/usr/share/gap/lib/grpfree.gd is in gap-libs 4r7p5-2.
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#W grpfree.gd GAP library Werner Nickel
##
##
#Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## Free groups are treated as special cases of finitely presented groups.
## In addition, elements of a free group are
## (associative) words, that is they have a normal form that allows an easy
## equalitity test.
##
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##
#F IsElementOfFreeGroup . . . . . . . . . . . . . elements in a free group
##
## <ManSection>
## <Func Name="IsElementOfFreeGroup" Arg='obj'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareSynonym( "IsElementOfFreeGroup", IsAssocWordWithInverse );
DeclareSynonym( "IsElementOfFreeGroupFamily",IsAssocWordWithInverseFamily );
#############################################################################
##
#F FreeGroup( [<wfilt>,]<rank> )
#F FreeGroup( [<wfilt>,]<rank>, <name> )
#F FreeGroup( [<wfilt>,]<name1>, <name2>, ... )
#F FreeGroup( [<wfilt>,]<names> )
#F FreeGroup( [<wfilt>,]infinity, <name>, <init> )
##
## <#GAPDoc Label="FreeGroup">
## <ManSection>
## <Heading>FreeGroup</Heading>
## <Func Name="FreeGroup" Arg='[wfilt, ]rank[, name]'
## Label="for given rank"/>
## <Func Name="FreeGroup" Arg='[wfilt, ]name1, name2, ...'
## Label="for various names"/>
## <Func Name="FreeGroup" Arg='[wfilt, ]names'
## Label="for a list of names"/>
## <Func Name="FreeGroup" Arg='[wfilt, ]infinity, name, init'
## Label="for infinitely many generators"/>
##
## <Description>
## Called with a positive integer <A>rank</A>,
## <Ref Func="FreeGroup" Label="for given rank"/> returns
## a free group on <A>rank</A> generators.
## If the optional argument <A>name</A> is given then the generators are
## printed as <A>name</A><C>1</C>, <A>name</A><C>2</C> etc.,
## that is, each name is the concatenation of the string <A>name</A> and an
## integer from <C>1</C> to <A>range</A>.
## The default for <A>name</A> is the string <C>"f"</C>.
## <P/>
## Called in the second form,
## <Ref Func="FreeGroup" Label="for various names"/> returns
## a free group on as many generators as arguments, printed as
## <A>name1</A>, <A>name2</A> etc.
## <P/>
## Called in the third form,
## <Ref Func="FreeGroup" Label="for a list of names"/> returns
## a free group on as many generators as the length of the list
## <A>names</A>, the <M>i</M>-th generator being printed as
## <A>names</A><C>[</C><M>i</M><C>]</C>.
## <P/>
## Called in the fourth form,
## <Ref Func="FreeGroup" Label="for infinitely many generators"/>
## returns a free group on infinitely many generators, where the first
## generators are printed by the names in the list <A>init</A>,
## and the other generators by <A>name</A> and an appended number.
## <P/>
## If the extra argument <A>wfilt</A> is given, it must be either
## <C>IsSyllableWordsFamily</C> or <C>IsLetterWordsFamily</C> or
## <C>IsWLetterWordsFamily</C> or <C>IsBLetterWordsFamily</C>.
## This filter then specifies the representation used for the elements of
## the free group
## (see <Ref Sect="Representations for Associative Words"/>).
## If no such filter is given, a letter representation is used.
## <P/>
## (For interfacing to old code that omits the representation flag, use of
## the syllable representation is also triggered by setting the option
## <C>FreeGroupFamilyType</C> to the string <C>"syllable"</C>.)
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction( "FreeGroup" );
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##
#E
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