README

@
@  (void)ZZ( group, gram, divisors, options );
@
@  or
@
@  (void)ZZ( group, gram, divisors, options, num_sublattices, dim1, dim2, ... )
@
@  bravais_TYP *group;
@  matrix_TYP  *gram;
@  int *divisors;
@  char *options;     
@  int num_sublattices, dim1, ...
@
@  group: bravais group, the algorithm applies the ZZ-algorithm with regard
@         to the prime-divisors of the order of the group.
@  gram:  a gram matrix of a quadratic form that is invariant under the group
@         This form must be totally anisotropic.
@  divisors: an array of integers that REALLY MUST HAVE 100 (ONEHUNDRET) 
@            entries. The index of the array specifies the prime number and the
@            contents of the array the multiplicity of the prime as divisor of
@            the group order. The ZZ function does not need the multiplicity
@            it just uses a subset of the prime divisors of the group order 
@            to compute irreducible constituents of the matrix representation 
@            of the group modulo those primes. Thus it is all right to set
@            the entries of the array to some non-zero number, e. g. if one 
@            wants to compute the irreducible constituents modulo 2 and 
@            modulo 5, then one has to write
@             
@              divisors[2] = 1; divisors[5] = 1;
@
@            All other entries must be set to zero. (at least those that belong 
@            to prime number indices). 
@
@            If one simply wants to compute the irreducible constituents for
@            all divisors of the group order, it suffices to specify the 
@            value NULL for the argument divisors.
@
@  options: a string of characters, (i.e. "n30l24rq"), supported are:
@  num_sublattices, dim1, ... : see option "p". Must only be specified if the
@                               option "p" was specified
@
@           "n#": terminate after computation of "#" centerings
@           "l#": terminate afer  "#" iterations of the algorithm
@           "r" : use the "lll"-algorithm on the Z-bases of the centerings
@           "q" : "quit-mode" - suppress messages on stdout/stderr
@           "v" : "verbose-mode" - opposite of "q"
@           "t" : create a file in the current directory that
@                 contains additional information. See also options "ugsb"
@                 This feature is on by default and the file name defaults
@                 to ZZ.tmp. If this option is given the argument
@                 "none", then no output file is created.
@           "u" : computes elementary divisors of the matrices that contain
@                 the bases of the invariant sublattices (i.e. of
@                 group->zentr[i]) and writes them to the
@                 outputfile.
@           "g" : computes the elementary divisors of the gram-matrices of
@                 the invariant sublattices and writes them to the output file.
@                 Implies option "t".
@           "s" : "shortlist" - prints in short form the messages that are
@                 suppressed by "q". Independent of "q" option
@           "b" : "print change of base only" -- suppresses the output of
@                 the gram-matrices and elementary devisors to the output file.
@           "p" : "projections" -- compute only thos sublattices, that have
@                 surjective projections on a given number of sublattices
@                 with a given dimension. The number of the sublattices is
@                 given by the first argument after "options", that is, by
@                 "num_sublattices". The dimension of the first sublattice
@                 is given by "dim1", the second by the argument "dim2" etc
@
@                 NOTE: the number of the "dim#" arguments MUST match the
@                       "num_sublattices"
@
@                 Given this information, the algorithm devides the original
@                 lattice in sublattices that are spanned by
@                 <e_1, ..., e_dim1>,
@                 <e_(dim1+1), ..., e_(dim1+dim2)>, etc
@   
@   The computed centerings are stored in "group->zentr" as Z-bases
@   (matrix_TYP **zentr). The number of centerings is stored in 
@   "group->zentr_no".
@
@   The functions exits by calling carat_exit() in case of an error of if
@   the parameters are inconsistent.
@
@   NOTE: the bravais group is supposed to operate on a lattice of column
@         vectors. "SPALTENKONVENTION"
@
@  TODO:
@        write more documentation.
@