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anu-nq(1) -- 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</M> (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</M> (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</M> (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)
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