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 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.
The ANU nq program is Copyright (C) by Werner Nickel.
The GAP nq manual
/usr/share/gap/pkg/nq/doc/manual.pdf