|
#############################################################################
##
## 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 generic methods polycyclic rewriting systems.
##
#############################################################################
##
#F IsIdenticalObjFamiliesColObjObj( <rws>, <obj>, <obj> )
##
BindGlobal( "IsIdenticalObjFamiliesColObjObj", function( a, b, c )
return IsIdenticalObj( a!.underlyingFamily, b )
and IsIdenticalObj( b, c );
end );
#############################################################################
##
#F IsIdenticalObjFamiliesColObjObjObj( <rws>, <obj>, <obj>, <obj> )
##
BindGlobal( "IsIdenticalObjFamiliesColObjObjObj", function( a, b, c, d )
return IsIdenticalObj( a!.underlyingFamily, b )
and IsIdenticalObj( b, c )
and IsIdenticalObj( b, d );
end );
#############################################################################
##
#F IsIdenticalObjFamiliesColXXXObj( <col>, <obj>, <obj> )
##
BindGlobal( "IsIdenticalObjFamiliesColXXXObj", function( a, b, c )
return IsIdenticalObj( a!.underlyingFamily, c );
end );
#############################################################################
##
#F IsIdenticalObjFamiliesColXXXXXXObj( <rws>, <obj>, <obj>, <obj> )
##
BindGlobal( "IsIdenticalObjFamiliesColXXXXXXObj", function( a, b, c, d )
return IsIdenticalObj( a!.underlyingFamily, d );
end );
#############################################################################
##
#F FinitePolycyclicCollector_IsConfluent( <col> )
##
BindGlobal( "FinitePolycyclicCollector_IsConfluent", function( col, failed )
local gens, rods, k, gk, j, gj, i, gi, r1, r2, R, R1;
gens := GeneratorsOfRws(col);
rods := RelativeOrders(col);
# be verbose for debugging
Info( InfoTiming + InfoConfluence, 2,
"'IsConfluent' starting part 1" );
R := Runtime(); R1 := R;
# consistency relations: gk * ( gj * gi ) = ( gk * gj ) * gi
for k in [ 1 .. Length(gens) ] do
gk := gens[k];
for j in [ 1 .. k - 1 ] do
gj := gens[j];
for i in [ 1 .. j - 1 ] do
gi := gens[i];
r1 := ReducedProduct(col, gk, ReducedProduct(col, gj, gi));
r2 := ReducedProduct(col, ReducedProduct(col, gk, gj), gi);
if r1 <> r2 then
if failed = false then
return false;
else
Add( failed, [ 1, gk, gj, gi ] );
fi;
fi;
od;
od;
od;
# be verbose for debugging
Info( InfoTiming + InfoConfluence, 2,
"'IsConfluent' part 1 took ", Runtime()-R, " ms, ",
"starting part 2" );
R := Runtime();
# consistency relations: gj^ej-1 * ( gj * gi ) = ( gj^ej-1 * gj ) * gi
for j in [ 1 .. Length(gens) ] do
gj := gens[j];
for i in [ 1 .. j - 1 ] do
gi := gens[i];
r1 := ReducedProduct( col, ReducedPower( col, gj, rods[j]-1 ),
ReducedProduct( col, gj, gi ) );
r2 := ReducedProduct( col, ReducedProduct( col,
ReducedPower( col, gj, rods[j]-1 ), gj ), gi );
if r1 <> r2 then
if failed = false then
return false;
else
Add( failed, [ 2, gj, rods[j]-1, gj, gi ] );
fi;
fi;
od;
od;
# be verbose for debugging
Info( InfoTiming + InfoConfluence, 2,
"'IsConfluent' part 2 took ", Runtime()-R, " ms, ",
"starting part 3" );
R := Runtime();
# consistency relations: gj * ( gi^ei-1 * gi ) = ( gj * gi^ei-1 ) * gi
for j in [ 1 .. Length( gens ) ] do
gj := gens[j];
for i in [ 1 .. j - 1 ] do
gi := gens[i];
r1 := ReducedProduct( col, gj, ReducedProduct( col,
ReducedPower( col, gi, rods[i]-1 ), gi ) );
r2 := ReducedProduct( col, ReducedProduct( col, gj,
ReducedPower( col, gi, rods[i]-1 ) ), gi );
if r1 <> r2 then
if failed = false then
return false;
else
Add( failed, [ 3, gj, gi, rods[i]-1, gi ] );
