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#############################################################################
##
#W rwspcclt.gd GAP Library Frank Celler
##
#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
##
## This file contains operations for polycyclic rewriting systems, with or
## without torsion free generators. There are two subcategories, namely
## polycyclic rewriting systems defined by a power/commutator presentation
## and rws defined by a power/conjugate presentation.
##
## Any implementation of a collector must at least specify a way to
## construct such a collector and must implement methods for `SetPower' and
## `CollectWordOrFail'. A power/commutator collector must also implement
## `SetCommutator', a power/conjugate collector `SetConjugate'. The
## operation `CollectWordOrFail' allows a collector to return `fail' if
## the given stacks were too small, however in this case
## `CollectWordOrFail' is responsible for enlarging the stacks. The
## default method for `CollectWord' uses `CollectWordOrFail' and copy.
##
## The default method for `ReducedForm' uses `CollectWordOrFail' in order to
## compute the reduced form.
##
## Polycyclic rewriting systems assume that the underlying structures are
## groups, therefore they have the feature `IsBuiltFromGroup'.
##
## Polycyclic rewriting systems must also specify how to construct a word in
## the underlying free group given an exponent vector. The operation is
## `ObjExponents'.
##
## As in most applications you will start with an empty collector, fill in
## most of the commutators and powers, and then start collecting, a
## collector can be up to date or out of date. If the feature
## `IsUpToDatePolycyclicCollector' is present, then `CollectWord' can be
## used. Otherwise `UpdatePolycyclicCollector' must be called before using
## `CollectWord'.
##
## WARNING: you must *never* ever install an implications for
## `IsUpToDatePolycyclicCollector' because it is reset when the presentation
## is changed.
##
#############################################################################
##
#C IsPolycyclicCollector( <obj> )
##
## <ManSection>
## <Filt Name="IsPolycyclicCollector" Arg='obj' Type='Category'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareCategory(
"IsPolycyclicCollector",
IsRewritingSystem and IsBuiltFromGroup );
#############################################################################
##
#C IsPowerConjugateCollector( <obj> )
##
## <ManSection>
## <Filt Name="IsPowerConjugateCollector" Arg='obj' Type='Category'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareCategory(
"IsPowerConjugateCollector",
IsPolycyclicCollector );
#############################################################################
##
#C IsPowerCommutatorCollector( <obj> )
##
## <ManSection>
## <Filt Name="IsPowerCommutatorCollector" Arg='obj' Type='Category'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareCategory(
"IsPowerCommutatorCollector",
IsPolycyclicCollector );
#############################################################################
##
#A RelativeOrders( <col> )
##
## <ManSection>
## <Attr Name="RelativeOrders" Arg='col'/>
##
## <Description>
## The list of relative orders corresponding to <A>col</A>.
## </Description>
## </ManSection>
##
DeclareAttribute( "RelativeOrders", IsRewritingSystem );
#############################################################################
##
#P IsUpToDatePolycyclicCollector( <col> )
##
DeclareFilter("IsUpToDatePolycyclicCollector");
#############################################################################
##
#O OutdatePolycyclicCollector( <col> )
##
## <ManSection>
## <Oper Name="OutdatePolycyclicCollector" Arg='col'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"OutdatePolycyclicCollector",
[ IsPolycyclicCollector and IsMutable ] );
#############################################################################
##
#O UpdatePolycyclicCollector( <col> )
##
## <ManSection>
## <Oper Name="UpdatePolycyclicCollector" Arg='col'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"UpdatePolycyclicCollector",
[ IsPolycyclicCollector ] );
#############################################################################
##
#O CollectWord( <col>, <v>, <w> )
##
DeclareOperation(
"CollectWord",
[ IsPolycyclicCollector, IsList, IsObject ] );
#############################################################################
##
#O CollectWordOrFail( <col>, <v>, <w> )
##
## <ManSection>
## <Oper Name="CollectWordOrFail" Arg='col, v, w'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"CollectWordOrFail",
[ IsPolycyclicCollector, IsList, IsObject ] );
#############################################################################
##
#O NonTrivialRightHandSides( <col> )
##
## <ManSection>
## <Oper Name="NonTrivialRightHandSides" Arg='col'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"NonTrivialRightHandSides",
[ IsPolycyclicCollector ] );
#############################################################################
##
#O ObjByExponents( <col>, <data> )
##
## <ManSection>
## <Oper Name="ObjByExponents" Arg='col, data'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"ObjByExponents",
[ IsPolycyclicCollector, IsObject ] );
#############################################################################
##
#O SetCommutator( <col>, <i>, <j>, <rhs> )
##
## <ManSection>
## <Oper Name="SetCommutator" Arg='col, i, j, rhs'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"SetCommutator",
[ IsPolycyclicCollector and IsMutable, IsObject, IsObject, IsObject ] );
DeclareOperation(
"SetCommutatorNC",
[ IsPolycyclicCollector and IsMutable, IsObject, IsObject, IsObject ] );
