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# 4 Options for ACE

### Sections

1. Passing ACE Options
2. Warnings regarding Options
3. Abbreviations and mixed case for ACE Options
4. Honouring of the order in which ACE Options are passed
5. What happens if no ACE Strategy Option or if no ACE Option is passed
6. Interpretation of ACE Options
7. An Example of passing Options
8. The KnownACEOptions Record
9. The ACEStrategyOptions List
10. ACE Option Synonyms
11. Non-ACE-binary Options
12. ACE Parameter Options
13. General ACE Parameter Options that Modify the Enumeration Process
14. ACE Parameter Options Modifying C Style Definitions
15. ACE Parameter Options for R Style Definitions
16. ACE Parameter Options for Deduction Handling
17. Technical ACE Parameter Options
18. ACE Parameter Options controlling ACE Output
19. ACE Parameter Options that give Names to the Group and Subgroup
20. Options for redirection of ACE Output
21. Other Options

ACE offers a wide range of options to direct and guide a coset enumeration, most of which are available from GAP through the interface provided by the ACE Package. We describe most of the options available via the interface in this chapter; other options, termed strategies, are defined in Chapter Strategy Options for ACE. (Strategies are merely special options of ACE that set a number of options described in this chapter, all at once.) Yet other options, for which interactive function alternatives are provided in Chapter Functions for Using ACE Interactively, or which most GAP users are unlikely to need, are described in Appendix Other ACE Options. From within a GAP session, one may see the complete list of ACE options, after loading the ACE Package (see Section Loading the ACE Package), by typing

    gap> RecNames(KnownACEOptions);
    [ "aceinfile", "aceignore", "aceignoreunknown", "acenowarnings", "aceecho",
      "aceincomment", "aceexampleoptions", "silent", "lenlex", "semilenlex",
      "incomplete", "sg", "rl", "aep", "ai", "ao", "aceoutfile", "asis", "begin",
      "start", "bye", "exit", "qui", "cc", "cfactor", "ct", "check", "redo",
      "compaction", "continu", "cycles", "dmode", "dsize", "default", "ds", "dr",
      "dump", "easy", "echo", "enumeration", "felsch", "ffactor", "fill",
      "group", "generators", "relators", "hard", "help", "hlt", "hole",
      "lookahead", "loop", "max", "mendelsohn", "messages", "monitor", "mode",
      "nc", "normal", "no", "options", "oo", "order", "path", "pmode", "psize",
      "sr", "print", "purec", "purer", "rc", "recover", "contiguous", "rep",
      "rfactor", "rt", "row", "sc", "stabilising", "sims", "standard",
      "statistics", "stats", "style", "subgroup", "system", "text", "time", "tw",
      "trace", "workspace" ]

(See Section The KnownACEOptions Record.) 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 ACE option, simply type: ```?option` option``'', where option is one of the options listed above without any quotes, e.g.

    gap> ?option echo

will display the section in this manual that describes the `echo` option.

We begin this chapter with several sections discussing the nature of the options provided. Please spend some time reading these sections. To continue onto the next section on-line using GAP's help browser, type:

    gap> ?>

## 4.1 Passing ACE Options

Options are passed to the ACE interface functions in either of the two usual mechanisms provided by GAP, namely:

- options may be set globally using the function `PushOptions` (see Chapter Options Stack in the GAP Reference Manual); or

- options may be appended to the argument list of any function call, separated by a colon from the argument list (see Function Calls in the GAP Reference Manual), in which case they are then passed on recursively to any subsequent inner function call, which may in turn have options of their own.

In general, if ACE is to be used interactively one should avoid using the global method of passing options. In fact, it is recommended that prior to calling `ACEStart` the `OptionsStack` be empty.

## 4.2 Warnings regarding Options

As mentioned above, one can set options globally using the function `PushOptions` (see Chapter Options Stack in the GAP Reference Manual); however, options pushed onto `OptionsStack`, in this way, remain there until an explicit `PopOptions()` call is made. In contrast, options passed in the usual way behind a colon following a function's arguments (see Function Calls in the GAP Reference Manual) are local, and disappear from `OptionsStack` after the function has executed successfully; nevertheless, a function, that is passed options this way, will also see any global options or any options passed down recursively from functions calling that function, unless those options are over-ridden by options passed via the function. Also note that duplication of option names for different programs may lead to misinterpretations. Since a non-empty `OptionsStack` is potentially a mine-field for the unwary user, the function `ResetOptionsStack` (see ResetOptionsStack in the Reference Manual) is now in the GAP library and

- `FlushOptionsStack() F`

  introduced in version 3.001 of the ACE Package to perform the same function, is now a synonym for `ResetOptionsStack`; it simply executes `PopOptions()` until `OptionsStack` is empty.

  However, `ResetOptionsStack` (or `FlushOptionsStack`) does not wipe out the options already passed to an interactive ACE process. We have provided `GetACEOptions` (see GetACEOptions) to keep track of options that the ACE binary process still considers active, which may or may not be still on the `OptionsStack`. There is the interactive `SetACEOptions` (see SetACEOptions) to change such options, or, of course, you can always elect to use `ACEQuit` (see ACEQuit) and then start a new interactive ACE process.

  Finally, if `ACEIgnoreUnknownDefault := false` (see ACEIgnoreUnknownDefault), there will be situations where an ACE interface function needs to be told explicitly to ignore options passed down recursively to it from calling functions. For this purpose we have provided the options `aceignore` (see option aceignore) and `aceignoreunknown` (see option aceignoreunknown).

  ## 4.3 Abbreviations and mixed case for ACE Options

  Except for limitations imposed by GAP e.g. clashes with GAP keywords and blank spaces not allowed in keywords, the options of the ACE interface are the same as for the binary; so, for example, the options can appear in upper or lower case (or indeed, mixed case) and most may be abbreviated. Below we only list the options in all lower case, and in their longest form; where abbreviation is possible we give the shortest abbreviation in the option's description e.g. for the `mendelsohn` option we state that its shortest abbreviation is `mend`, which means `mende`, `mendel` etc., and indeed, `Mend` and `MeND`, are all valid abbreviations of that option. Some options have synonyms e.g. `cfactor` is an alternative for `ct`.

