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/**************************************************************************** ** *A tietze.h GAP source Volkmar Felsch ** *A @(#)$Id: tietze.h,v 3.1 1992/11/16 18:57:36 martin Rel $ ** *Y Copyright 1990-1992, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany ** ** This file defines the functions for computing with finite presentations. ** *H $Log: tietze.h,v $ *H Revision 3.1 1992/11/16 18:57:36 martin *H initial revision under RCS *H */ /**************************************************************************** ** *F TzRelExponent1( <relator> ) . . . . find the exponent of a Tietze relator ** ** 'TzRelExponent1' determines the exponent of the given relator, i. e. the ** maximal integer n such that the relator can be expresses as an nth power. */ extern TypHandle TzRelExponent1 P(( TypHandle hdRel )); /**************************************************************************** ** *F FunTzRelator( <hdCall> ) . . . . . . . convert a word to a Tietze relator ** ** 'FunTzRelator' converts a word in the group generators to a Tietze re- ** lator, i.e. a free and cyclically reduced word in the Tietze generators. ** It returns 'HdFalse" if it cannot convert the given word. */ extern TypHandle FunTzRelator P(( TypHandle hdCall )); /**************************************************************************** ** *F FunTzWord( <hdCall> ) . . . . . . . . convert a Tietze relator to a word ** ** 'FunTzWord' converts a Tietze relator to a word in the group generators. */ extern TypHandle FunTzWord P(( TypHandle hdCall )); /**************************************************************************** ** *F FunTzSortC(<hdCall>) . . . . . . . . . . . . sort the relators by length */ extern TypHandle FunTzSortC P(( TypHandle hdCall )); /**************************************************************************** ** *F FunTzRenumberGens(<hdCall>) . . . . . . . renumber the Tietze generators */ extern TypHandle FunTzRenumberGens P(( TypHandle hdCall )); /**************************************************************************** ** *F FunTzReplaceGens(<hdCall>) . . . replace Tietze generators by other ones */ extern TypHandle FunTzReplaceGens P(( TypHandle hdCall )); /**************************************************************************** ** *F FunTzSubstituteGen(<hdCall>) . . replace a Tietze generator by some word */ extern TypHandle FunTzSubstituteGen P(( TypHandle hdCall )); /**************************************************************************** ** *F FunTzOccurrences( <hdCall> ) . . . . . . occurrences of Tietze generators ** ** 'FunTzOccurrences' implements the internal function 'TzOccurrences'. */ extern TypHandle FunTzOccurrences P(( TypHandle hdCall )); /**************************************************************************** ** *F FunTzOccurrencesPairs(<hdCall>) occurrences of pairs of Tietze generators */ extern TypHandle FunTzOccurrencesPairs P(( TypHandle hdCall )); /**************************************************************************** ** *F FunTzSearchC(<hdCall>) . . . . . find subword matches in Tietze relators ** ** 'FunTzSearchC' implements the internal function 'TzSearchC'. */ extern TypHandle FunTzSearchC P(( TypHandle hdCall )); /**************************************************************************** ** *F InitTietze() . . . . . . . . . . . . . . . . . initialize tietze package ** ** 'InitTietze' initializes the Tietze package. */ extern void InitTietze P(( void ));
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