cf_hnf.h File Reference

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Functions
CFMatrix *FACTORY_PUBLIC	cf_HNF (CFMatrix &A)
	The input matrix A is square matrix of integers output: the Hermite Normal Form of A; that is, the unique m x m matrix whose rows span L, such that. More...
CFMatrix *FACTORY_PUBLIC	cf_LLL (CFMatrix &A)
	performs LLL reduction. More...

Function Documentation

cf_HNF()

CFMatrix *FACTORY_PUBLIC cf_HNF

(

CFMatrix &

A

)

The input matrix A is square matrix of integers output: the Hermite Normal Form of A; that is, the unique m x m matrix whose rows span L, such that.

• lower triangular,
• the diagonal entries are positive,
• any entry below the diagonal is a non-negative number strictly less than the diagonal entry in its column.

Note

: uses NTL

The input matrix A is square matrix of integers output: the Hermite Normal Form of A; that is, the unique m x m matrix whose rows span L, such that.

W is computed as the Hermite Normal Form of A; that is, W is the unique m x m matrix whose rows span L, such that

• W is lower triangular,
• the diagonal entries are positive,
• any entry below the diagonal is a non-negative number strictly less than the diagonal entry in its column.

Definition at line 44 of file cf_hnf.cc.

{
#ifdef HAVE_FLINT
  fmpz_mat_t FLINTM;
  convertFacCFMatrix2Fmpz_mat_t(FLINTM,A);
  fmpz_mat_hnf(FLINTM,FLINTM);
  CFMatrix *r=convertFmpz_mat_t2FacCFMatrix(FLINTM);
  fmpz_mat_clear(FLINTM);
  return r;
#elif defined(HAVE_NTL)
  mat_ZZ *AA=convertFacCFMatrix2NTLmat_ZZ(A);
  ZZ DD=convertFacCF2NTLZZ(determinant(A,A.rows()));
  mat_ZZ WW;
  HNF(WW,*AA,DD);
  delete AA;
  return convertNTLmat_ZZ2FacCFMatrix(WW);
#else
  factoryError("NTL/FLINT missing: cf_HNF");
  return NULL; // avoid warning
#endif
}

cf_LLL()

CFMatrix *FACTORY_PUBLIC cf_LLL

(

CFMatrix &

A

)

performs LLL reduction.

B is an m x n matrix, viewed as m rows of n-vectors. m may be less than, equal to, or greater than n, and the rows need not be linearly independent. B is transformed into an LLL-reduced basis, and the return value is the rank r of B. The first m-r rows of B are zero.

More specifically, elementary row transformations are performed on B so that the non-zero rows of new-B form an LLL-reduced basis for the lattice spanned by the rows of old-B. The default reduction parameter is delta=3/4, which means that the squared length of the first non-zero basis vector is no more than 2^{r-1} times that of the shortest vector in the lattice.

Note

: uses NTL or FLINT

Definition at line 66 of file cf_hnf.cc.

{
#ifdef HAVE_FLINT
  fmpz_mat_t FLINTM;
  convertFacCFMatrix2Fmpz_mat_t(FLINTM,A);
  fmpq_t delta,eta;
  fmpq_init(delta); fmpq_set_si(delta,1,1);
  fmpq_init(eta); fmpq_set_si(eta,3,4);
  fmpz_mat_lll_storjohann(FLINTM,delta,eta);
  CFMatrix *r=convertFmpz_mat_t2FacCFMatrix(FLINTM);
  fmpz_mat_clear(FLINTM);
  return r;
#elif defined(HAVE_NTL)
  mat_ZZ *AA=convertFacCFMatrix2NTLmat_ZZ(A);
  ZZ det2;
  LLL(det2,*AA,0L);
  CFMatrix *r= convertNTLmat_ZZ2FacCFMatrix(*AA);
  delete AA;
  return r;
#else
  factoryError("NTL/FLINT missing: cf_LLL");
  return NULL; // avoid warning
#endif
}