  The complete list of ACE options known to the ACE interface functions, their abbreviations and the values that they are known to take may be gleaned from the `KnownACEOptions` record (see Section The KnownACEOptions Record).

  Options for the ACE interface functions `ACECosetTableFromGensAndRels`, `ACECosetTable`, `ACEStats` and `ACEStart` (see Chapter Functions for Using ACE Interactively), comprise the few non-ACE-binary options (`silent`, `aceinfile`, `aceoutfile`, `aceignore`, `aceignoreunknown`, `acenowarnings`, `aceincomment`, `aceecho` and `echo`) discussed in Section Non-ACE-binary Options, (almost) all single-word ACE binary options and `purer` and `purec`. The options `purer` and `purec` give the ACE binary options `pure r` and `pure c`, respectively; (they are the only multiple-word ACE binary options that do not have a single word alternative). The only single-word ACE binary options that are not available via the ACE interface are abbreviations that clash with GAP keywords (e.g. `fi` for `fill`, `rec` for `recover` and `continu` for `continue`). The detail of this paragraph is probably of little importance to the GAP user; these comments have been included for the user who wishes to reconcile the respective functionalities of the ACE interface and the ACE standalone, and are probably of most value to standalone users.

  ## 4.4 Honouring of the order in which ACE Options are passed

  It is important to realize that ACE's options (even the non-strategy options) are not orthogonal, i.e. the order in which they are put to ACE can be important. For this reason, except for a few options that have no effect on the course of an enumeration, the order in which options are passed to the ACE interface is preserved when those same options are passed to the ACE binary. One of the reasons for the non-orthogonality of options is to protect the user from obtaining invalid enumerations from bad combinations of options; another reason is that commonly one may specify a strategy option and override some of that strategy's defaults; the general rule is that the later option prevails. By the way, it's not illegal to select more than one strategy, but it's not sensible; as just mentioned, the later one prevails.

  ## 4.5 What happens if no ACE Strategy Option or if no ACE Option is passed

  If an ACE interface function (`ACECosetTableFromGensAndRels`, `ACEStats`, `ACECosetTable` or `ACEStart`) is given no strategy option, the `default` strategy (see Chapter Strategy Options for ACE) is selected, and a number of options that ACE needs to have a value for are given default values, prior to the execution of any user options, if any. This ensures that ACE has a value for all its ``run parameters''; three of these are defined from the ACE interface function arguments; and the remaining ``run parameters'', we denote by ``ACE Parameter Options''. For user convenience, we have provided the `ACEParameterOptions` record (see ACEParameterOptions), the fields of which are the ``ACE Parameter Options''. The value of each field (option) of the `ACEParameterOptions` record is either a default value or (in the case of an option that is set by a strategy) a record of default values that ACE assumes when the user does not define a value for the option (either indirectly by selecting a strategy option or directly).

  If the `default` strategy does not suffice, most usually a user will select one of the other strategies from among the ones listed in Chapter Strategy Options for ACE, and possibly modify some of the options by selecting from the options in this chapter. It's not illegal to select more than one strategy, but it's not sensible; as mentioned above, the later one prevails.

  ## 4.6 Interpretation of ACE Options

  Options may be given a value by an assignment to the name (such as `time :=` val``); or be passed without assigning a value, in which case GAP treats the option as boolean and sets the option to the value `true`, which is then interpreted by the ACE interface functions. Technically speaking the ACE binary itself does not have boolean options, though it does have some options which are declared by passing without a value (e.g. the `hard` strategy option) and others that are boolean in the C-sense (taking on just the values 0 or 1). The behaviour of the ACE interface functions (`ACECosetTableFromGensAndRels`, `ACEStats`, `ACECosetTable` or `ACEStart`) is essentially to restore as much as is possible a behaviour that mimics the ACE standalone; a `false` value is always translated to 0 and `true` may be translated to any of no-value, 0 or 1. Any option passed with an assigned value val other than `false` or `true` is passed with the value val to the ACE binary. Since this may appear confusing, let's consider some examples.

  - The `hard` strategy option (see option hard) should be passed without a value, which in turn is passed to the ACE binary without a value. However, the ACE interface function cannot distinguish the option `hard` being passed without a value, from it being passed via `hard := true`. Passing `hard := false` or `hard :=` val`` for any non-`true` val will however produce a warning message (unless the option `acenowarnings` is passed) that the value 0 (for `false`) or val is unknown for that option. Nevertheless, despite the warning, in this event, the ACE interface function passes the value to the ACE binary. When the ACE binary sees a line that it doesn't understand it prints a warning and simply ignores it. (So passing `hard := false` will produce warnings, but will have no ill effects.) The reason we still pass unknown values to the ACE binary is that it's conceivable a future version of the ACE binary might have several `hard` strategies, in which case the ACE interface function will still complain (until it's made aware of the new possible values) but it will perform in the correct manner if a value expected by the ACE binary is passed.

  - The `felsch` strategy option (see option felsch) may be passed without a value (which chooses the felsch 0 strategy) or with the values 0 or 1. Despite the fact that GAP sees this option as boolean; it is not. There are two Felsch strategies: felsch 0 and felsch 1. To get the felsch 1 strategy, the user must pass `felsch := 1`. If the user were to pass `felsch := false` the result would be the felsch 0 strategy (since `false` is always translated to 0), i.e. the same as how `felsch := true` would be interpreted. We could protect the user more from such ideosyncrasies, but we have erred on the side of simplicity in order to make the interface less vulnerable to upgrades of the ACE binary.

  The lesson from the two examples is: check the documentation for an option to see how it will be interpreted. In general, options documented (in this chapter) as only being no-value options can be safely thought of as boolean (i.e. you will get what you expect by assigning `true` or `false`), whereas strategy (no-value) options should not be thought of as boolean (a `false` assignment will not give you what you might have expected).

  Options that are unknown to the ACE interface functions and not ignored (see below), that are passed without a value, are always passed to the ACE binary as no-value options (except when the options are ignored); the user can over-ride this behaviour simply by assigning the intended value. Note that it is perfectly safe to allow the ACE binary to be passed unknown options, since ACE simply ignores options it doesn't understand, issues an error message (which is just a warning and is output by GAP unless `acenowarnings` (see option acenowarnings) is passed) and continues on with any other options passed in exactly the way it would have if the ``unknown'' options had not been passed.

