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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Frank Celler.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains the operations for groups defined by rewriting
## systems.
##
## `GroupByRws' tries to convert a rewriting system into a group. The
## generic method requires that the underlying structure is a group.
## Rewriting system constructors should set the rewriting system feature
## `IsBuiltFromGroup' in this case.
##
#############################################################################
##
#C IsElementsFamilyByRws . category of elements family constructed with RWS
##
DeclareCategory(
"IsElementsFamilyByRws",
IsFamily );
#############################################################################
##
#O MultiplicativeElementsWithInversesFamilyByRws( <rws> ) . . . this family
##
## <ManSection>
## <Oper Name="MultiplicativeElementsWithInversesFamilyByRws" Arg='rws'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"MultiplicativeElementsWithInversesFamilyByRws",
[ IsRewritingSystem ] );
#############################################################################
##
#C IsMultiplicativeElementWithInverseByRws . . . category of these elements
##
DeclareCategory(
"IsMultiplicativeElementWithInverseByRws",
IsMultiplicativeElementWithInverse );
#############################################################################
##
#O ElementByRws( <fam>, <elm> ) . . . . . . . . . construct such an element
##
## <ManSection>
## <Oper Name="ElementByRws" Arg='fam, elm'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"ElementByRws",
[ IsElementsFamilyByRws, IsObject ] );
#############################################################################
##
#O GroupByRws( <rws> ) . . . . . . . . . . . . construct a group from a RWS
##
## <ManSection>
## <Oper Name="GroupByRws" Arg='rws'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"GroupByRws",
[ IsRewritingSystem ] );
#############################################################################
##
#O GroupByRwsNC( <rws> ) . . . . . . . . . . . construct a group from a RWS
##
## <ManSection>
## <Oper Name="GroupByRwsNC" Arg='rws'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"GroupByRwsNC",
[ IsRewritingSystem ] );
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