In this chapter we describe in detail all the options used by functions of the ANUPQ package. Note that by ``options'' we mean GAP options that are passed to functions after the arguments and separated from the arguments by a colon as described in Chapter Function Calls in the Reference Manual. The user is strongly advised to read Section Hints and Warnings regarding the use of Options.
lists all the GAP options defined for functions of the ANUPQ package:
gap> AllANUPQoptions(); [ "AllDescendants", "BasicAlgorithm", "Bounds", "CapableDescendants", "ClassBound", "CustomiseOutput", "Exponent", "Filename", "GroupName", "Identities", "Metabelian", "NumberOfSolubleAutomorphisms", "OrderBound", "OutputLevel", "PcgsAutomorphisms", "PqWorkspace", "Prime", "PrintAutomorphisms", "PrintPermutations", "QueueFactor", "RankInitialSegmentSubgroups", "RedoPcp", "RelativeOrders", "Relators", "SetupFile", "SpaceEfficient", "StandardPresentationFile", "StepSize", "SubList", "TreeDepth", "pQuotient" ]
The following global variable gives a partial breakdown of where the above options are used.
is a record of lists of names of admissible ANUPQ options, such that
each field is either the name of a ``key'' ANUPQ function or
(for a miscellaneous list of functions) and the corresponding value is
the list of option names that are admissible for the function (or
miscellaneous list of functions).
Also, from within a GAP session, you may use GAP's help browser
(see Chapter The Help System in the GAP Reference Manual); to
find out about any particular ANUPQ option, simply type: ``
'', where option is one of the options listed above without
any quotes, e.g.
gap> ?option Prime
will display the sections in this manual that describe the
option. In fact the first 4 are for the functions that have
Prime as an
option and the last actually describes the option. So follow up by
This is also the pattern for other options (the last section of the list always describes the option; the other sections are the functions with which the option may be used).
In the section following we describe in detail all ANUPQ options. To continue onto the next section on-line using GAP's help browser, type:
Specifies that the p-quotient for the prime p should be computed.
Specifies that the p-quotient to be computed has lower exponent-p class at most n. If this option is omitted a default of 63 (which is the maximum possible for the
pqprogram) is taken, except for
PqDescendants(see PqDescendants) and in a special case of
PqPCover(see PqPCover). Let F be the argument (or start group of the process in the interactive case) for the function; then for
PqDescendantsthe default is
) + 1, and for the special case of
PqPCoverthe default is
This option is only available for the standard presentation functions. It specifies that a p-quotient of the group argument of the function or group of the process is the pc p-group Q, where Q is of class less than the provided (or default) value of
pQuotientis provided, then the option
Primeif also provided, is ignored; the prime p is discovered by computing
Specifies that the p-quotient to be computed has exponent n. For an interactive process,
Exponentdefaults to a previously supplied value for the process. Otherwise (and non-interactively), the default is 0, which means that no exponent law is enforced.
Specifies that the relators sent to the
pqprogram should be rels instead of the relators of the argument group F (or start group in the interactive case) of the calling function; rels should be a list of strings in the string representations of the generators of F, and F must be an fp group (even if the calling function accepts a pc group). This option provides a way of giving relators to the
pqprogram, without having them pre-expanded by GAP, which can sometimes effect a performance loss of the order of 100 (see Section The Relators Option).
pqprogram does not use
/to indicate multiplication by an inverse and uses square brackets to represent (left normed) commutators. Also, even though the
pqprogram accepts relations, all elements of rels must be in relator form, i.e. a relation of form
must be written as
)^-1and then put in a pair of double-quotes to make it a string. See the example below.
PqParseWord(see PqParseWord). If they are ok, a message to say so is
MetabelianSpecifies that the largest metabelian p-quotient subject to any other conditions specified by other options be constructed. By default this restriction is not enforced.
Specifies that the
pqprogram should refer to the group by the name name (a string). If
GroupNameis not set and the group has been assigned a name via
SetName(see SetName) it is set as the name the
pqprogram should use. Otherwise, the ``generic'' name
"[grp]"is set as a default.