  An option is ignored if it is unknown to the ACE interface functions and one of the following is true:

  - the global variable `ACEIgnoreUnknownDefault` is set to `false` (see ACEIgnoreUnknownDefault) or,

  - the `aceignoreunknown` option (see option aceignoreunknown) is passed, or

  - the `aceignore` option is passed and the option is an element of the list value of `aceignore` (see option aceignore).

  It is actually recommended that the user set `ACEIgnoreUnknownDefault` to `false`, since this will allow the user to see when ACE functions have been passed options that are ``unknown'' to the ACE package. In this way the user will be informed about misspelt options, for example. So it's a good debugging tool. Also, if the ACE binary is updated with a version with new options then these will not be known by the package (the GAP part) and it will be necessary to set `ACEIgnoreUnknownDefault` to `false` in order for the new options to be passed to the binary. When an ACE function is invoked indirectly by some function that was called with non-ACE options the warning messages may begin to be annoying, and it's then a simple matter to set `ACEIgnoreUnknownDefault` back to the ACE 3.003 default value of `true`.

  Warning messages regarding unknown options are printed unless the `acenowarnings` (see option acenowarnings) is passed or the option is ignored.

  To see how options are interpreted by an ACE interface function, pass the `echo` option.

  As mentioned above, any option that the ACE binary doesn't understand is simply ignored and a warning appears in the output from ACE. If this occurs, you may wish to check the input fed to ACE and the output from ACE, which when ACE is run non-interactively are stored in files whose full path names are recorded in the record fields `ACEData.infile` and `ACEData.outfile`, respectively. Alternatively, both interactively and non-interactively one can set the `InfoLevel` of `InfoACE` to 3 (see SetInfoACELevel), to see the output from ACE, or to 4 to also see the commands directed to ACE.

  ## 4.7 An Example of passing Options

  Continuing with the example of Section Using ACE Directly to Generate a Coset Table, one could set the `echo` option to be true, use the `hard` strategy option, increase the workspace to 107 words and turn messaging on (but to be fairly infrequent) by setting `messages` to a large positive value as follows:

      gap> ACECosetTable(fgens, rels, [c]
      >                  : echo, hard, Wo := 10^7, mess := 10000);;

  As mentioned in the previous section, `echo` may be thought of as a boolean option, whereas `hard` is a strategy option (and hence should be thought of as a no-value option). Also, observe that two options have been abbreviated: `Wo` is a mixed case abbreviation of `workspace`, and `mess` is an abbreviation of `messages`.

  ## 4.8 The KnownACEOptions Record

- `KnownACEOptions V`

  is a GAP record whose fields are the ACE options known to the ACE interface; each field (known ACE option) is assigned to a list of the form `[`i`,` ListOrFunction`]`, where ``i`` is an integer representing the length of the shortest abbreviation of the option and ``ListOrFunction`` is either a list of (known) allowed values or a boolean function that may be used to determine if the given value is a (known) valid value e.g.

      gap> KnownACEOptions.compaction;
      [ 3, [ 0 .. 100 ] ]

  indicates that the option `compaction` may be abbreviated to `com` and the (known) valid values are in the (integer) range 0 to 100; and

      gap> KnownACEOptions.ct;
      [ 2, <Operation "IS_INT"> ]

  indicates that there is essentially no abbreviation of `ct` (since its shortest abbreviation is of length 2), and a value of `ct` is known to be valid if `IsInt` returns true for that value.

  For user convenience, we provide the function

- `ACEOptionData(` optname`) F`

  which for a string optname representing an ACE option (or a guess of one) returns a record with the following fields:

  `name`
    optname (unchanged);

  `known`
    `true` if optname is a valid mixed case abbreviation of a known ACE option, and false otherwise;

  `fullname`
    the lower case unabbreviated form of optname if the `known` field is set `true`, or optname in all lower case, otherwise;

  `synonyms`
    a list of known ACE options synonymous with optname, in lowercase unabbreviated form, if the `known` field is set `true`, or a list containing just optname in all lower case, otherwise;

  `abbrev`
    the shortest lowercase abbreviation of optname if the `known` field is set `true`, or optname in all lower case, otherwise.

  For more on synonyms of ACE options, see ACEOptionSynonyms.

  The function `ACEOptionData` provides the user with all the query facility she should ever need; nevertheless, we provide the following functions.

- `IsKnownACEOption(` optname`) F`

  returns `true` if optname is a mixed case abbreviation of a field of `KnownACEOptions`, or `false` otherwise. `IsKnownACEOption(`optname`);` is equivalent to

  `ACEOptionData(`optname`).known;`

- `ACEPreferredOptionName(` optname`) F`

  returns the lowercase unabbreviated first alternative of optname if it is a known ACE option, or optname in lowercase, otherwise. `ACEPreferredOptionName(`optname`);` is equivalent to

  `ACEOptionData(`optname`).synonyms[1];`

- `IsACEParameterOption(` optname`) F`

  returns true if optname is an ``ACE parameter option''. (ACE Parameter Options are described in Section ACEParameterOptions). `IsACEParameterOption(`optname`);` is equivalent to

  `ACEPreferredOptionName(`optname`) in RecNames(ACEParameterOptions);`

- `IsACEStrategyOption(` optname`) F`

  returns true if optname is an ``ACE strategy option'' (see Section The ACEStrategyOptions list). `IsACEStrategyOption(`optname`);` is equivalent to

  `ACEPreferredOptionName(`optname`) in ACEStrategyOptions;`

  ## 4.9 The ACEStrategyOptions List

- `ACEStrategyOptions V`

  is a GAP list that contains the strategy options known to the ACE interface functions:

      gap> ACEStrategyOptions;
      [ "default", "easy", "felsch", "hard", "hlt", "purec", "purer", "sims" ]

  See Chapter Strategy Options for ACE for details regarding the ACE strategy options.

  ## 4.10 ACE Option Synonyms

- `ACEOptionSynonyms V`

  is a GAP record. A number of known ACE options have synonyms. The fields of the `ACEOptionSynonyms` record are the ``preferred'' option names and the values assigned to the fields are the lists of synonyms of those option names. What makes an option name ``preferred'' is somewhat arbitrary (in most cases, it is simply the shortest of a list of synonyms). For a ``preferred'' option name optname that has synonyms, the complete list of synonyms may be obtained by concatenating `[` optname`]` and `ACEOptionSynonyms.(`optname`)`, e.g.

      gap> Concatenation( [ "messages" ], ACEOptionSynonyms.("messages") );
      [ "messages", "monitor" ]

  More generally, for an arbitrary option name optname its list of synonyms (which may be a list of one element) may be obtained as the `synonyms` field of the record returned by `ACEOptionData(`optname`)` (see ACEOptionData).

