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<h1>D Other ACE Options</h1><p>
<P>
<H3>Sections</H3>
<oL>
<li> <A HREF="CHAP00D.htm#SECT001">Experimentation Options</a>
<li> <A HREF="CHAP00D.htm#SECT002">Options that Modify a Presentation</a>
<li> <A HREF="CHAP00D.htm#SECT003">Mode Options</a>
<li> <A HREF="CHAP00D.htm#SECT004">Options that Interact with the Operating System</a>
<li> <A HREF="CHAP00D.htm#SECT005">Query Options</a>
<li> <A HREF="CHAP00D.htm#SECT006">Options that Modify the Coset Table</a>
<li> <A HREF="CHAP00D.htm#SECT007">Options for Comments</a>
</ol><p>
<p>
Here we list all the known <font face="Gill Sans,Helvetica,Arial">ACE</font> options not provided earlier. Most
of the options provided here have interactive function alternatives
(each such alternative is noted at the end of the section describing
the corresponding option and introduced by ``<strong>INTERACTIVELY</strong>, use
...''). A few options have only limited usefulness from <font face="Gill Sans,Helvetica,Arial">GAP</font>; many
options, users will normally only wish to use if generating an input
file, by using the option <code>aceinfile</code> (see <a href="CHAP004.htm#SSEC011.7">option aceinfile</a>).
However all options here are functional, both interactively and
non-interactively.
<p>
<p>
<h2><a name="SECT001">D.1 Experimentation Options</a></h2>
<p><p>
<p>
<dl compact>
<p>
<dt><a name = "SSEC001.1"></a>
<dt><li><code>aep:=</code><var>val</var><code> <dd></code>
Runs the enumeration for <code>a</code>ll <code>e</code>quivalent <code>p</code>resentations;
<var>val</var> is in the integer range 1 to 7.
<p>
The <code>aep</code> option runs an enumeration for combinations of relator
ordering, relator rotations, and relator inversions.
<p>
The argument <var>val</var> is considered as a binary number. Its three bits
are treated as flags, and control relator rotations (the 2<sup>0</sup> bit),
relator inversions (the 2<sup>1</sup> bit) and relator orderings (the 2<sup>2</sup>
bit), respectively; where 1 means ``active'' and 0 means
``inactive''. (See below for an example).
<p>
The <code>aep</code> option first performs a ``priming run'' using the options as
they stand. In particular, the <code>asis</code> and <code>messages</code> options are
honoured.
<p>
It then turns <code>asis</code> on and <code>messages</code> off (i.e. sets <code>messages</code> to
0), and generates and tests the requested equivalent presentations.
The maximum and minimum values attained by <code>m</code> (the maximum number of
coset numbers defined at any stage) and <code>t</code> (the total number of coset
numbers defined) are tracked, and each time a new ``record'' is found,
the relators used and the summary result line is printed. See
Appendix <a href="CHAP00A.htm">The Meanings of ACE's output messages for a discussion of
the statistics <code>m</code> and <code>t</code>. To observe these messages either set the
<code>InfoLevel</code> of <code>InfoACE</code> to 3 or non-interactively you can peruse the
<font face="Gill Sans,Helvetica,Arial">ACE</font> output file (see <a href="CHAP004.htm#SSEC011.8">option aceoutfile</a>).
<p>
Normally when a non-interactive <font face="Gill Sans,Helvetica,Arial">ACE</font> interface function is called,
the option <code>start</code> (see <a href="CHAP00D.htm#SSEC003.2">option start</a>), is quietly inserted after all
the options provided by the user, to initiate a coset enumeration.
Since the <code>aep</code> option invokes an enumeration, the quiet insertion of
the <code>start</code> option is neither needed nor done, when a non-interactive
<font face="Gill Sans,Helvetica,Arial">ACE</font> interface function is called with the <code>aep</code> option.
<p>
The order in which the equivalent presentations are generated and
tested has no particular significance, but note that the presentation
as given <strong>after</strong> the initial priming run) is the <strong>last</strong> presentation
to be generated and tested, so that the group's relators are left
<code>unchanged</code> by running the <code>aep</code> option, (not that a non-interactive
user cares).
<p>
As discussed by Cannon, Dimino, Havas and Watson <a href="biblio.htm#CDHW73"><cite>CDHW73</cite></a> and
Havas and Ramsay <a href="biblio.htm#HR01"><cite>HR01</cite></a> such equivalent presentations can yield
large variations in the number of coset numbers required in an
enumeration. For this command, we are interested in this variation.
<p>
After the final presentation is run, some additional status
information messages are printed to the <font face="Gill Sans,Helvetica,Arial">ACE</font> output file:
<p>
<ul>
<p>
<li> the number of runs which yielded a finite index;
<p>
<li> the total number of runs (excluding the priming run); and
<p>
<li> the range of values observed for <code>m</code> and <code>t</code>.
<p>
</ul>
<p>
As an example (drawn from the discussion in <a href="biblio.htm#HR99ace"><cite>HR99ace</cite></a>) consider the
enumeration of the 448 coset numbers of the subgroup
〈<i>a</i><sup>2</sup>,<i>a</i><sup>−1</sup><i>b</i> 〉 of the group
<br clear="all" /><table border="0" width="100%"><tr><td><table align="center" cellspacing="0" cellpadding="2"><tr><td nowrap="nowrap" align="center"> (8,7 | 2,3) = 〈<i>a</i>,<i>b</i> | <i>a</i><sup>8</sup> = <i>b</i><sup>7</sup> = (<i>ab</i>)<sup>2</sup> = (<i>a</i><sup>−1</sup><i>b</i>)<sup>3</sup> = 1 〉·</td></tr></table></td></tr></table>
There are 4!=24 relator orderings and 2<sup>4</sup>=16 combinations of
relator or inverted relator. Exponents are taken into account when
rotating relators, so the relators given give rise to 1, 1, 2 and 2
rotations respectively, for a total of 1·1·2·2=4 combinations. So,
for <code>aep</code> = 7 (resp. 3), 24·16·4=1536 (resp. 16·4=64)
equivalent presentations are tested.