fi;
fi;
od;
od;
# be verbose for debugging
Info( InfoTiming + InfoConfluence, 2,
"'IsConfluent' part 3 took ", Runtime()-R, " ms, ",
"starting part 4" );
R := Runtime();
# consistency relations: gi * ( gi^ei-1 * gi ) = ( gi * gi^ei-1 ) * gi
for i in [ 1 .. Length( gens ) ] do
gi := gens[i];
r1 := ReducedProduct( col, gi, ReducedProduct( col,
ReducedPower( col, gi, rods[i]-1 ), gi ) );
r2 := ReducedProduct( col, ReducedProduct( col, gi,
ReducedPower( col, gi, rods[i]-1 ) ), gi );
if r1 <> r2 then
if failed = false then
return false;
else
Add( failed, [ 4, gi, gi, rods[i]-1, gi ] );
fi;
fi;
od;
Info( InfoTiming + InfoConfluence, 2,
"'IsConfluent' part 4 took, ", Runtime()-R, " ms" );
Info( InfoTiming + InfoConfluence, 1,
"'IsConfluent' took ", Runtime()-R1, " ms" );
# we passed all consistency checks
if failed = false then
return true;
else
return IsEmpty(failed);
fi;
end );
#############################################################################
##
#M IsConfluent( <col> )
##
#############################################################################
InstallMethod( IsConfluent,
"method for finite polycyclic rewriting systems",
true,
[ IsPolycyclicCollector and IsFinite ],
0,
function( col )
return FinitePolycyclicCollector_IsConfluent( col, false );
end );
#############################################################################
InstallMethod( IsConfluent,
"generic method for polycyclic rewriting systems",
true,
[ IsPolycyclicCollector ],
0,
function( pcp )
local n, k, j, i, ev1, ev2, g, orders;
n := NumberGeneratorsOfRws(pcp);
g := GeneratorsOfRws(pcp);
orders := RelativeOrders(pcp);
# k (j i) = (k j) i
for k in [n,n-1..1] do
for j in [k-1,k-2..1] do
for i in [j-1,j-2..1] do
Info( InfoConfluence, 2, "check ", k, " ", j, " ", i, "\n" );
ev1 := ReducedProduct( pcp, g[k],
ReducedProduct( pcp, g[j], g[i] ) );
ev2 := ReducedProduct( pcp, ReducedProduct( pcp, g[k], g[j] ),
g[i] );
if ev1 <> ev2 then
Print( "Inconsistency at ", k, " ", j, " ", i, "\n" );
return false;
fi;
od;
od;
od;
# j^m i = j^(m-1) (j i)
for j in [n,n-1..1] do
for i in [j-1,j-2..1] do
if orders[j] <> 0 then
Info( InfoConfluence, 2, "check ", j, "^m ", i, "\n" );
ev1 := ReducedProduct( pcp, ReducedPower(pcp, g[j], orders[j]),
g[i] );
ev2 := ReducedProduct( pcp,
ReducedPower( pcp, g[j], orders[j]-1 ),
ReducedProduct( pcp, g[j], g[i] ) );
if ev1 <> ev2 then
Print( "Inconsistency at ", j, "^m ", i, "\n" );
return false;
fi;
fi;
od;
od;
# j * i^m = (j i) * i^(m-1)
for j in [n,n-1..1] do
for i in [j-1,j-2..1] do
if orders[i] <> 0 then
Info( InfoConfluence, 2, "check ", j, " ", i, "^m\n" );
ev1 := ReducedProduct( pcp, g[j],
ReducedPower(pcp, g[i], orders[i]) );
ev2 := ReducedProduct( pcp,
ReducedProduct( pcp, g[j], g[i] ),
ReducedPower(pcp, g[i], orders[i]-1) );
if ev1 <> ev2 then
Print( "Inconsistency at ", j, " ", i, "^m\n" );
return false;
fi;
fi;
od;
od;
# i^m i = i i^m
for i in [n,n-1..1] do
if orders[i] <> 0 then
ev1 := ReducedProduct( pcp, g[i],
ReducedPower( pcp, g[i], orders[i] ) );
ev2 := ReducedProduct( pcp,
ReducedPower( pcp, g[i], orders[i] ),
g[i] );
if ev1 <> ev2 then
Print( "Inconsistency at ", i, "^(m+1)\n" );
return false;
fi;
fi;
od;
# j = (j -i) i
for i in [n,n-1..1] do
if orders[i] = 0 then
for j in [i+1..n] do
Info(InfoConfluence, 2, "check ", j, " ", -i, " ", i, "\n");
ev1 := ReducedProduct( pcp,
ReducedProduct( pcp, g[j],
ReducedInverse( pcp,
g[i] )),
g[i] );
if ev1 <> g[j] then
