45.12 Tietze Options

is a record whose components direct the heuristics applied by the Tietze transformation functions.

You may alter the value of any of these Tietze options by just assigning a new value to the respective record component.

The following Tietze options are recognized by GAP:

protected:

The first protected generators in a presentation P are protected from being eliminated by the Tietze transformations functions. There are only two exceptions: The option protected is ignored by the functions TzEliminate(P,gen) and TzSubstitute(P,n,eliminate) because they explicitly specify the generator to be eliminated. The default value of protected is 0.

eliminationsLimit:

Whenever the elimination phase of the TzGo command is entered for a presentation P, then it will eliminate at most eliminationsLimit generators (except for further ones which have turned out to be trivial). Hence you may use the eliminationsLimit parameter as a break criterion for the TzGo command. Note, however, that it is ignored by the TzEliminate command. The default value of eliminationsLimit is 100.

expandLimit:

Whenever the routine for eliminating more than 1 generators is called for a presentation P by the TzEliminate command or the elimination phase of the TzGo command, then it saves the given total length of the relators, and subsequently it checks the current total length against its value before each elimination. If the total length has increased to more than expandLimit per cent of its original value, then the routine returns instead of eliminating another generator. Hence you may use the expandLimit parameter as a break criterion for the TzGo command. The default value of expandLimit is 150.

generatorsLimit:

Whenever the elimination phase of the TzGo command is entered for a presentation P with n generators, then it will eliminate at most n - generatorsLimit generators (except for generators which turn out to be trivial). Hence you may use the generatorsLimit parameter as a break criterion for the TzGo command. The default value of generatorsLimit is 0.

lengthLimit:

The Tietze transformation commands will never eliminate a generator of a presentation P, if they cannot exclude the possibility that the resulting total length of the relators exceeds the value of lengthLimit. The default value of lengthLimit is infinity.

loopLimit:

Whenever the TzGo command is called for a presentation P, then it will loop over at most loopLimit of its basic steps. Hence you may use the loopLimit parameter as a break criterion for the TzGo command. The default value of loopLimit is infinity.

printLevel:

Whenever Tietze transformation commands are called for a presentation P with printLevel = 0, they will not provide any output except for error messages. If printLevel = 1, they will display some reasonable amount of output which allows you to watch the progress of the computation and to decide about your next commands. In the case printLevel = 2, you will get a much more generous amount of output. Finally, if printLevel = 3, various messages on internal details will be added. The default value of printLevel is 1.

saveLimit:

Whenever the TzSearch command has finished its main loop over all relators of a presentation P, then it checks whether during this loop the total length of the relators has been reduced by at least saveLimit per cent. If this is the case, then TzSearch repeats its procedure instead of returning. Hence you may use the saveLimit parameter as a break criterion for the TzSearch command and, in particular, for the search phase of the TzGo command. The default value of saveLimit is 10.

searchSimultaneous:

Whenever the TzSearch or the TzSearchEqual command is called for a presentation P, then it is allowed to handle up to searchSimultaneous short relators simultaneously (see for the description of the TzSearch command for more details). The choice of this parameter may heavily influence the performance as well as the result of the TzSearch and the TzSearchEqual commands and hence also of the search phase of the TzGo command. The default value of searchSimultaneous is 20.

prints the current values of the Tietze options of the presentation P.

gap> TzPrintOptions( P );
#I  protected          = 0
#I  eliminationsLimit  = 100
#I  expandLimit        = 150
#I  generatorsLimit    = 0
#I  lengthLimit        = infinity
#I  loopLimit          = infinity
#I  printLevel         = 1
#I  saveLimit          = 10
#I  searchSimultaneous = 20

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