<p>
<strong>Notes:</strong>
There is no way to stop the <code>aep</code> option before it has completed,
other than killing the task. So do a reality check beforehand on the
size of the search space and the time for each enumeration. If you are
interested in finding a ``good'' enumeration, it can be very helpful,
in terms of running time, to put a tight limit on the number of coset
numbers via the <code>max</code> option. You may also have to set <code>compaction</code> =
100 to prevent time-wasting attempts to recover space via
compaction. This maximises throughput by causing the ``bad''
enumerations, which are in the majority, to overflow quickly and
abort. If you wish to explore a very large search-space, consider
firing up many copies of <font face="Gill Sans,Helvetica,Arial">ACE</font>, and starting each with a ``random''
equivalent presentation. Alternatively, you could use the <code>rep</code> command.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEAllEquivPresentations</code>
(see <a href="CHAP006.htm#SSEC004.1">ACEAllEquivPresentations</a>).
<p>
<a name = "SSEC001.2"></a>
<dt><li><code>rep:=</code><var>val</var><code></code>
<dt><dt><li><code>rep:= [</code><var>val</var><code>, </code><var>Npresentations</var><code>] <dd></code>
Run the enumeration for <code>r</code>andom <code>e</code>quivalent <code>p</code>resentations;
<var>val</var> is in the integer range 1 to 7;
<var>Npresentations</var> must be a positive integer.
<p>
The <code>rep</code> (random equivalent presentations) option complements the
<code>aep</code> option. It generates and tests some random equivalent
presentations. The argument <var>val</var> acts as for <code>aep</code>. It is also
possible to set the number <var>Npresentations</var> of random presentations
used (by default, eight are used), by using the extended syntax
<code>rep:=[</code><var>val</var><code>,</code><var>Npresentations</var><code>]</code>.
<p>
The routine first turns <code>asis</code> on and <code>messages</code> off (i.e. sets
<code>messages</code> to 0), and then generates and tests the requested number of
random equivalent presentations. For each presentation, the relators
used and the summary result line are printed. To observe these
messages either set the <code>InfoLevel</code> of <code>InfoACE</code> to at least 3 or
non-interactively you can peruse the <font face="Gill Sans,Helvetica,Arial">ACE</font> output file (see <a href="CHAP004.htm#SSEC011.8">option aceoutfile</a>).
<p>
Normally when a non-interactive <font face="Gill Sans,Helvetica,Arial">ACE</font> interface function is called,
the option <code>start</code> (see <a href="CHAP00D.htm#SSEC003.2">option start</a>), is quietly inserted after all
the options provided by the user, to initiate a coset enumeration.
Since the <code>rep</code> option invokes an enumeration, the quiet insertion of
the <code>start</code> option is neither needed nor done, when a non-interactive
<font face="Gill Sans,Helvetica,Arial">ACE</font> interface function is called with the <code>rep</code> option.
<p>
<strong>Notes:</strong>
The relator inversions and rotations are ``genuinely'' random. The
relator permuting is a little bit of a kludge, with the ``quality'' of
the permutations tending to improve with successive presentations.
When the <code>rep</code> command completes, the presentation active is the
<strong>last</strong> one generated, (not that the non-interactive user cares).
<p>
<strong>Guru Notes:</strong>
It might appear that neglecting to restore the original presentation
is an error. In fact, it is a useful feature! Suppose that the space
of equivalent presentations is too large to exhaustively test. As
noted in the entry for <code>aep</code>, we can start up multiple copies of <code>aep</code>
at random points in the search-space. Manually generating <code>random</code>
equivalent presentations to serve as starting-points is tedious and
error-prone. The <code>rep</code> option provides a simple solution; simply run
<code>rep := 7</code> before <code>aep := 7</code>.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACERandomEquivPresentations</code>
(see <a href="CHAP006.htm#SSEC004.2">ACERandomEquivPresentations</a>).
<p>
</dl>
<p>
<p>
<h2><a name="SECT002">D.2 Options that Modify a Presentation</a></h2>
<p><p>
<p>
<dl compact>
<p>
<dt><a name = "SSEC002.1"></a>
<dt><li><code>group:=</code><var>grpgens</var><code> <dd></code>
Defines the <code>group</code> generators; <var>grpgens</var> should be an integer (that
is the number of generators) or a string that is the concatenation of,
or a list of, single-lowercase-letter group generator names, i.e. it
should be in a form suitable for the <font face="Gill Sans,Helvetica,Arial">ACE</font> binary to interpret.
(Shortest abbreviation: <code>gr</code>.)
<p>
The group generators should normally be input as one of the arguments
of an <font face="Gill Sans,Helvetica,Arial">ACE</font> interface function, though this option may be useful when
<code>ACEStart</code> (see <a href="CHAP006.htm#SSEC001.1">ACEStart</a>) is called with the single argument 0. This option may also be useful for re-using an interactive process for a
new enumeration, rather than using <code>ACEQuit</code> to kill the process and
<code>ACEStart</code> to initiate a new process. If the generators each have
names that as strings are single lowercase letters, those same strings
are used to represent the same generators by <font face="Gill Sans,Helvetica,Arial">ACE</font>; otherwise, <font face="Gill Sans,Helvetica,Arial">ACE</font>
will represent each generator by an integer, numbered sequentially
from 1.