Specifies that the pc presentation should satisfy the laws defined by each function in the list funcs. This option may be called by
PqPCover(see Pq). Each function in the list funcs must return a word in its arguments (there may be any number of arguments). Let identity be one such function in funcs. Then as each lower exponent p-class quotient is formed, instances identity (w1 , ..., wn ) are added as relators to the pc presentation, where w1 , ..., wn are words in the pc generators of the quotient. At each class the class and number of pc generators is
InfoANUPQlevel 1, the number of instances is
InfoANUPQlevel 2, and the instances that are evaluated are
InfoANUPQlevel 3. As usual timing information is
InfoANUPQlevel 2; and details of the processing of each instance from the
pqprogram (which is often quite voluminous) is
InfoANUPQlevel 3. Try the examples
"11gp-3-Engel-Id"which demonstrate the usage of the
Identitiesoption; these are run using
PqExample(see PqExample). Take note of Note 1. below in relation to the example
"B2-4-Id"; the companion example
"B2-4"generates the same group using the
Exponentoption. These examples are discussed at length in Section The Identities Option and PqEvaluateIdentities Function.
InfoANUPQlevel to 3 or more when setting the
Identitiesoption may slow down the computation considerably, by overloading GAP with io operations.
Identitiesoption is implemented at the GAP level. An identity that is just an exponent law should be specified using the
Exponentoption (see option Exponent), which is implemented at the C level and is highly optimised and so is much more efficient.
Identitiesoption, by including other restrictions, e.g. by using the
ClassBoundoption (see option ClassBound).
Specifies the level of ``verbosity'' of the information output by the ANU
pqprogram when computing a pc presentation; n must be an integer in the range 0 to 3.
OutputLevel := 0displays at most one line of output and is the default;
OutputLevel := 1displays (usually) slightly more output and
OutputLevels of 2 and 3 are two levels of verbose output. To see these messages from the
InfoANUPQlevel must be set to at least 1 (see InfoANUPQ). See Section Hints and Warnings regarding the use of Options for an example of how
OutputLevelcan be used as a troubleshooting tool.
RedoPcpSpecifies that the current pc presentation (for an interactive process) stored by the
pqprogram be scrapped and clears the current values stored for the options
Metabelianand also clears the
pCoverfields of the data record of the process.
Non-interactively, this option directs that
pqshould not be called and that an input file with name filename (a string), containing the commands necessary for the ANU
pqstandalone, be constructed. The commands written to filename are also
Info-ed behind a ``
ToPQ>'' prompt at
InfoANUPQlevel 4 (see InfoANUPQ). Except in the case following, the calling function returns
true. If the calling function is the non-interactive version of one of
PqEpimorphismand the group provided as argument is trivial given with an empty set of generators, then no setup file is written and
failis returned (the
pqprogram cannot do anything useful with such a group). Interactively,
Since commands emitted to the
pq program may depend on knowing what the
``current state'' is, to form a setup file some ``close enough guesses''
may sometimes be necessary; when this occurs a warning is
InfoWarning level 1. To determine whether the ``close
enough guesses'' give an accurate setup file, it is necessary to run the
command without the
SetupFile option, after either setting the
InfoANUPQ level to at least 4 (the setup file script can then be
compared with the ``
ToPQ> '' commands that are
Info-ed) or setting a
pq command log file by using
ToPQLog (see ToPQLog).
Non-interactively, this option sets the memory used by the
pqprogram. It sets the maximum number of integer-sized elements to allocate in its main storage array. By default, the
pqprogram sets this figure to 10000000. Interactively,
PqWorkspaceis ignored; the memory used in this case may be set by giving
PqStarta second argument (see PqStart).
PcgsAutomorphisms := falseLet G be the group associated with the calling function (or associated interactive process). Passing the option
PcgsAutomorphismswithout a value (or equivalently setting it to
true), specifies that a polycyclic generating sequence for the automorphism group (which must be soluble) of G, be computed and passed to the
pqprogram. This increases the efficiency of the computation; it also prevents the
pqfrom calling GAP for orbit-stabilizer calculations. By default,
PcgsAutomorphismsis set to the value returned by
) ), and uses the package AutPGrp to compute
)if it is installed. This flag is set to
falsein the background according to the above criterion by the function
PqDescendants(see PqDescendants and PqDescendants!interactive).
PcgsAutomorphisms is used when the automorphism group of G is
insoluble, an error message occurs.
Specifies that only descendants of size at most pn , where n is a non-negative integer, be generated. Note that you cannot set both
For a positive integer n,
StepSizespecifies that only those immediate descendants which are a factor pn bigger than their parent group be generated.
StepSizespecifies that the integers of list are the step sizes for each additional class.
Sets the rank of the initial segment subgroup chosen to be n. By default, this has value 0.