  ## 4.11 Non-ACE-binary Options

- `NonACEbinOptions V`

  is a GAP list of options that have meaning only for the ACE Package interface, i.e. options in `KnownACEOptions` that are not ACE binary options; each such option is described in detail below. Except for the options listed in `NonACEbinOptions` and those options that are excluded via the `aceignore` and `aceignoreunknown` options (described below), all options that are on the `OptionsStack` when an ACE interface function is called, are passed to the ACE binary. Even options that produce the warning message: ```unknown (maybe new) or bad`'', by virtue of not being a field of `KnownACEOptions`, are passed to the ACE binary (except that the options `purer` and `purec` are first translated to `pure r` and `pure c`, respectively). When the ACE binary encounters an option that it doesn't understand it issues a warning and simply ignores it; so options accidentally passed to ACE are unlikely to pose problems.

  We also mention here, since it is related to an option of this section, the following.

- `ACEIgnoreUnknownDefault V`

  is a global variable (not an option) that is initially set by the ACE package to `true`, and is the default action that ACE takes for options that are unknown to the ACE package (but may be new options provided in a new version of the ACE binary). Despite the fact that it is normally set `true`, it is recommended (especially for the novice user of the ACE package) to set `ACEIgnoreUnknownDefault := false`; the worst that can happen is being annoyed by a profusion of warnings of unknown options. For individual functions, the user may use the option `aceignoreunknown` (see option aceignoreunknown) to over-ride the setting of `ACEIgnoreUnknownDefault`.

  Here now, are the few options that are available to the GAP interface to ACE that have no counterpart in the ACE standalone:

- `silent
  ` Inhibits an `Error` return when generating a coset table.

  If a coset enumeration that invokes `ACECosetTableFromGensAndRels` does not finish within the preset limits, an error is raised by the interface to GAP, unless the option `silent` or `incomplete` (see option incomplete) has been set; in the former case, `fail` is returned. This option is included to make the behaviour of `ACECosetTableFromGensAndRels` compatible with that of the function `CosetTableFromGensAndRels` it replaces. If the option `incomplete` is also set, it overrides option `silent`.

- `lenlex
  ` Ensures that `ACECosetTable` and `ACECosetTableFromGensAndRels` output a coset table that is `lenlex` standardised.

  The `lenlex` scheme, numbers cosets in such a way that their ``preferred'' (coset) representatives, in an alphabet consisting of the user-submitted generators and their inverses, are ordered first according to `length` and then according to a `lexical` ordering. In order to describe what the `lenlex` scheme's `lexical` ordering is, let us consider an example. Suppose the generators submitted by the user are, in user-supplied order, `[x, y, a, b]`, and represent the inverses of these generators by the corresponding uppercase letters: `[X, Y, A, B]`, then the `lexical` ordering of `lenlex` is that derived from defining `x < X < y < Y < a < A < b < B`.

  Notes: In some circumstances, ACE prefers to swap the first two generators; such cases are detected by the function `IsACEGeneratorsInPreferredOrder` (see IsACEGeneratorsInPreferredOrder). In such cases, special action is taken to avoid ACE swapping the first two generators; this action is described in the notes for `ACEStandardCosetNumbering` (see ACEStandardCosetNumbering). When this special action is invoked, a side-effect is that any setting of the `asis` (see option asis) option by the user is ignored.

  The `lenlex` standardisation scheme is the default coset table standardisation scheme of GAP (since version 4.3). However, `semilenlex` was the standardisation scheme for versions of GAP up to GAP 4.2. Both schemes are described in detail in Section Coset Table Standardisation Schemes.

- `semilenlex
  ` Ensures that `ACECosetTable` and `ACECosetTableFromGensAndRels` output a coset table that is `semilenlex` standardised.

  The `semilenlex` scheme, numbers cosets in such a way that their ``preferred'' (coset) representatives, in an alphabet consisting of only the user-submitted generators, are ordered first according to `length` and then according to a `lexical` ordering.

  Note: Up to GAP 4.2, `semilenlex` was the default standardisation scheme used by GAP (see also option lenlex).

- `incomplete
  ` Allows the return of an `incomplete` coset table, when a coset enumeration does not finish within preset limits.

  If a coset enumeration that invokes `ACECosetTableFromGensAndRels` or `ACECosetTable` does not finish within the preset limits, an error is raised by the interface to GAP, unless the option `silent` (see option silent) or `incomplete` has been set; in the latter case, a partial coset table, that is a valid GAP list of lists, is returned. Each position of the table without a valid coset number entry is filled with a zero. If the option `silent` is also set, `incomplete` prevails. Since GAP 4.3, an incomplete table is returned reduced (i.e. with insignificant coset numbers --- those appearing only in their place of definition --- removed) and `lenlex` standardised (regardless of whether the `semilenlex` option is in force). (For GAP 4.2, an incomplete table was returned unstandardised unless the `lenlex` option (see option lenlex) was also set, and the table was also not reduced.) When an incomplete table is returned, a warning is emitted at `InfoACE` or `InfoWarning` level 1.

- `aceinfile:=`filename`
  ` Creates an ACE input file filename for use with the standalone only; filename should be a string. (Shortest abbreviation: `acein`.)

  This option is only relevant to `ACECosetTableFromGensAndRels` and is ignored if included as an option for invocations of `ACEStats` and `ACEStart`. If this option is used, GAP creates an input file with filename filename only, and then exits (i.e. the ACE binary is not called). This option is provided for users who wish to work directly with the ACE standalone. The full path to the input file normally used by ACE (i.e. when option `aceinfile` is not used) is stored in `ACEData.infile`.

- `aceoutfile:=`filename`
  ` Redirects ACE output to file filename; filename should be a string. (Shortest abbreviation: `aceo`.)

  This is actually a synonym for the `ao` option. Please refer to option ao, for further discussion of this option.