<p>
To convert a <font face="Gill Sans,Helvetica,Arial">GAP</font> list <var>fgens</var> of free group generators into a form
suitable for the <code>group</code> option, use the construction:
<code>ToACEGroupGenerators(</code><var>fgens</var><code>)</code> (see <a href="CHAP006.htm#SSEC003.5">ToACEGroupGenerators</a>). It is
<strong>strongly recommended</strong> that users of the <code>group</code> option use this
construction.
<p>
<strong>Notes:</strong>
Any use of the <code>group</code> command which actually defines generators
invalidates any previous enumeration, and stays in effect until the
next <code>group</code> command. Any words for the group or subgroup must be
entered using the nominated generator format, and all printout will
use this format. A valid set of generators is the minimum information
necessary before <font face="Gill Sans,Helvetica,Arial">ACE</font> will attempt an enumeration.
<p>
<strong>Guru Notes:</strong>
The columns of the coset table are allocated in the same order as the
generators are listed, insofar as this is possible, given that the
first two columns must be a generator/inverse pair or a pair of
involutions. The ordering of the columns can, in some cases, affect
the definition sequence of cosets and impact the statistics of an
enumeration.
<p>
<dt><a name = "SSEC002.2"></a>
<dt><li><code>relators:=</code><var>relators</var><code> <dd></code>
Defines the group <code>relators</code>; <var>relators</var> must be a string or list of
strings that the <font face="Gill Sans,Helvetica,Arial">ACE</font> binary can interpret as words in the group
generators. (Shortest abbreviation: <code>rel</code>.)
<p>
The group relators should normally be input as one of the arguments of
an <font face="Gill Sans,Helvetica,Arial">ACE</font> interface function, but this option may occasionally be
useful with interactive processes (see <a href="CHAP00D.htm#SSEC002.1">option group</a>). If <var>wordList</var>
is an empty list, the group is free.
<p>
To convert a <font face="Gill Sans,Helvetica,Arial">GAP</font> list <var>rels</var> of relators in the free group
generators <var>fgens</var> into a form suitable for the <code>relators</code> option, use
the construction: <code>ToACEWords(</code><var>fgens</var><code>, </code><var>rels</var><code>)</code> (see <a href="CHAP006.htm#SSEC003.6">ToACEWords</a>).
<p>
<dt><a name = "SSEC002.3"></a>
<dt><li><code>generators:=</code><var>subgens</var><code> <dd></code>
Defines the subgroup <code>generators</code>; <var>subgens</var> must be a string or list
of strings that the <font face="Gill Sans,Helvetica,Arial">ACE</font> binary can interpret as words in the group
generators. (Shortest abbreviation: <code>gen</code>.)
<p>
The subgroup generators should normally be input as one of the
arguments of an <font face="Gill Sans,Helvetica,Arial">ACE</font> interface function, but this option may
occasionally be useful with interactive processes (see <a href="CHAP00D.htm#SSEC002.1">option group</a>). By default, there are no subgroup generators and the subgroup
is trivial. This command allows a list of subgroup generating words to
be entered.
<p>
To convert a <font face="Gill Sans,Helvetica,Arial">GAP</font> list <var>sgens</var> of subgroup generators in the free
group generators <var>fgens</var> into a form suitable for the <code>generators</code> option, use the construction: <code>ToACEWords(</code><var>fgens</var><code>, </code><var>sgens</var><code>)</code>
(see <a href="CHAP006.htm#SSEC003.6">ToACEWords</a>).
<p>
<dt><a name = "SSEC002.4"></a>
<dt><li><code>sg:=</code><var>subgens</var><code> <dd></code>
Adds the words in <var>subgens</var> to any <code>s</code>ubgroup <code>g</code>enerators already
present; <var>subgens</var> must be a string or list of strings that the <font face="Gill Sans,Helvetica,Arial">ACE</font>
binary can interpret as words in the group generators.
<p>
The enumeration must be (re)<code>start</code>ed or <code>redo</code>ne, it cannot be
<code>continu</code>ed.
<p>
To convert a <font face="Gill Sans,Helvetica,Arial">GAP</font> list <var>sgens</var> of subgroup generators in the free
group generators <var>fgens</var> into a form suitable for the <code>generators</code> option, use the construction: <code>ToACEWords(</code><var>fgens</var><code>, </code><var>sgens</var><code>)</code>
(see <a href="CHAP006.htm#SSEC003.6">ToACEWords</a>).
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEAddSubgroupGenerators</code>
(see <a href="CHAP006.htm#SSEC007.4">ACEAddSubgroupGenerators</a>).
<p>
<dt><a name = "SSEC002.5"></a>
<dt><li><code>rl:=</code><var>relators</var><code> <dd></code>
Appends the <code>r</code>elator <code>l</code>ist <var>relators</var> to the existing list of
relators present; <var>relators</var> must be a string or list of strings that
the <font face="Gill Sans,Helvetica,Arial">ACE</font> binary can interpret as words in the group generators.
<p>
The enumeration must be (re)<code>start</code>ed or <code>redo</code>ne, it cannot be
<code>continu</code>ed.
<p>
To convert a <font face="Gill Sans,Helvetica,Arial">GAP</font> list <var>rels</var> of relators in the free group
generators <var>fgens</var> into a form suitable for the <code>rl</code> option, use the
construction: <code>ToACEWords(</code><var>fgens</var><code>, </code><var>rels</var><code>)</code> (see <a href="CHAP006.htm#SSEC003.6">ToACEWords</a>).
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEAddRelators</code> (see <a href="CHAP006.htm#SSEC007.3">ACEAddRelators</a>).
<p>
<dt><a name = "SSEC002.6"></a>
<dt><li><code>ds:=</code><var>list</var><code> <dd></code>
<code>D</code>eletes <code>s</code>ubgroup generators; <var>list</var> must be a list of positive
integers.
