README

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@ FILE: mink_red.c
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@ matrix_TYP *mink_red(G, Trf)
@ matrix_TYP *G, *Trf;
@
@ calculates a matrices A and Trf such that A = Trf * G * Trf^{tr}
@ is Minkowski_reduced
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@ FILE: pair_red.c
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@ void pr_red(G, T, n)
@ int **G, **T, n;
@
@  applies a pair_reduction to the 2-dimensional array G of size n x n
@  and makes the simutaneous row operations on the array T of the same size
@ The function can be called with T = NULL
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@ matrix_TYP *pair_red(Gram, Tr)
@ matrix_TYP *Gram, *Tr;
@
@ calculates matrices A and Tr such that A = Tr * Gram * Tr^{tr}
@ is pair_reduced.
@ The function can be called with Tr = NULL
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@ FILE:  reduction_sort.c
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@ void reduction_sort(G,T,n)
@ int **G, **T, n;
@
@ make simultaneous row and colum permutations on the twodimensional
@ array G of size n x n such that G[i][i] <= G[j][j] for 0<=i<=j<n.
@ Simultaneously the row operations are applied to T, that
@ has to be an array of the same size or NULL
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@ FILE: short_reduce.c
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@ matrix_TYP *short_reduce(A, SV, Trf)
@ matrix_TYP *A, *SV, *Trf;
@
@ short_reduce make a reduction of the matrix A using the shortvectors
@ given in SV.
@ If an entry in SV is 1 or -1 the vector is used to make A better
@ afterwards the vectors in SV are transformed and the same is tried
@ again.
@ A and SV are not changed in this function.
@ the result is the reduced matrix and the transformation is
@ applied to the matrix Trf.
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@ matrix_TYP *pr_short_red(A, Trf)
@ matrix_TYP *A, *Trf;
@
@ The same as short_reduce but before and after using this function
@ a pair_redduction is used.
@ The shortest vectors are calculated by the function itsself.
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