- `aceignore:=`optionList`
  ` Directs an ACE function to ignore the options in optionList; optionList should be a list of strings. (Shortest abbreviation: `aceig`.)

  If a function called with its own options, in turn calls an ACE function for which those options are not intended, the ACE function will pass those options to the ACE binary. If those options are unknown to the ACE interface (and `ACEIgnoreUnknownDefault := false` and `aceignoreunknown` is not passed; see ACEIgnoreUnknownDefault and option aceignoreunknown) a warning is issued. Options that are unknown to the ACE binary are simply ignored by ACE (and a warning that the option was ignored appears in the ACE output, which the user will not see unless the `InfoLevel` of `InfoACE` or `InfoWarning` is set to 1). This option enables the user to avoid such options being passed at all, thus avoiding the warning messages and also any options that coincidentally are ACE options but are not intended for the ACE function being called.

- `aceignoreunknown
  ` Directs an ACE function to ignore any options not known to the ACE interface. (Shortest abbreviation: `aceignoreu`.)

  This option is provided for similar reasons to `aceignore`. Normally, it is safe to include it, to avoid aberrant warning messages from the ACE interface. However, fairly obviously, it should not be passed without a value (or set to `true`) in the situation where a new ACE binary has been installed with new options that are not listed among the fields of `KnownACEOptions`, which you intend to use. Omitting the `aceignoreunknown` option is equivalent to setting it to the value of `ACEIgnoreUnknownDefault` (see ACEIgnoreUnknownDefault); i.e. it is superfluous if `ACEIgnoreUnknownDefault := true` unless `aceignoreunknown` is set to `false`.

- `acenowarnings
  ` Inhibits the warning message ```unknown (maybe new) or bad option`'' for options not listed in `KnownACEOptions`. (Shortest abbreviation: `acenow`.)

  This option suppresses the warning messages for unknown options (to the ACE interface), but unlike `aceignore` and `aceignoreunknown` still allows them to be passed to the ACE binary.

- `echo`
- `echo:=2
  ` Echoes arguments and options (and indicates how options were handled).

  Unlike the previous options of this section, there is an ACE binary option `echo`. However, the `echo` option is handled by the ACE interface and is not passed to the ACE binary. (If you wish to put `echo` in a standalone script use the `aceecho` option following.) If `echo` is passed with the value 2 then a list of the options (together with their values) that are set via ACE defaults are also echoed to the screen.

- `aceecho
  ` The ACE binary's `echo` command.

  This option is only included so that a user can put an `echo` statement in an ACE standalone script. Otherwise, use `echo` (above).

- `aceincomment:=`string`
  ` Print comment string in the ACE input; string must be a string. (Shortest abbreviation: `aceinc`.)

  This option prints the comment string behind a sharp sign (`#`) in the input to ACE. Only useful for adding comments (that ACE ignores) to standalone input files.

- `aceexampleoptions
  ` An internal option for `ACEExample`.

  This option is passed internally by `ACEExample` to the ACE interface function it calls, when one invokes `ACEExample` with options. Its purpose is to provide a mechanism for the over-riding of an example's options by the user. The option name is deliberately long and has no abbreviation to discourage user use.

  ## 4.12 ACE Parameter Options

- `ACEParameterOptions V`

  is a GAP record, whose fields are the ``ACE Parameter Options''. The ``ACE Parameter Options'' are options which, if not supplied a value by the user, are supplied a default value by ACE. In fact, the ``ACE Parameter Options'' are those options that appear (along with `Group Generators`, `Group Relators` and `Subgroup Generators`, which are defined from ACE interface function arguments) in the ``Run Parameters'' block of ACE output, when, for example, the `messages` option is non-zero.

  For each field (ACE parameter option) of the `ACEParameterOptions` record, the value assigned is the default value (or a record of default values) that are supplied by ACE when the option is not given a value by the user (either indirectly by selecting a strategy option or directly).

  In the cases where the value of a field of the `ACEParameterOptions` record is itself a record, the fields of that record are `default` and strategies for which the value assigned by that strategy differs from the `default` strategy. A ``strategy'', here, is the strategy option itself, if it is only a no-value option, or the strategy option concatenated with any of its integer values (as strings), otherwise (e.g. `felsch0` and `sims9` are strategies, and `hlt` is both a strategy and a strategy option). As an exercise, the reader might like to try to reproduce the table at the beginning of Chapter Strategy Options for ACE using the `ACEParameterOptions` record. (Hint: you first need to select those fields of the `ACEParameterOptions` record whose values are records with at least two fields.)

  Note: Where an ``ACE Parameter Option'' has synonyms, only the ``preferred'' option name (see ACEOptionSynonyms) appears as a field of `ACEParameterOptions`. The complete list of ``ACE Parameter Options'' may be obtained by

      gap> Concatenation( List(RecNames(ACEParameterOptions),
      >                        optname -> ACEOptionData(optname).synonyms) );
      [ "asis", "ct", "cfactor", "compaction", "dmode", "dsize", "enumeration",
        "fill", "ffactor", "hole", "lookahead", "loop", "max", "mendelsohn",
        "messages", "monitor", "no", "path", "pmode", "psize", "rt", "rfactor",
        "row", "subgroup", "time", "workspace" ]

  We describe the ``ACE Parameter Options'' in the Sections General ACE Parameter Options that Modify the Enumeration Process, ACE Parameter Options Modifying C Style Definitions, ACE Parameter Options for R Style Definitions, ACE Parameter Options for Deduction Handling, Technical ACE Parameter Options, ACE Parameter Options controlling ACE Output, and ACE Parameter Options that give Names to the Group and Subgroup, following.

  ## 4.13 General ACE Parameter Options that Modify the Enumeration Process

- `asis
  ` Do not reduce relators. (Shortest abbreviation: `as`.)

  By default, ACE freely and cyclically reduces the relators, freely reduces the subgroup generators, and sorts relators and subgroup generators in length-increasing order. If you do not want this, you can switch it off by setting the `asis` option.

  Notes: As well as allowing you to use the presentation as it is given, this is useful for forcing definitions to be made in a prespecified order, by introducing dummy (i.e., freely trivial) subgroup generators. (Note that the exact form of the presentation can have a significant impact on the enumeration statistics.) For some fine points of the influence of `asis` being set on the treatment of involutory generators see the ACE standalone manual.