<p>
This command allows subgroup generators to be deleted from the
presentation. If the generators are numbered from 1 in the output of,
say, the <code>sr</code> command (see <a href="CHAP00D.htm#SSEC005.7">option sr</a>), then the generators listed in
<code></code><var>list</var><code></code> are deleted; <code></code><var>list</var><code></code> must be a strictly increasing sequence.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEDeleteSubgroupGenerators</code>
(see <a href="CHAP006.htm#SSEC007.6">ACEDeleteSubgroupGenerators</a>).
<p>
<dt><a name = "SSEC002.7"></a>
<dt><li><code>dr:=</code><var>list</var><code> <dd></code>
<code>D</code>eletes relators; <var>list</var> must be a list of positive integers.
<p>
This command allows group relators to be deleted from the
presentation. If the relators are numbered from 1 in the output of,
say, the <code>sr</code> command (see <a href="CHAP00D.htm#SSEC005.7">option sr</a>), then the relators listed in
<code></code><var>list</var><code></code> are deleted; <code></code><var>list</var><code></code> must be a strictly increasing sequence.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEDeleteRelators</code> (see <a href="CHAP006.htm#SSEC007.5">ACEDeleteRelators</a>).
<p>
<dt><a name = "SSEC002.8"></a>
<dt><li><code>cc:=</code><var>val</var><code> <dd></code>
Makes <code>c</code>oset <var>val</var> <code>c</code>oincide with coset 1; <var>val</var> should be a
positive integer.
<p>
Prints out the representative of coset <code></code><var>val</var><code></code>, and adds it to the
subgroup generators; i.e., forces coset <code></code><var>val</var><code></code> to coincide with coset
1, the subgroup.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACECosetCoincidence</code>
(see <a href="CHAP006.htm#SSEC007.7">ACECosetCoincidence</a>).
<p>
<a name = "SSEC002.9"></a>
<dt><li><code>rc:=</code><var>val</var><code></code>
<dt><li><code>rc:= [</code><var>val</var><code>]</code>
<dt><dt><li><code>rc:= [</code><var>val</var><code>, </code><var>attempts</var><code>] <dd></code>
Enforce <code>r</code>andom <code>c</code>oincidences; <var>val</var> and <var>attempts</var> must be positive
integers.
<p>
This option attempts upto <var>attempts</var> (or, in the first and second
forms, 8) times to find nontrivial subgroups with index a multiple of
<var>val</var> by repeatedly making random coset numbers coincident with coset
1 and seeing what happens. The starting coset table must be non-empty,
but should not be complete. For each attempt, we repeatedly add random
coset representatives to the subgroup and <code>redo</code> the enumeration. If
the table becomes too small, the attempt is aborted, the original
subgroup generators restored, and another attempt made. If an attempt
succeeds, then the new set of subgroup generators is retained.
<p>
<strong>Guru Notes:</strong>
A coset number can have many different coset representatives. Consider
running <code>standard</code> before <code>rc</code>, to canonicise the table and hence the
coset representatives.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACERandomCoincidences</code>
(see <a href="CHAP006.htm#SSEC007.8">ACERandomCoincidences</a>).
<p>
</dl>
<p>
<p>
<h2><a name="SECT003">D.3 Mode Options</a></h2>
<p><p>
<p>
<dl compact>
<p>
<dt><a name = "SSEC003.1"></a>
<dt><li><code>mode <dd></code>
Prints the possible enumeration <code>mode</code>s.
(Shortest abbreviation: <code>mo</code>.)
<p>
Prints the possible enumeration <code>mode</code>s (i.e. which of <code>continu</code>,
<code>redo</code> or <code>start</code> are possible (see <a href="CHAP00D.htm#SSEC003.4">option continu</a>, <a href="CHAP00D.htm#SSEC003.3">option redo</a>
and <a href="CHAP00D.htm#SSEC003.2">option start</a>).
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEModes</code> (see <a href="CHAP006.htm#SSEC002.1">ACEModes</a>).
<p>
<a name = "SSEC003.2"></a>
<dt><li><code>begin</code>
<dt><a name = "SSEC003.2"></a>
<dt><li><code>start <dd></code>
Start an enumeration. (Shortest abbreviation of <code>begin</code> is <code>beg</code>.)
<p>
Any existing information in the table is cleared, and the enumeration
starts from coset 1 (i.e., the subgroup).
<p>
Normally when a non-interactive <font face="Gill Sans,Helvetica,Arial">ACE</font> interface function is called,
the option <code>start</code> (see <a href="CHAP00D.htm#SSEC003.2">option start</a>), is quietly inserted after all
the options provided by the user, to initiate a coset enumeration;
however, this is not done, if the user herself supplies either the
<code>begin</code> or <code>start</code> option.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEStart</code> (see <a href="CHAP006.htm#SSEC001.1">ACEStart</a>).
<p>
<a name = "SSEC003.3"></a>
<dt><li><code>check</code>
<dt><a name = "SSEC003.3"></a>
<dt><li><code>redo <dd></code>
<code>Redo</code> an extant enumeration, using the current parameters.
<p>
As opposed to <code>start</code> (see <a href="CHAP00D.htm#SSEC003.2">option start</a>), which clears an existing
coset table, any existing information in the table is retained, and
the enumeration is restarted from coset 1 (i.e., the subgroup).
<p>
<strong>Notes:</strong>
This option is really intended for the case where additional relators
(option <code>rl</code>; see <a href="CHAP00D.htm#SSEC002.5">option rl</a>) and/or subgroup generators (option
<code>sg</code>; see <a href="CHAP00D.htm#SSEC002.4">option sg</a>) have been introduced. The current table, which
may be incomplete or exhibit a finite index, is still <strong>valid</strong>.