Print( "Inconsistency at ", j, " ", -i, " ", i, "\n" );
return false;
fi;
od;
fi;
od;
# i = -j (j i)
for j in [n,n-1..1] do
if orders[j] = 0 then
for i in [j-1,j-2..1] do
Info(InfoConfluence, 2, "check ", -j, " ", j, " ", i, "\n");
ev1 := ReducedProduct( pcp, ReducedInverse( pcp, g[j] ),
ReducedProduct( pcp, g[j], g[i] ) );
if ev1 <> g[i] then
Print( "Inconsistency at ", -j, " ", j, " ", i, "\n" );
return false;
fi;
if orders[i] = 0 then
Info(InfoConfluence,2,"check ",-j," ",j," ",-i,"\n");
ev1 := ReducedProduct( pcp, ReducedInverse( pcp, g[j] ),
ReducedProduct( pcp, g[j],
ReducedInverse( pcp, g[i] ) ) );
if ev1 <> ReducedInverse( pcp, g[i] ) then
Print( "Inconsistency at ", -j, " ", j, " ", -i, "\n" );
return false;
fi;
fi;
od;
fi;
od;
return true;
end );
#############################################################################
InstallOtherMethod( IsConfluent,
true,
[ IsPolycyclicCollector and IsFinite,
IsList ],
0,
FinitePolycyclicCollector_IsConfluent );
#############################################################################
##
#M OutdatePolycyclicCollector( <col> )
##
#############################################################################
InstallMethod( OutdatePolycyclicCollector,
true,
[ IsPolycyclicCollector and IsMutable ],
0,
function( col )
ResetFilterObj( col, IsUpToDatePolycyclicCollector );
end );
#############################################################################
##
#M ViewObj( <col> )
##
#############################################################################
InstallMethod( ViewObj, true, [ IsPolycyclicCollector ], 0,
function( col )
Print( "<<polycyclic collector>>");
end );
#############################################################################
InstallMethod( ViewObj, true, [ IsPowerConjugateCollector ], 0,
function( col )
Print( "<<polycyclic collector with conjugates>>");
end );
#############################################################################
InstallMethod( ViewObj, true, [ IsPowerCommutatorCollector ], 0,
function( col )
Print( "<<polycyclic collector with commutators>>");
end );
#############################################################################
##
#M PrintObj( <col> )
##
#############################################################################
InstallMethod( PrintObj, true, [ IsPolycyclicCollector ], 0,
function( col )
Print( "<<polycyclic collector>>");
end );
#T install a better `PrintObj' method!
#############################################################################
InstallMethod( PrintObj, true, [ IsPowerConjugateCollector ], 0,
function( col )
Print( "<<polycyclic collector with conjugates>>");
end );
#T install a better `PrintObj' method!
#############################################################################
InstallMethod( PrintObj, true, [ IsPowerCommutatorCollector ], 0,
function( col )
Print( "<<polycyclic collector with commutators>>");
end );
#T install a better `PrintObj' method!
#############################################################################
##
#M CollectWord( <col>, <v>, <w> )
##
InstallMethod( CollectWord,
IsIdenticalObjFamiliesColXXXObj,
[ IsPolycyclicCollector,
IsList,
IsMultiplicativeElementWithInverse ],
0,
function( col, v, w )
local vv, i;
vv := ShallowCopy(v);
while CollectWordOrFail( col, v, w ) = fail do
for i in [ 1 .. Length(v) ] do
v[i] := vv[i];
od;
od;
return true;
end );
#############################################################################
##
#M CollectWordOrFail( <col>, <v>, <w> )