- `ct:=`val``
- `cfactor:=`val`
  ` Number of C style definitions per pass; ``val`` should be an integer. (Shortest abbreviation of `cfactor` is `c`.)

  The absolute value of ``val`` sets the number of C style definitions per pass through the enumerator's main loop. The sign of ``val`` sets the style. The possible combinations of the values of `ct` and `rt` (described below) are given in the table of enumeration styles in Section Enumeration Style.

- `rt:=`val``
- `rfactor:=`val`
  ` Number of R style definitions per pass; ``val`` should be an integer. (Shortest abbreviation of `rfactor` is `r`.)

  The absolute value of ``val`` sets the number of R style definitions per pass through the enumerator's main loop. The sign of ``val`` sets the style. The possible combinations of the values of `ct` (described above) and `rt` are given in the table of enumeration styles in Section Enumeration Style.

- `no:=`val`
  ` The number of group relators to include in the subgroup; ``val`` should be an integer greater than or equal to -1.

  It is sometimes helpful to include the group relators into the list of the subgroup generators, in the sense that they are applied to coset number 1 at the start of an enumeration. A value of 0 for this option turns this feature off and the (default) argument of -1 includes all the relators. A positive argument includes the specified number of relators, in order. The `no` option affects only the C style procedures.

- `mendelsohn
  ` Turns on mendelsohn processing. (Shortest abbreviation: `mend`.)

  Mendelsohn style processing during relator scanning/closing is turned on by giving this option. Off is the default, and here relators are scanned only from the start (and end) of a relator. Mendelsohn ``on'' means that all (different) cyclic permutations of a relator are scanned.

  The effect of Mendelsohn style processing is case-specific. It can mean the difference between success or failure, or it can impact the number of coset numbers required, or it can have no effect on an enumeration's statistics.

  Note: Processing all cyclic permutations of the relators can be very time-consuming, especially if the presentation is large. So, all other things being equal, the Mendelsohn flag should normally be left off.

  ## 4.14 ACE Parameter Options Modifying C Style Definitions

  The next three options are relevant only for making C style definitions (see Section Enumeration Style). Making definitions in C style, that is filling the coset table line by line, it can be very advantageous to switch to making definitions from the preferred definition stack. Possible definitions can be extracted from this stack in various ways and the two options `pmode` and `psize` (see option pmode and option psize respectively) regulate this. However it should be clearly understood that making all definitions from a preferred definition stack one may violate the condition of Mendelsohn's theorem, and the option `fill` (see option fill) can be used to avoid this.

- `fill:=`val``
- `ffactor:=`val`
  ` Controls the preferred definition strategy by setting the fill factor; ``val`` must be a non-negative integer. (Shortest abbreviation of `fill` is `fil`, and shortest abbreviation of `ffactor` is `f`.)

  Unless prevented by the fill factor, gaps of length one found during deduction testing are preferentially filled (see Hav91). However, this potentially violates the formal requirement that all rows in the coset table are eventually filled (and tested against the relators). The fill factor is used to ensure that some constant proportion of the coset table is always kept filled. Before defining a coset number to fill a gap of length one, the enumerator checks whether `fill` times the completed part of the table is at least the total size of the table and, if not, fills coset table rows in standard order (i.e. C style; see Section Enumeration Style) instead of filling gaps.

  An argument of 0 selects the default value of ë5(n+2)/4 û, where n is the number of columns in the table. This default fill factor allows a moderate amount of gap-filling. If `fill` is 1, then there is no gap-filling. A large value of `fill` can cause what is in effect infinite looping (resolved by the coset enumeration failing). However, in general, a large value does work well. The effects of the various gap-filling strategies vary widely. It is not clear which values are good general defaults or, indeed, whether any strategy is always ``not too bad''.

  This option is identified as `Fi` in the ``Run Parameters'' block (obtained when `messages` is non-zero) of the ACE output, since for the ACE binary, `fi` is an allowed abbreviation of `fill`. However, `fi` is a GAP keyword and so the shortest abbreviation of `fill` allowed by the interface functions is `fil`.

- `pmode:=`val`
  ` Option for preferred definitions; ``val`` should be in the integer range 0 to 3. (Shortest abbreviation: `pmod`.)

  The value of the `pmode` option determines which definitions are preferred. If the argument is 0, then Felsch style definitions are made using the next empty table slot. If the argument is non-zero, then gaps of length one found during relator scans in Felsch style are preferentially filled (subject to the value of `fill`). If the argument is 1, they are filled immediately, and if it is 2, the consequent deduction is also made immediately (of course, these are also put on the deduction stack). If the argument is 3, then the gaps of length one are noted in the preferred definition queue.

  Provided such a gap survives (and no coincidence occurs, which causes the queue to be discarded) the next coset number will be defined to fill the oldest gap of length one. The default value is either 0 or 3, depending on the strategy selected (see Chapter Strategy Options for ACE). If you want to know more details, read the code.

- `psize:=`val`
  ` Size of preferred definition queue; ``val`` must be 0 or 2n, for some integer n > 0. (Shortest abbreviation: `psiz`.)

  The preferred definition queue is implemented as a ring, dropping earliest entries. An argument of 0 selects the default size of 256. Each queue slot takes two words (i.e., 8 bytes), and the queue can store up to 2n-1 entries.

  ## 4.15 ACE Parameter Options for R Style Definitions

- `row:=`val`
  ` Set the ``row filling'' option; ``val`` is either 0 or 1.

  By default, ``row filling'' is on (i.e. `true` or 1). To turn it off set `row` to `false` or 0 (both are translated to 0 when passed to the ACE binary). When making HLT style (i.e. R style; see Section Enumeration Style) definitions, rows of the coset table are scanned for holes after its coset number has been applied to all relators, and definitions are made to fill any holes encountered. This will, in particular, guarantee fulfilment of the condition of Mendelsohn's Theorem. Failure to do so can cause even simple enumerations to overflow.

- `lookahead:=`val`
  ` Lookahead; ``val`` should be in the integer range 0 to 4. (Shortest abbreviation: `look`.)