However, the additional data may allow the enumeration to complete, or
cause a collapse to a smaller index.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACERedo</code> (see <a href="CHAP006.htm#SSEC002.3">ACERedo</a>).
<p>
<a name = "I0"></a>
<dt><a name = "SSEC003.4"></a>
<dt><li><code>continu <dd></code>
<code>Continu</code>es the current enumeration, building upon the existing table.
(Shortest abbreviation: <code>cont</code>.)
<p>
If a previous run stopped without producing a finite index you can, in
principle, change any of the parameters and <code>continu</code>e on. Of course,
if you make any changes which invalidate the current table, you won't
be allowed to <code>continue</code>, although you may be allowed to <code>redo</code>
(see <a href="CHAP00D.htm#SSEC003.3">option redo</a>). If <code>redo</code> is not allowed, you must re-<code>start</code>
(see <a href="CHAP00D.htm#SSEC003.2">option start</a>).
<p>
<strong>Note:</strong> The <font face="Gill Sans,Helvetica,Arial">ACE</font> standalone allows the option <code>continue</code>, but this
is a <font face="Gill Sans,Helvetica,Arial">GAP</font> keyword, and so <font face="Gill Sans,Helvetica,Arial">GAP</font> users must use
(mixed-case abbreviations of) <code>continu</code>.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEContinue</code> (see <a href="CHAP006.htm#SSEC002.2">ACEContinue</a>).
<p>
</dl>
<p>
<p>
<h2><a name="SECT004">D.4 Options that Interact with the Operating System</a></h2>
<p><p>
<p>
<dl compact>
<p>
<a name = "SSEC004.1"></a>
<dt><li><code>ai</code>
<dt><dt><li><code>ai:=</code><var>filename</var><code> <dd></code>
<code>A</code>lter <code>i</code>nput to standard input or <var>filename</var>; <var>filename</var> must be a
string.
<p>
By default, commands to <font face="Gill Sans,Helvetica,Arial">ACE</font> are read from standard input (i.e., the
keyboard). With no value <code>ai</code> causes <font face="Gill Sans,Helvetica,Arial">ACE</font> to revert to reading from
standard input; otherwise, the <code>ai</code> command closes the current input
file, and opens <code></code><var>filename</var><code></code> as the source of commands. If
<code></code><var>filename</var><code></code> can't be opened, input reverts to standard input.
<p>
<strong>Notes:</strong>
If you switch to taking input from (another) file, remember to switch
back before the end of that file; otherwise the <code>EOF</code> there will cause
<font face="Gill Sans,Helvetica,Arial">ACE</font> to terminate.
<p>
<a name = "SSEC004.2"></a>
<dt><li><code>bye</code>
<a name = "SSEC004.2"></a>
<dt><li><code>exit</code>
<dt><a name = "SSEC004.2"></a>
<dt><li><code>qui <dd></code>
Quit <font face="Gill Sans,Helvetica,Arial">ACE</font>. (Shortest abbreviation of <code>qui</code> is <code>q</code>.)
<p>
This quits <font face="Gill Sans,Helvetica,Arial">ACE</font> nicely, printing the date and the time. An <code>EOF</code>
(end-of-file; i.e., <code>^d</code>) has the same effect, so proper
termination occurs if <font face="Gill Sans,Helvetica,Arial">ACE</font> is taking its input from a script file.
<p>
Note that <code>qui</code> actually abbreviates the corresponding <font face="Gill Sans,Helvetica,Arial">ACE</font>
directive <code>quit</code>, but since <code>quit</code> is a <font face="Gill Sans,Helvetica,Arial">GAP</font> keyword it is not
available via the <font face="Gill Sans,Helvetica,Arial">GAP</font> interface to <font face="Gill Sans,Helvetica,Arial">ACE</font>.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEQuit</code> (see <a href="CHAP006.htm#SSEC001.2">ACEQuit</a>).
<p>
<dt><a name = "SSEC004.3"></a>
<dt><li><code>system:=</code><var>string</var><code> <dd></code>
Does a shell escape, to execute <var>string</var>; <var>string</var> must be a string.
(Shortest abbreviation: <code>sys</code>.)
<p>
Since <font face="Gill Sans,Helvetica,Arial">GAP</font> already provides <code>Exec()</code> for this purpose, this option
is unlikely to have a use.
<p>
</dl>
<p>
<p>
<h2><a name="SECT005">D.5 Query Options</a></h2>
<p><p>
<p>
<dl compact>
<p>
<dt><a name = "SSEC005.1"></a>
<dt><li><code>cycles <dd></code>
Prints out the table in <code>cycles</code>. (Shortest abbreviation: <code>cy</code>.)
<p>
This option prints out the permutation representation.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACECycles</code> (see <a href="CHAP006.htm#SSEC005.16">ACECycles</a>).
<p>
<a name = "SSEC005.2"></a>
<dt><li><code>dump</code>
<dt><li><code>dump:=</code><var>level</var><code></code>
<dt><li><code>dump:= [</code><var>level</var><code>]</code>
<dt><dt><li><code>dump:= [</code><var>level</var><code>, </code><var>detail</var><code>] <dd></code>
<code>Dump</code> the internal variables of <font face="Gill Sans,Helvetica,Arial">ACE</font>; <var>level</var> must be an integer in
the range 0 to 2, and <var>detail</var> must be 0 or 1.
(Shortest abbreviation: <code>d</code>.)