##
## NOTE: you must install a method for your collector *and* the flag
## 'IsUpToDatePolycyclicCollector'.
##
#############################################################################
InstallMethod( CollectWordOrFail,
IsIdenticalObjFamiliesColXXXObj,
[ IsPolycyclicCollector,
IsList,
IsMultiplicativeElementWithInverse ],
0,
function( col, v, w )
if not IsUpToDatePolycyclicCollector(col) then
UpdatePolycyclicCollector(col);
if not IsUpToDatePolycyclicCollector(col) then
Error( "'UpdatePolycyclicCollector' must set the feature ",
"'IsUpToDatePolycyclicCollector'" );
fi;
fi;
return CollectWordOrFail( col, v, w );
end );
#############################################################################
InstallMethod( CollectWordOrFail,
IsIdenticalObjFamiliesColXXXObj,
[ IsPolycyclicCollector and IsUpToDatePolycyclicCollector,
IsList,
IsMultiplicativeElementWithInverse ], 0,
function( col, v, w )
Error( "no generic method for 'CollectWordOrFail' is known" );
end );
#############################################################################
##
#M ReducedForm( <col>, <word> )
##
InstallMethod( ReducedForm,
"CollectWordOrFail",
IsIdenticalObjFamiliesRwsObj,
[ IsPolycyclicCollector,
IsMultiplicativeElementWithInverse ],
0,
function( col, word )
local l;
# collect <word> into the empty list
l := ListWithIdenticalEntries( NumberGeneratorsOfRws(col), 0);
if CollectWordOrFail( col, l, word ) = fail then
return ReducedForm( col, word );
fi;
# and construct the corresponding word
return ObjByExponents( col, l );
end );
#############################################################################
##
#M ReducedPower( <col>, <obj>, <pow> )
##
InstallMethod( ReducedPower,
"ReducedInverse/CollectWordOrFail",
IsIdenticalObjFamiliesRwsObjXXX,
[ IsPolycyclicCollector,
IsMultiplicativeElementWithInverse,
IsInt ],
0,
function( col, obj, pow )
local res, tmp;
# if <pow> is negative invert <obj> first
if pow < 0 then
obj := ReducedInverse( col, obj );
pow := -pow;
fi;
# if <pow> is zero, reduce the identity
if pow = 0 then
return ReducedOne(col);
# catch some trivial cases
elif pow <= 5 then
if pow = 1 then
return obj;
elif pow = 2 then
res := ListWithIdenticalEntries( NumberGeneratorsOfRws(col), 0 );
if CollectWordOrFail( col, res, obj ) = fail then
return ReducedPower( col, obj, pow );
fi;
if CollectWordOrFail( col, res, obj ) = fail then
return ReducedPower( col, obj, pow );
fi;
return ObjByExponents( col, res );
elif pow = 3 then
res := ListWithIdenticalEntries( NumberGeneratorsOfRws(col), 0 );
if CollectWordOrFail( col, res, obj ) = fail then
return ReducedPower( col, obj, pow );
fi;
if CollectWordOrFail( col, res, obj ) = fail then
return ReducedPower( col, obj, pow );
fi;
if CollectWordOrFail( col, res, obj ) = fail then
return ReducedPower( col, obj, pow );
fi;
return ObjByExponents( col, res );
elif pow = 4 then
res := ListWithIdenticalEntries( NumberGeneratorsOfRws(col), 0 );
if CollectWordOrFail( col, res, obj ) = fail then
return ReducedPower( col, obj, pow );
fi;
if CollectWordOrFail( col, res, obj ) = fail then
return ReducedPower( col, obj, pow );
fi;
tmp := ObjByExponents( col, res );
if CollectWordOrFail( col, res, tmp ) = fail then
return ReducedPower( col, obj, pow );
fi;
return ObjByExponents( col, res );
elif pow = 5 then
res := ListWithIdenticalEntries( NumberGeneratorsOfRws(col), 0 );
if CollectWordOrFail( col, res, obj ) = fail then
return ReducedPower( col, obj, pow );
fi;
if CollectWordOrFail( col, res, obj ) = fail then
return ReducedPower( col, obj, pow );
fi;
tmp := ObjByExponents( col, res );
if CollectWordOrFail( col, res, tmp ) = fail then
return ReducedPower( col, obj, pow );
fi;
if CollectWordOrFail( col, res, obj ) = fail then
return ReducedPower( col, obj, pow );
fi;
return ObjByExponents( col, res );
fi;
fi;
# divide et impera (this is slightly faster then repeated squaring r2l)
if RemInt( pow, 2 ) = 1 then
res := ReducedPower( col, obj, QuoInt(pow-1,2) );
res := ReducedProduct( col, res, res );
