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 wich 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

                                          November 2020                                 ANU-NQ(1)