<p>
The value of <var>level</var> determines which of the three levels of <font face="Gill Sans,Helvetica,Arial">ACE</font> to
dump. (You will need to read the standalone manual <code>acce3001.dvi</code> in
the <code>standalone-doc</code> directory to understand what Levels 0, 1 and 2
are all about.) The value of <var>detail</var> determines the amount of detail
(<code></code><var>detail</var><code> = 0</code> means less detail). The first form (with no arguments)
selects <code></code><var>level</var><code> = 0, </code><var>detail</var><code> = 0</code>. The second form of this command
makes <code></code><var>detail</var><code> = 0</code>. This option is intended for gurus; the source code should be consulted to see what the output means.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEDumpVariables</code> (see <a href="CHAP006.htm#SSEC005.23">ACEDumpVariables</a>).
<p>
<dt><a name = "SSEC005.3"></a>
<dt><li><code>help <dd></code>
Prints the <font face="Gill Sans,Helvetica,Arial">ACE</font> help screen. (Shortest abbreviation: <code>h</code>.)
<p>
This option prints the list of options of the <font face="Gill Sans,Helvetica,Arial">ACE</font> binary. Note that
this list is longer than a standard screenful.
<p>
<a name = "SSEC005.4"></a>
<dt><li><code>nc</code>
<dt><li><code>nc:=</code><var>val</var><code></code>
<a name = "SSEC005.4"></a>
<dt><li><code>normal</code>
<dt><dt><li><code>normal:=</code><var>val</var><code> <dd></code>
Check or attempt to enforce normal closure; <var>val</var> must be 0 or 1.
<p>
This option tests the subgroup for normal closure within the group. If
a conjugate of a subgroup generator by a generator, is determined to
belong to a coset other than coset 1, it is printed out, and if <code></code><var>val</var><code>
= 1</code>, then any such conjugate is also added to the subgroup
generators. With no argument or if <code></code><var>val</var><code> = 0</code>, <font face="Gill Sans,Helvetica,Arial">ACE</font> does not add
any new subgroup generators.
<p>
<strong>Notes:</strong>
The method of determination of whether a conjugate of a subgroup
generator is in the subgroup, is by testing whether it can be traced
from coset 1 to coset 1 (see <code>trace</code>: <a href="CHAP00D.htm#SSEC005.12">option trace</a>).
<p>
The resultant subgroup need not be normally closed after executing option <code>nc</code> with the value 1. It is still possible that some
conjugates of the newly added subgroup generators will not be elements
of the subgroup.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEConjugatesForSubgroupNormalClosure</code>
(see <a href="CHAP006.htm#SSEC007.10">ACEConjugatesForSubgroupNormalClosure</a>).
<p>
<dt><a name = "SSEC005.5"></a>
<dt><li><code>options <dd></code>
Dumps version information of the <font face="Gill Sans,Helvetica,Arial">ACE</font> binary.
(Shortest abbreviation: <code>opt</code>.)
<p>
A rather unfortunate name for an option; this command dumps details of
the ``options'' included in the version of <font face="Gill Sans,Helvetica,Arial">ACE</font> when the <font face="Gill Sans,Helvetica,Arial">ACE</font>
binary was compiled.
<p>
A typical output, is as follows:
<p>
<pre>
Executable built:
Sat Feb 27 15:57:59 EST 1999
Level 0 options:
statistics package = on
coinc processing messages = on
dedn processing messages = on
Level 1 options:
workspace multipliers = decimal
Level 2 options:
host info = on
</pre>
<p>
<strong>INTERACTIVELY</strong> and non-interactively, use the command
<code>ACEBinaryVersion();</code> (see <a href="CHAP006.htm#SSEC005.25">ACEBinaryVersion</a>) for this information,
instead, unless you want it in an <font face="Gill Sans,Helvetica,Arial">ACE</font> standalone input file.
<p>
<a name = "SSEC005.6"></a>
<dt><li><code>oo:=</code><var>val</var><code></code>
<dt><a name = "SSEC005.6"></a>
<dt><li><code>order:=</code><var>val</var><code> <dd></code>
Print a coset representative of a coset number with order a multiple
of <var>val</var> modulo the subgroup; <var>val</var> must be an integer.
<p>
This option finds a coset with order a multiple of <code>|</code><var>val</var><code>|</code> modulo
the subgroup, and prints out its coset representative. If <code></code><var>val</var><code> <
0</code>, then all coset numbers meeting the requirement are printed. If
<code></code><var>val</var><code> > 0</code>, then just the first coset number meeting the requirement
is printed. Also, <code></code><var>val</var><code> = 0</code> is permitted; this special value effects
the printing of the orders (modulo the subgroup) of all coset numbers.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEOrders</code> (see <a href="CHAP006.htm#SSEC005.18">ACEOrders</a>), for the case
<code></code><var>val</var><code> = 0</code>, or <code>ACEOrder</code> (see <a href="CHAP006.htm#SSEC005.19">ACEOrder</a>), otherwise.
<p>
<a name = "SSEC005.7"></a>
<dt><li><code>sr</code>
<dt><dt><li><code>sr:=</code><var>val</var><code> <dd></code>
Print out parameters of the current presentation; <var>val</var> must be an
integer in the range 0 to 5.
<p>
No argument, or <code></code><var>val</var><code> = 0</code>, prints out the <code>Group Name</code>, the group's
<code>relators</code>, <code>Subgroup Name</code> and the subgroup's generators. If val
= 1</code>, then the <code>Group Generators</code> and the current setting of the ``run
parameters'' is also printed. The printout is the same as that
produced at the start of a run when option <code>messages</code> (see <a href="CHAP004.htm#SSEC018.1">option messages</a>) is non-zero. Also, <var>val</var> equal to 2, 3, 4, or 5 print out
just the <code>Group Name</code>, just the group's relators, just the Subgroup
Name</code>, or just the subgroup's generators, respectively.