  Although HLT style strategies are fast, they are local, in the sense that the implications of any definitions/deductions made while applying coset numbers may not become apparent until much later. One way to alleviate this problem is to perform lookaheads occasionally; that is, to test the information in the table, looking for deductions or concidences. ACE can perform a lookahead when the table overflows, before the compaction routine is called. Lookahead can be done using the entire table or only that part of the table above the current coset number, and it can be done R style (scanning coset numbers from the beginning of relators) or C style (testing all definitions in all essentially different positions).

  The following are the effects of the possible values of `lookahead`:

  - 0 disables lookahead;
  - 1 does a partial table lookahead, R style;
  - 2 does a whole table lookahead, C style;
  - 3 does a whole table lookahead, R style; and
  - 4 does a partial table lookahead, C style.

  The default is 1 if the `hlt` strategy is used and 0 otherwise; see Chapter Strategy Options for ACE.

  Section Enumeration Style describes the various enumeration styles, and, in particular, R style and C style.

  ## 4.16 ACE Parameter Options for Deduction Handling

- `dmode:=`val`
  ` Deduction mode; ``val`` should be in the integer range 0 to 4. (Shortest abbreviation: `dmod`.)

  A completed table is only valid if every table entry has been tested in all essentially different positions in all relators. This testing can either be done directly (`felsch` strategy; see option felsch) or via relator scanning (`hlt` strategy; see option hlt). If it is done directly, then more than one deduction (i.e., table entry) can be waiting to be processed at any one time. So the untested deductions are stored in a stack. Normally this stack is fairly small but, during a collapse, it can become very large.

  This command allows the user to specify how deductions should be handled. The value val has the following interpretations:

  - 0: discard deductions if there is no stack space left;

  - 1: as for 0, but purge any redundant coset numbers on the top of the stack at every coincidence;

  - 2: as for 0, but purge all redundant coset numbers from the stack at every coincidence;

  - 3: discard the entire stack if it overflows; and

  - 4: if the stack overflows, double the stack size and purge all redundant coset numbers from the stack.

  The default deduction mode is either 0 or 4, depending on the strategy selected (see Chapter Strategy Options for ACE), and it is recommended that you stay with the default. If you want to know more details, read the well-commented C code.

  Notes: If deductions are discarded for any reason, then a final relator check phase will be run automatically at the end of the enumeration, if necessary, to check the result.

- `dsize:=`val`
  ` Deduction stack size; ``val`` should be a non-negative integer. (Shortest abbreviation: `dsiz`.)

  Sets the size of the (initial) allocation for the deduction stack. The size is in terms of the number of deductions, with one deduction taking two words (i.e., 8 bytes). The default size, of 1000, can be selected by a value of 0. See the `dmode` entry for a (brief) discussion of deduction handling.

  ## 4.17 Technical ACE Parameter Options

  The following options do not affect how the coset enumeration is done, but how it uses the computer's resources. They might thus affect the runtime as well as the range of problems that can be tackled on a given machine.

- `workspace:=`val`
  ` Workspace size in words (default 106); ``val`` should be an expression that evaluates to a positive integer, or a string of digits ending in a `k`, `M` or `G` representing a multiplication factor of 103, 106 or 109, respectively e.g. both `workspace := 2 * 10^6` and `workspace := "2M"` specify a workspace of 2×106 words. Actually, if the value of `workspace` is entered as a string, each of `k`, `M` or `G` will be accepted in either upper or lower case. (Shortest abbreviation: `wo`.)

  By default, ACE has a physical table size of 106 words (i.e., 4 ×106 bytes in the default 32-bit environment). The number of coset numbers in the table is the table size divided by the number of columns. Although the number of coset numbers is limited to 231-1 (if the C `int` type is 32 bits), the table size can exceed the 4GByte 32-bit limit if a suitable machine is used.

- `time:=`val`
  ` Maximum execution time in seconds; ``val`` must be an integer greater than or equal to -1. (Shortest abbreviation: `ti`.)

  The `time` command puts a time limit (in seconds) on the length of a run. The default is -1 which is no time limit. If the argument is ³ 0 then the total elapsed time for this call is checked at the end of each pass through the enumerator's main loop, and if it's more than the limit the run is stopped and the current table returned.

  Note that a limit of 0 performs exactly one pass through the main loop, since 0 ³ 0.

  The time limit is approximate, in the sense that the enumerator may run for a longer, but never a shorter, time. So, if there is, e.g., a big collapse (so that the time round the loop becomes very long), then the run may run over the limit by a large amount.

  Notes: The time limit is CPU-time, not wall-time. As in all timing under UNIX, the clock's granularity (usually 10 milliseconds) and the system load can affect the timing; so the number of main loop iterations in a given time may vary.

- `loop:=`val`
  ` Loop limit; ``val`` should be a non-negative integer.

  The core enumerator is organised as a state machine, with each step performing an ``action'' (i.e., lookahead, compaction) or a block of actions (i.e., |`ct`| coset number definitions, |`rt`| coset number applications). The number of passes through the main loop (i.e., steps) is counted, and the enumerator can make an early return when this count hits the value of `loop`. A value of 0, the default, turns this feature off.

  Guru Notes: You can do lots of really neat things using this feature, but you need some understanding of the internals of ACE to get real benefit from it.

- `path
  ` Turns on path compression.

  To correctly process multiple concidences, a union-find must be performed. If both path compression and weighted union are used, then this can be done in essentially linear time (see, e.g., CLR90). Weighted union alone, in the worst-case, is worse than linear, but is subquadratic. In practice, path compression is expensive, since it involves many coset table accesses. So, by default, path compression is turned off; it can be turned on by `path`. It has no effect on the result, but may affect the running time and the internal statistics.

  Guru Notes: The whole question of the best way to handle large coincidence forests is problematic. Formally, ACE does not do a weighted union, since it is constrained to replace the higher-numbered of a coincident pair. In practice, this seems to amount to much the same thing! Turning path compression on cuts down the amount of data movement during coincidence processing at the expense of having to trace the paths and compress them. In general, it does not seem to be worthwhile.

- `compaction:=`val`
  ` Percentage of dead coset numbers to trigger compaction; ``val`` should be an integer (percentage) in the integer range 0 to 100. (Shortest abbreviation: `com`.)

  The option `compaction` sets the percentage of dead coset numbers needed to trigger compaction of the coset table, during an enumeration. A dead coset (number) is a coset number found to be coincident with a smaller coset number. The default is 10 or 100, depending on the strategy used (see Chapter Strategy Options for ACE).

