NAME

       anu-nq - The nq command line interface

SYNOPSIS

       anu-nq  [-a]  [-M]  [-d]  [-g] [-v] [-s] [-f] [-c] [-m] [-t <n>] [-l <n>] [-r <n>] [-n <n>] [-e <n>] [-y]
       [-o] [-p] [-E] [presentation] [class]

DESCRIPTION

       This is the man page for the ANU nq program. It briefly documents the parameters. The main  documentation
       is part of the GAP nq documentation which is available in html and pdf format.

       The  options  -l,  -r  and  -e  can  be  used to enforce Engel conditions on the nilpotent quotient to be
       calculated. All these options have to be followed by  a  positive  integer  <n>.  Their  meaning  is  the
       following:

       -n <k> This  option forces the first k generators to be left or right Engel element if also the option -l
              or -r (or both) is present. Otherwise it is ignored.

       -l <n> This forces the first k generators <M>g_1,...,g_k</M> of the  nilpotent  quotient  Q  to  be  left
              n-Engel elements, i.e., they satisfy <M>[x,...,x,g_i] = 1 (x occurring n-times) for all x in Q and
              <M>1 <= i <= k</M>. If the option -n is not used, then k = 1.

       -r <n> This  forces  the  first  k  generators <M>g_1,...,g_k</M> of the nilpotent quotient Q to be right
              n-Engel elements,i.e., they satisfy <M>[g_i,x,..,x] = 1 (x occurring n-times) for all x in  Q  and
              <M>1 <= i <= k</M>. If the option -n is not used, then k = 1.

       -e <n> This  enforces  the n-th Engel law on Q, i.e., <M>[x,y,..,y] = 1 (y occurring n-times) for all x,y
              in Q.

       -t <n> This option specifies how much CPU time the program is allowed to use. It will terminate after <n>
              seconds of CPU time. If <n> is followed (without space) by one of the  letters  m,  h  or  d,  <n>
              specifies the time in minutes, hours or days, respectively.

       The  other  options  have  the following meaning. Care has to be taken when the options -s or -c are used
       since the resulting nilpotent quotient need NOT satisfy the required Engel condition. The reason for this
       is that a smaller set of test words is used if one of  these  two  options  are  present.  Although  this
       smaller  set  of test words seems to be sufficient to enforce the required Engel condition, this fact has
       not been proven.

       -a     For each factor of the lower central series a file  is  created  in  the  current  directory  that
              contains  an  integer matrix describing the factor as abelian group. The first number in that file
              is the number of columns of the matrix. Then the matrix follows in row major order. The matrix for
              the i-th factor is put into the file presentation.abinv.<i>.

       -p     toggles printing of the pc presentation for the nilpotent quotient at the end of a calculation.

       -s     This option causes the program to check  only  semigroup  words  in  the  generating  set  of  the
              nilpotent  quotient  when  an Engel condition is enforced. If none of the options -l, -r or -e are
              present, it is ignored.

       -f     This option causes to check semiwords in the generating set of the nilpotent  quotient  first  and
              then  all  other  words that need to be checked. It is ignored if the option -s is used or none of
              the options -l, -r or -e are present.

       -c     This option stops checking the Engel law at each class if all the checks of a certain  weight  did
              not yield any non-trivial instances of the law.

       -d     Switch on debug mode and perform checks during the computation. Not yet implemented.

       -o     In  checking  Engel  identities, instances are process in the order of increased weight. This flag
              reverses the order.

       -y     Enforce the identities <M>x^8</M> and <M>[ [x1,x2,x3], [x4,x5,x6] ]</M> on the nilpotent quotient.

       -v     Switch on verbose mode.

       -g     Produce GAP output. Presently the GAP output consists only of a sequence of integer matrices whose
              rows are relations of the factors of the lower central series as abelian groups. This will  change
              as soon as GAP can handle infinite polycyclic groups.

       -E     the last n generators are Engel generators. This works in conjunction with option -n.

       -m     output  the  relation matrix for each factor of the lower central series. The matrices are written
              to files with the names 'matrix.cl' where cl is replaced by the number of the factor in the  lower
              central  series. Each file contains first the number of columns of the matrix and then the rows of
              the matrix. The matrix is written as each relation is produced and  is  not  in  upper  triangular
              form.

       -M     output  the  relation  matrix  before  and after relations have been enforced. This results in two
              groups of files with names 'pres.nilp.cl' and 'pres.mult.cl' where pres is the name of  the  input
              files and cl is the class. The matrices are in upper triangular form.

COPYRIGHT

       The ANU nq program is Copyright (C) by Werner Nickel.

SEE ALSO

       The GAP nq manual /usr/share/gap/pkg/nq/doc/manual.pdf

                                                  January 2024                                         ANU-NQ(1)