<p>
<strong>Notes:</strong>
The <code>sr</code> option should only be used <strong>after</strong> an enumeration run;
otherwise, the value 0 for some options will be unreliable. To ensure
this occurs non-interactively, ensure one of the options that invokes
an enumeration: <code>start</code> (see <a href="CHAP00D.htm#SSEC003.2">option start</a>) or <code>aep</code> (see <a href="CHAP00D.htm#SSEC001.1">option aep</a>) or <code>rep</code> (see <a href="CHAP00D.htm#SSEC001.2">option rep</a>), precedes the <code>sr</code> option. (When an
enumeration-invoking option is included non-interactively the quiet
inclusion step of the <code>start</code> option is omitted.)
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEGroupGenerators</code> (see <a href="CHAP006.htm#SSEC005.1">ACEGroupGenerators</a>),
<code>ACERelators</code> (see <a href="CHAP006.htm#SSEC005.2">ACERelators</a>), <code>ACESubgroupGenerators</code> (see
<a href="CHAP006.htm#SSEC005.3">ACESubgroupGenerators</a>), and <code>ACEParameters</code> (see <a href="CHAP006.htm#SSEC005.10">ACEParameters</a>).
<p>
<a name = "SSEC005.8"></a>
<dt><li><code>print</code>
<dt><li><code>print:=</code><var>val</var><code></code>
<dt><li><code>print:= [</code><var>val</var><code>]</code>
<dt><li><code>print:= [</code><var>val</var><code>, </code><var>last</var><code>]</code>
<dt><dt><li><code>print:= [</code><var>val</var><code>, </code><var>last</var><code>, </code><var>by</var><code>] <dd></code>
Compact and print the coset table; <var>val</var> must be an integer, and
<var>last</var> and <var>by</var> must be positive integers.
(Shortest abbreviation: <code>pr</code>.)
<p>
In the first (no value) form, <code>print</code> prints the entire coset table,
without orders or coset representatives. In the second and third
forms, the absolute value of <var>val</var> is taken to be the last line of the table to be printed (and 1 is taken to be the first); in the fourth
and fifth forms, <code>|</code><var>val</var><code>|</code> is taken to be the first line of the table
to be printed, and <var>last</var> is taken to be the number of the last line
to be printed. In the last form, the table is printed from line
<code>|</code><var>val</var><code>|</code> to line <var>last</var> in steps of <var>by</var>. If <var>val</var> is negative, then
the orders modulo the subgroup (if available) and coset
representatives are printed also.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEDisplayCosetTable</code>
(see <a href="CHAP006.htm#SSEC005.12">ACEDisplayCosetTable</a>).
<p>
<a name = "SSEC005.9"></a>
<dt><li><code>sc:=</code><var>val</var><code></code>
<dt><a name = "SSEC005.9"></a>
<dt><li><code>stabilising:=</code><var>val</var><code> <dd></code>
Print out the coset numbers whose elements normalise the subgroup;
<var>val</var> must be an integer.
(Shortest abbreviation of <code>stabilising</code> is <code>stabil</code>.)
<p>
If <code></code><var>val</var><code> > 0</code>, the first <code></code><var>val</var><code></code> non-trivial (i.e. other than coset
1) coset numbers whose elements normalise the subgroup are printed. If
<code></code><var>val</var><code> = 0</code>, all non-trivial coset numbers whose elements normalise
the subgroup, plus their representatives, are printed. If <code></code><var>val</var><code> <
0</code>, the first <code>|</code><var>val</var><code>|</code> non-trivial coset numbers whose elements
normalise the subgroup, plus their representatives, are printed.
<p>
<strong>Note:</strong>
The name of this option is an historical hangover. It is named for the
property that elements that ``normalise'' a subgroup, may be said to
``stabilise'' that subgroup when they act ``by conjugation''. Also,
the option <code>normal</code> (see <a href="CHAP00D.htm#SSEC005.4">option normal</a>) already performs a different
function.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACECosetsThatNormaliseSubgroup</code>
(see <a href="CHAP006.htm#SSEC005.21">ACECosetsThatNormaliseSubgroup</a>).
<p>
<a name = "SSEC005.10"></a>
<dt><li><code>statistics</code>
<dt><a name = "SSEC005.10"></a>
<dt><li><code>stats <dd></code>
Dump enumeration statistics.
(Shortest abbreviation of <code>statistics</code> is <code>stat</code>.)
<p>
If the statistics package is compiled into the <font face="Gill Sans,Helvetica,Arial">ACE</font> code, which it
is by default (see the <code>options</code> <a href="CHAP00D.htm#SSEC005.5">option options</a> option), then this option dumps the statistics accumulated during the most recent
enumeration. See the <code>enum.c</code> source file for the meaning of the
variables.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEDumpStatistics</code> (see <a href="CHAP006.htm#SSEC005.24">ACEDumpStatistics</a>).
<p>
<dt><a name = "SSEC005.11"></a>
<dt><li><code>style <dd></code>
Prints the current enumeration style.
<p>
This option prints the current enumeration style, as deduced from the
current <code>ct</code> and <code>rt</code> parameters (see <a href="CHAP003.htm#SECT001">Enumeration Style</a>).
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEStyle</code> (see <a href="CHAP006.htm#SSEC005.22">ACEStyle</a>).
<p>
<a name = "SSEC005.12"></a>
<dt><li><code>tw:= [</code><var>val</var><code>, </code><var>word</var><code>]</code>
<dt><a name = "SSEC005.12"></a>
<dt><li><code>trace:= [</code><var>val</var><code>, </code><var>word</var><code>] <dd></code>
Trace <code></code><var>word</var><code></code> through the coset table, starting at coset <code></code><var>val</var><code></code>;
<var>val</var> must be a positive integer, and <var>word</var> must be a word in the
group generators.