  Compaction recovers the space allocated to coset numbers which are flagged as dead. It results in a table where all the active coset numbers are numbered contiguously from 1, and with the remainder of the table available for new coset numbers.

  The coset table is compacted when a definition of a coset number is required, there is no space for a new coset number available, and provided that the given percentage of the coset table contains dead coset numbers. For example, if `compaction` = 20 then compaction will occur only if 20% or more of the coset numbers in the table are dead. An argument of 100 means that compaction is never performed, while an argument of 0 means always compact, no matter how few dead coset numbers there are (provided there is at least one, of course).

  Compaction may be performed multiple times during an enumeration, and the table that results from an enumeration may or may not be compact, depending on whether or not there have been any coincidences since the last compaction (or from the start of the enumeration, if there have been no compactions).

  Notes: In some strategies (e.g., `hlt`; see option hlt) a lookahead phase may be run before compaction is attempted. In other strategies (e.g., `sims := 3`; see option sims) compaction may be performed while there are outstanding deductions; since deductions are discarded during compaction, a final lookahead phase will (automatically) be performed.

  Compacting a table ``destroys'' information and history, in the sense that the coincidence list is deleted, and the table entries for any dead coset numbers are deleted.

- `max:=`val`
  ` Sets the maximum coset number that can be defined; ``val`` should be 0 or an integer greater than or equal to 2.

  By default (which is the case `max`=0), all of the workspace is used, if necessary, in building the coset table. So the table size (in terms of the number of rows) is an upper bound on how many coset numbers can be alive at any one time. The `max` option allows a limit to be placed on how much physical table space is made available to the enumerator. Enough space for at least two coset numbers (i.e., the subgroup and one other) must be made available.

  Notes: If the `easy` strategy (see option easy) is selected, so that `compaction` (see option compaction) is off (i.e. set to 100) and `lookahead` (see option lookahead) is off (i.e. set to 0), and `max` is set to a positive integer, then coset numbers are not reused, and hence `max` bounds the total number `totcosets` (see Section Coset Statistics Terminology) of coset numbers defined during an enumeration.

  On the other hand, if one (or both) of `compaction` or `lookahead` is not off, then some reuse of coset numbers may occur, so that, for the case where `max` is a positive integer, the value of `totcosets` may be greater than `max`.

  However, whenever `max` is set to a positive integer, both activecosets (the number of alive coset numbers at the end of an enumeration) and maxcosets (the maximum number of alive coset numbers at any point of an enumeration) are bounded by `max`. See Section Coset Statistics Terminology, for a discussion of the terminology: activecosets and maxcosets.

- `hole:=`val`
  ` Maximum percentage of holes allowed during an enumeration; ``val`` should be an integer in the range -1 to 100. (Shortest abbreviation: `ho`.)

  This is an experimental feature which allows an enumeration to be terminated when the percentage of holes in the table exceeds a given value. In practice, calculating this is very expensive, and it tends to remain constant or decrease throughout an enumeration. So the feature doesn't seem very useful. The default value of -1 turns this feature off. If you want more details, read the source code.

  ## 4.18 ACE Parameter Options controlling ACE Output

- `messages:=`val``
- `monitor:=`val`
  ` Sets the verbosity of output from ACE; val should be an integer. (Shortest abbreviation of `messages` is `mess`, and shortest abbreviation of `monitor` is `mon`.)

  By default, val = 0, for which ACE prints out only a single line of information, giving the result of each enumeration. If val is non-zero then the presentation and the parameters are echoed at the start of the run, and messages on the enumeration's status as it progresses are also printed out. The absolute value of val sets the frequency of the progress messages, with a negative sign turning hole monitoring on. Note that, hole monitoring is expensive, so don't turn it on unless you really need it.

  Note that, ordinarily, one will not see these messages: non-interactively, these messages are directed to file `ACEData.outfile` (or filename, if option `aceoutfile :=` filename``, or `ao :=` filename``, is used), and interactively these messages are simply not displayed. However, one can change this situation both interactively and non-interactively by setting the `InfoLevel` of `InfoACE` to 3 via

      gap> SetInfoACELevel(3);

  Then ACE's messages are displayed prepended with ```#I` ''. Please refer to Appendix The Meanings of ACE's output messages, where the meanings of ACE's output messages are fully discussed.

  ## 4.19 ACE Parameter Options that give Names to the Group and Subgroup

  These options may be safely ignored; they only give names to the group or subgroup within the ACE output, and have no effect on the enumeration itself.

- `enumeration:=`string`
  ` Sets the `Group Name` to string; string, must of course be a string. (Shortest abbreviation: `enum`.)

  The ACE binary has a two-word synonym for this option: `Group Name` and this is how it is identified in the ``Run Parameters'' block of the ACE output when `messages` has a non-zero value. The default `Group Name` is `"G"`.

- `subgroup:=`string`
  ` Sets the `Subgroup Name` to string; string must of course be a string. (Shortest abbreviation: `subg`.)

  The default `Subgroup Name` is `"H"`.

  ## 4.20 Options for redirection of ACE Output

- `ao:=`filename``
- `aceoutfile:=`filename`
  ` Redirects (`a`lters) `o`utput to filename; filename should be a string.

  Non-interactively, ACE's output is normally directed to a temporary file whose full path is stored in `ACEData.outfile`, which is parsed to produce a coset table or a list of statistics. This option causes ACE's output to be directed to filename instead, presumably because the user wishes to see (and keep) data output by the ACE binary, other than the coset table output from `ACECosetTableFromGensAndRels` or the statistics output by `ACEStats`. Please refer to Appendix The Meanings of ACE's output messages, where we discuss the meaning of the additional data to be found in the ACE binary's output. The option `aceoutfile` is a GAP-introduced synonym for `ao`, that is translated to `ao` before submission to the ACE binary. Do not use option `aceoutfile` when running the standalone directly. Happily, `ao` can also be regarded as mnemonical for `aceoutfile`.

  ## 4.21 Other Options

  ACE has a number of other options, but the GAP user will not ordinarily need them, since, in most cases, alternative interactive functions exist. These remaining options have been relegated to Appendix Other ACE Options. The options listed there may be used both interactively and non-interactively, but many are probably best used directly via the ACE standalone.

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