DeclareOperation(
"SetCommutatorANC",
[ IsPolycyclicCollector and IsMutable, IsObject, IsObject, IsObject ] );
#############################################################################
##
#O SetConjugate( <col>, <i>, <j>, <rhs> )
##
## <ManSection>
## <Oper Name="SetConjugate" Arg='col, i, j, rhs'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"SetConjugate",
[ IsPolycyclicCollector and IsMutable, IsObject, IsObject, IsObject ] );
DeclareOperation(
"SetConjugateNC",
[ IsPolycyclicCollector and IsMutable, IsObject, IsObject, IsObject ] );
DeclareOperation(
"SetConjugateANC",
[ IsPolycyclicCollector and IsMutable, IsObject, IsObject, IsObject ] );
#############################################################################
##
#O SetPower( <col>, <i>, <rhs> )
##
## <ManSection>
## <Oper Name="SetPower" Arg='col, i, rhs'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"SetPower",
[ IsPolycyclicCollector and IsMutable, IsObject, IsObject ] );
DeclareOperation(
"SetPowerNC",
[ IsPolycyclicCollector and IsMutable, IsObject, IsObject ] );
DeclareOperation(
"SetPowerANC",
[ IsPolycyclicCollector and IsMutable, IsObject, IsObject ] );
#############################################################################
##
#O SetRelativeOrder( <col>, <i>, <order> )
##
## <ManSection>
## <Oper Name="SetRelativeOrder" Arg='col, i, order'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"SetRelativeOrder",
[ IsPolycyclicCollector and IsMutable, IsObject, IsObject ] );
DeclareOperation(
"SetRelativeOrderNC",
[ IsPolycyclicCollector and IsMutable, IsObject, IsObject ] );
#############################################################################
##
#O GetCommutatorNC( <col>, <h>, <g> )
##
## <ManSection>
## <Oper Name="GetCommutatorNC" Arg='col, h, g'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"GetCommutatorNC",
[ IsPolycyclicCollector, IsObject, IsObject ] );
#############################################################################
##
#O GetConjugateNC( <col>, <h>, <g> )
##
## <ManSection>
## <Oper Name="GetConjugateNC" Arg='col, h, g'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"GetConjugateNC",
[ IsPolycyclicCollector, IsObject, IsObject ] );
#############################################################################
##
#O GetPowerNC( <col>, <g> )
##
## <ManSection>
## <Oper Name="GetPowerNC" Arg='col, g'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"GetPowerNC",
[ IsPolycyclicCollector, IsObject ] );
#############################################################################
##
#O SingleCollector( <fgrp>, <orders> )
##
## creates a single collector to the free group <fgrp> and the relative
## orders <orders>.
##
DeclareOperation(
"SingleCollector",
[ IsObject, IsObject ] );
#############################################################################
##
#O SingleCollectorByGenerators( <fam>, <gens>, <orders> )
##
## <ManSection>
## <Oper Name="SingleCollectorByGenerators" Arg='fam, gens, orders'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"SingleCollectorByGenerators",
[ IsFamily, IsList, IsList ] );
#T 1997/01/16 fceller was old `NewConstructor'
#############################################################################
##
#O CombinatorialCollector( <fgrp>, <orders> )
##
## <ManSection>
## <Oper Name="CombinatorialCollector" Arg='fgrp, orders'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"CombinatorialCollector",
[ IsObject, IsObject ] );
#############################################################################
##
#O CombinatorialCollectorByGenerators( <fam>, <gens>, <orders> )
##
## <ManSection>
## <Oper Name="CombinatorialCollectorByGenerators" Arg='fam, gens, orders'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"CombinatorialCollectorByGenerators",
[ IsFamily, IsList, IsList ] );
#############################################################################
##
#O DeepThoughtCollector( <fgrp>, <orders> )
##
## <ManSection>
## <Oper Name="DeepThoughtCollector" Arg='fgrp, orders'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"DeepThoughtCollector",
[ IsObject, IsObject ] );
#############################################################################
##
#O DeepThoughtCollectorByGenerators( <fam>, <gens>, <orders> )
##
## <ManSection>
## <Oper Name="DeepThoughtCollectorByGenerators" Arg='fam, gens, orders'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation(
"DeepThoughtCollectorByGenerators",
[ IsFamily, IsList, IsList ] );
#############################################################################
##
#O EvaluateOverlapCBA . . . . . . . . . . . . . evaluate a consistency test
#O EvaluateOverlapBNA . . . . . . . . . . . . . evaluate a consistency test
#O EvaluateOverlapBAN . . . . . . . . . . . . . evaluate a consistency test
#O EvaluateOverlapANA . . . . . . . . . . . . . evaluate a consistency test
##
## <ManSection>
## <Oper Name="EvaluateOverlapCBA" Arg='...'/>
## <Oper Name="EvaluateOverlapBNA" Arg='...'/>
## <Oper Name="EvaluateOverlapBAN" Arg='...'/>
## <Oper Name="EvaluateOverlapANA" Arg='...'/>
##
## <Description>
## </Description>
## </ManSection>
##
DeclareOperation( "EvaluateOverlapCBA",
[ IsPolycyclicCollector, IsList, IsList, IsInt, IsInt, IsInt ] );
DeclareOperation( "EvaluateOverlapBNA",
[ IsPolycyclicCollector, IsList, IsList, IsInt, IsInt, IsInt ] );
DeclareOperation( "EvaluateOverlapBAN",
[ IsPolycyclicCollector, IsList, IsList, IsInt, IsInt, IsInt ] );
DeclareOperation( "EvaluateOverlapANA",
[ IsPolycyclicCollector, IsList, IsList, IsInt, IsInt ] );
#############################################################################
##
#E