SpaceEfficientSpecifies that the
pqprogram performs certain calculations of p-group generation more slowly but with greater space efficiency. This flag is frequently necessary for groups of large Frattini quotient rank. The space saving occurs because only one permutation is stored at any one time. This option is only available if the
PcgsAutomorphismsflag is set to
true(see option PcgsAutomorphisms). For an interactive process,
SpaceEfficientdefaults to a previously supplied value for the process. Otherwise (and non-interactively),
SpaceEfficientis by default
CapableDescendantsBy default, all (i.e. capable and terminal) descendants are computed. If this flag is set, only capable descendants are computed. Setting this option is equivalent to setting
AllDescendants := false(see option AllDescendants), except if both
AllDescendantsis essentially ignored.
AllDescendants := falseBy default, all descendants are constructed. If this flag is set to
false, only capable descendants are computed. Passing
AllDescendantswithout a value (which is equivalent to setting it to
true) is superfluous. This option is provided only for backward compatibility with the GAP 3 version of the ANUPQ package, where by default
AllDescendantswas set to
true). It is preferable to use
CapableDescendants(see option CapableDescendants).
Specifies that the descendants tree developed by
PqDescendantsTreeCoclassOne(see PqDescendantsTreeCoclassOne) should be extended to class class, where class is a positive integer.
Suppose that L is the list of descendants generated, then for a list sub of integers this option causes
). If an integer n is supplied,
Specifies that the number of soluble automorphisms of the automorphism group supplied by
PqPGSupplyAutomorphisms(see PqPGSupplyAutomorphisms) in a p-group generation calculation is n. By default, n is taken to be 0; n must be a non-negative integer. If n ³ 0 then a value for the option
RelativeOrders(see option RelativeOrders) must also be supplied.
Specifies the relative orders of each soluble automorphism of the automorphism group supplied by
PqPGSupplyAutomorphisms(see PqPGSupplyAutomorphisms) in a p-group generation calculation. The list list must consist of n positive integers, where n is the value of the option
NumberOfSolubleAutomorphisms(see option NumberOfSolubleAutomorphisms). By default list is empty.
BasicAlgorithmSpecifies that an algorithm that the
pqprogram calls its ``default'' algorithm be used for p-group generation. By default this algorithm is not used. If this option is supplied the settings of options
Specifies that fine tuning of the output is desired. The record rec should have any subset (or all) of the the following fields:
truespecifies algorithm trace data is desired. By default, one does not get algorithm trace data.
Not providing a field (or mis-spelling it!), specifies that the default
output is desired. As a convenience,
1 is also accepted as
any value that is neither
true is taken as
false. Also for
each list above, an unbound list entry is taken as
false. Thus, for
CustomiseOutput := rec(group := [,,1], autgroup := [,1])
specifies for the group output that only the presentation of immediate descendants is desired, for the automorphism group output only the automorphism group description of descendants should be printed, that there should be no algorithm trace data, and that the default output should be provided for the permutation group and orbit output.
Specifies that the file to which the standard presentation is written has name filename. If the first character of the string filename is not
/, filename is assumed to be the path of a writable file relative to the directory in which GAP was started. If this option is omitted it is written to the file with the name generated by the command
Filename( ANUPQData.tmpdir, "SPres" );, i.e. the file with name
"SPres"in the temporary directory in which the
Specifies a queue factor of n, where n should be a positive integer. This option may be used with
The queue factor is used when the
pq program uses automorphisms to close
a set of elements of the p-multiplicator under their action.
The algorithm used is a spinning algorithm: it starts with a set of vectors in echelonized form (elements of the p-multiplicator) and closes the span of these vectors under the action of the automorphisms. For this each automorphism is applied to each vector and it is checked if the result is contained in the span computed so far. If not, the span becomes bigger and the vector is put into a queue and the automorphisms are applied to this vector at a later stage. The process terminates when the automorphisms have been applied to all vectors and no new vectors have been produced.
For each new vector it is decided, if its processing should be delayed. If the vector contains too many non-zero entries, it is put into a second queue. The elements in this queue are processed only when there are no elements in the first queue left.
The queue factor is a percentage figure. A vector is put into the second queue if the percentage of its non-zero entries exceeds the queue factor.
Specifies a lower and upper bound on the indices of a list, where list is a pair of positive non-decreasing integers. See PqDisplayStructure and PqDisplayAutomorphisms where this option may be used.
Specifies that automorphism matrices be printed.
Specifies that permutations of the subgroups be printed.
Specifies that an output or input file to be written to or read from by the
pqprogram should have the name string.
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