anu-nq - The nq command line interface
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]
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.
The ANU nq program is Copyright (C) by Werner Nickel.
The GAP nq manual /usr/share/gap/pkg/nq/doc/manual.pdf