return ReducedProduct( col, obj, res );
else
res := ReducedPower( col, obj, QuoInt(pow,2) );
return ReducedProduct( col, res, res );
fi;
end );
#############################################################################
##
#M SetCommutator( <col>, <i>, <j>, <rhs> )
##
#############################################################################
InstallMethod( SetCommutator,"elements",
IsIdenticalObjFamiliesColObjObjObj,
[ IsPolycyclicCollector and IsMutable,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse ],
0,
function( col, gi, gj, rhs )
local g;
g := GeneratorsOfRws( col );
SetCommutator( col, Position( g, gi ), Position( g, gj ), rhs );
end );
#############################################################################
InstallMethod( SetCommutatorNC,"elements",
IsIdenticalObjFamiliesColObjObjObj,
[ IsPowerConjugateCollector and IsMutable,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse ],
0,
function( col, gi, gj, rhs )
local g;
g := GeneratorsOfRws( col );
SetCommutatorNC( col, Position( g, gi ), Position( g, gj ), rhs );
end );
#############################################################################
InstallMethod( SetCommutatorNC,"integers",
IsIdenticalObjFamiliesColXXXXXXObj,
[ IsPowerConjugateCollector and IsMutable,
IsInt,
IsInt,
IsMultiplicativeElementWithInverse ],
0,
function( col, i, j, rhs )
SetConjugateNC( col, i, j, GeneratorsOfRws(col)[i]*rhs );
end );
#############################################################################
InstallMethod( SetCommutator,"integers",
IsIdenticalObjFamiliesColXXXXXXObj,
[ IsPowerConjugateCollector and IsMutable,
IsInt,
IsInt,
IsObject ],
0,
function( col, i, j, rhs )
SetConjugate( col, i, j, GeneratorsOfRws(col)[i]*rhs );
end );
#############################################################################
##
#M SetConjugate( <col>, <i>, <j>, <rhs> )
##
#############################################################################
InstallMethod( SetConjugate,
IsIdenticalObjFamiliesColObjObjObj,
[ IsPolycyclicCollector and IsMutable,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse ],
0,
function( col, gi, gj, rhs )
local g;
g := GeneratorsOfRws( col );
SetConjugate( col, Position( g, gi ), Position( g, gj ), rhs );
end );
#############################################################################
InstallMethod( SetConjugateNC,
IsIdenticalObjFamiliesColObjObjObj,
[ IsPolycyclicCollector and IsMutable,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse ],
0,
function( col, gi, gj, rhs )
local g;
g := GeneratorsOfRws( col );
SetConjugateNC( col, Position( g, gi ), Position( g, gj ), rhs );
end );
#############################################################################
InstallMethod( SetConjugate,
IsIdenticalObjFamiliesColXXXXXXObj,
[ IsPowerCommutatorCollector and IsMutable,
IsInt,
IsInt,
IsMultiplicativeElementWithInverse ],
0,
function( col, i, j, rhs )
SetCommutator( col, i, j, GeneratorsOfRws(col)[i]^-1*rhs );
end );
#############################################################################
InstallMethod( SetConjugateNC,
IsIdenticalObjFamiliesColXXXXXXObj,
[ IsPowerCommutatorCollector and IsMutable,
IsInt,
IsInt,
IsMultiplicativeElementWithInverse ],
0,
function( col, i, j, rhs )
SetCommutatorNC( col, i, j, GeneratorsOfRws(col)[i]^-1*rhs );
end );
#############################################################################
##
#M SetPower( <col>, <i>, <rhs> )
##
#############################################################################
InstallMethod( SetPower,
IsIdenticalObjFamiliesColObjObj,
[ IsPolycyclicCollector and IsMutable,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse ],
0,
function( col, gi, rhs )
SetPower( col, Position(GeneratorsOfRws(col),gi), rhs );
end );
#############################################################################
InstallMethod( SetPowerNC,
IsIdenticalObjFamiliesColObjObj,
[ IsPolycyclicCollector and IsMutable,
IsMultiplicativeElementWithInverse,
