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IntegerRelations

  

LLL

  

find a reduced basis of a lattice

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

LLL(lvect, integer)

Parameters

lvect

-

list, set, or rtable of lists or Vectors, or a Matrix

integer

-

(optional) literal name

Description

• 

The LLL(lvect) command finds a reduced basis (in the sense of Lovasz) of the lattice specified by the (row) vectors of lvect using the LLL algorithm.

• 

If the lattice is generated by vectors with integer coefficients and the option integer is specified, then the reduction is performed using only integer arithmetic. This version is sometimes faster than the default version, which uses rational arithmetic.

• 

This function requires that the dimension of the subspace generated by the vectors equals the number of vectors.

Examples

withIntegerRelations:

LLL1,2,3,2,1,6

0,3,0,1,1,3

(1)

LLL1,2,3,2,1,6,'integer'

0,3,0,1,1,3

(2)

LLLMatrix1,2,3,1,0,1,0,1,1

101011011

(3)

References

  

Lenstra, A.K.; Lenstra, H.W.; and Lovasz, L. "Factoring Polynomials with Rational Coefficients." Math. Ann., Vol. 261. (1982): 515-534.

See Also

IntegerRelations

PolynomialTools[MinimalPolynomial]

 


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