL
• hermite(..., ChangeMatrix => ...)
• hermite(..., Limit => ...)
• hermite(..., Threshold => ...)
• isLLL(..., Threshold => ...)
• kernelLLL(..., Limit => ...)
• LLL(..., ChangeMatrix => ...) -- also find change of basis matrix
• LLL(..., Limit => ...)
• LLL(..., Strategy => ...) -- choose among different algorithms
• LLL(..., Threshold => ...) -- a rational number in the range (1/4,1], default is 3/4
• NTL -- use the all-integer LLL strategy from NTL library
• RealFP -- use double precision real numbers
• RealQP -- use quadruple precision real numbers
• RealQP1 -- use a combination of double precision and quad precision real numbers
• RealRR -- use arbitrary precision real numbers
• RealXD -- use extended exponent real numbers
• Threshold -- the LLL threshold, in interval (1/4,1]