<p>
This option prints the final coset number of the trace, if the trace
completes.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACETraceWord</code> (see <a href="CHAP006.htm#SSEC005.17">ACETraceWord</a>).
<p>
</dl>
<p>
<p>
<h2><a name="SECT006">D.6 Options that Modify the Coset Table</a></h2>
<p><p>
<p>
<dl compact>
<p>
<a name = "I1"></a>
<a name = "SSEC006.1"></a>
<dt><li><code>recover</code>
<dt><a name = "SSEC006.1"></a>
<dt><li><code>contiguous <dd></code>
<code>Recover</code> space used by dead coset numbers.
(Shortest abbreviation of <code>recover</code> is <code>reco</code>, and shortest
abbreviation of <code>contiguous</code> is <code>contig</code>.)
<p>
This option invokes the compaction routine on the table to recover the
space used by any dead coset numbers. A <code>CO</code> message line is printed
if any cosets were recovered, and a <code>co</code> line if none were. This
routine is called automatically if the <code>cycles</code>, <code>nc</code>, <code>print</code> or
<code>standard</code> options (see <a href="CHAP00D.htm#SSEC005.1">option cycles</a>, <a href="CHAP00D.htm#SSEC005.4">option nc</a>, <a href="CHAP00D.htm#SSEC005.8">option print</a>
and <a href="CHAP00D.htm#SSEC006.2">option standard</a>) are invoked.
<p>
<strong>INTERACTIVELY</strong>, use <code>ACERecover</code> (see <a href="CHAP006.htm#SSEC007.1">ACERecover</a>).
<p>
<dt><a name = "SSEC006.2"></a>
<dt><li><code>standard <dd></code>
Compacts <font face="Gill Sans,Helvetica,Arial">ACE</font>'s coset table and standardises the numbering of
cosets, according to the <code>lenlex</code> scheme (see Section <a href="CHAP003.htm#SECT004">Coset Table Standardisation Schemes</a>). (Shortest abbreviation: <code>st</code>.)
<p>
For a given ordering of the generators in the columns of the table, it
produces a canonical numbering of the cosets. This function does not
display the new table; use the <code>print</code> (see <a href="CHAP00D.htm#SSEC005.8">option print</a>) for that.
Such a table has the property that a scan of the successive rows of
the <strong>body</strong> of the table row by row, from left to right, encounters
previously unseen cosets in numeric order.
<p>
<strong>Notes:</strong>
In a <code>lenlex</code> standard table, the coset representatives are ordered
first according to length and then the lexicographic order defined by
the order the generators and their inverses head the columns. Note
that, since <font face="Gill Sans,Helvetica,Arial">ACE</font> avoids having an involutory generator in the first
column when it can, this lexicographic order does not necessarily
correspond with the order in which the generators were first put to
<font face="Gill Sans,Helvetica,Arial">ACE</font>. Two tables are equivalent only if their canonic forms are the
same. Invoking this option directly does <strong>not</strong> affect the <font face="Gill Sans,Helvetica,Arial">GAP</font> coset table obtained via <code>ACECosetTable</code>; use the <code>lenlex</code> (see <a href="CHAP004.htm#SSEC011.4">option lenlex</a>) option, if you want your table <code>lenlex</code> standardised. (The
<code>lenlex</code> option restarts the enumeration, if it is necessary to ensure
the generators have not been rearranged.)
<p>
<strong>Guru Notes:</strong>
In five of the ten standard enumeration strategies of Sims
<a href="biblio.htm#Sim94"><cite>Sim94</cite></a> (i.e. the five Sims strategies not provided by <font face="Gill Sans,Helvetica,Arial">ACE</font>),
the table is standardised repeatedly. This is expensive
computationally, but can result in fewer cosets being necessary. The
effect of doing this can be investigated in <font face="Gill Sans,Helvetica,Arial">ACE</font> by (repeatedly)
halting the enumeration (via restrictive options), standardising the
coset numbering, and continuing (see Section <a href="CHAP00C.htm#SECT002">Emulating Sims</a> for an
interactive example).
<p>
<strong>INTERACTIVELY</strong>, use <code>ACEStandardCosetNumbering</code>
(see <a href="CHAP006.htm#SSEC007.2">ACEStandardCosetNumbering</a>).
<p>
</dl>
<p>
<p>
<h2><a name="SECT007">D.7 Options for Comments</a></h2>
<p><p>
<p>
<dl compact>
<p>
<dt><a name = "SSEC007.1"></a>
<dt><li><code>text:=</code><var>string</var><code> <dd></code>
Prints <var>string</var> in the output; <var>string</var> must be a string.
<p>
This allows the user to add comments to the output from <font face="Gill Sans,Helvetica,Arial">ACE</font>.
<p>
<strong>Note:</strong>
Please avoid using this option to insert comments starting with three
asterisks: <code>***</code>, since this string is used as a sentinel internally
in flushing output from <font face="Gill Sans,Helvetica,Arial">ACE</font>.
<p>
<dt><a name = "SSEC007.2"></a>
<dt><li><code>aceincomment:=</code><var>string</var><code> <dd></code>
Prints comment <var>string</var> in the <font face="Gill Sans,Helvetica,Arial">ACE</font> input; <var>string</var> must be a string.
(Shortest abbreviation: <code>aceinc</code>.)
<p>
This option prints the comment <var>string</var> behind a sharp sign (<code>#</code>) in
the input to <font face="Gill Sans,Helvetica,Arial">ACE</font>. Only useful for adding comments (that <font face="Gill Sans,Helvetica,Arial">ACE</font>
ignores) to standalone input files.
<p>
</dl>
<p>
<p>
[<a href = "chapters.htm">Up</a>] [<a href ="CHAP00C.htm">Previous</a>] [<a href = "theindex.htm">Index</a>]
<P>
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