IsMultiplicativeElementWithInverse ],
0,
function( col, gi, rhs )
SetPowerNC( col, Position(GeneratorsOfRws(col),gi), rhs );
end );
#############################################################################
##
#M SetRelativeOrder( <col>, <i>, <ord> )
##
#############################################################################
InstallMethod( SetRelativeOrder,
IsIdenticalObjFamiliesColObjObj,
[ IsPolycyclicCollector and IsMutable,
IsMultiplicativeElementWithInverse,
IsInt ],
0,
function( col, gi, ord )
SetRelativeOrder( col, Position(GeneratorsOfRws(col),gi), ord );
end );
#############################################################################
InstallMethod( SetRelativeOrderNC,
IsIdenticalObjFamiliesColObjObj,
[ IsPolycyclicCollector and IsMutable,
IsMultiplicativeElementWithInverse,
IsInt ],
0,
function( col, gi, ord )
SetRelativeOrderNC( col, Position(GeneratorsOfRws(col),gi), ord );
end );
#############################################################################
##
#M EvaluateOverlapCBA . . . . . . . . . . . . . evaluate a consistency test
##
InstallMethod( EvaluateOverlapCBA,
"polyc. collector, 2 hom. lists, 3 pos. integers",
true,
[ IsPolycyclicCollector,
IsHomogeneousList, IsHomogeneousList,
IsPosInt, IsPosInt, IsPosInt ], 0,
function( coll, l, r, z, y, x )
local status;
## if this routine is used for computing tails, then the tail t is
## t = l-r
## (z y) x = y z^y x
repeat
l[y] := 1;
status := CollectWordOrFail( coll, l, GetConjugateNC( coll, z, y ) );
if status = true then
status := CollectWordOrFail( coll, l,
coll![SCP_RWS_GENERATORS][x] );
fi;
until status = true;
## z (y x) = x z^x y^x
repeat
r[x] := 1;
status := CollectWordOrFail( coll, r, GetConjugateNC( coll, z, x ) );
if status = true then
status := CollectWordOrFail( coll, r,
GetConjugateNC( coll, y, x ) );
fi;
until status = true;
end );
#############################################################################
##
#M EvaluateOverlapBNA . . . . . . . . . . . . . evaluate a consistency test
##
InstallMethod( EvaluateOverlapBNA,
"polyc. collector, 2 hom. lists, 3 pos. integers",
true,
[ IsPolycyclicCollector,
IsHomogeneousList, IsHomogeneousList,
IsPosInt, IsPosInt, IsPosInt ], 0,
function( coll, l, r, b, n, a )
local status;
## if this routine is used for computing tails, then the tail t is
## t = l-r
## b^n a
repeat
status := CollectWordOrFail( coll, l, GetPowerNC( coll, b ) );
if status = true then
status := CollectWordOrFail( coll, l,
coll![SCP_RWS_GENERATORS][a] );
fi;
until status = true;
## b^(n-1) (b a) = b^(n-1) a b^a
repeat
r[b] := n-1;
status := CollectWordOrFail( coll, r,
coll![SCP_RWS_GENERATORS][a] );
if status = true then
status := CollectWordOrFail( coll, r,
GetConjugateNC( coll, b, a ) );
fi;
until status = true;
end );
#############################################################################
##
#M EvaluateOverlapBAN . . . . . . . . . . . . . evaluate a consistency test
##
InstallMethod( EvaluateOverlapBAN,
"polyc. collector, 2 hom. lists, 3 pos. integers",
true,
[ IsPolycyclicCollector,
IsHomogeneousList, IsHomogeneousList,
IsPosInt, IsPosInt, IsPosInt ], 0,
function( coll, l, r, z, y, n )
local status;
## if this routine is used for computing tails, then the tail t is
## t = l-r
## (z y) y^(n-1) = y z^y y^(n-1)
repeat
l[y] := 1;
status := CollectWordOrFail( coll, l, GetConjugateNC( coll, z, y ) );
if status = true then
status := CollectWordOrFail( coll, l,
coll![SCP_RWS_GENERATORS][y]^(n-1) );
fi;
until status = true;
## z * y^n
repeat
r[z] := 1;
until CollectWordOrFail( coll, r, GetPowerNC( coll, y ) ) = true;
end );
#############################################################################
##
#M EvaluateOverlapANA . . . . . . . . . . . . . evaluate a consistency test
##
InstallMethod( EvaluateOverlapANA,
"polyc. collector, 2 hom. lists, 3 pos. integers",
true,
[ IsPolycyclicCollector,
IsHomogeneousList, IsHomogeneousList,
IsPosInt, IsPosInt ], 0,
function( coll, l, r, a, n )
local status;
## (a^n) a
repeat
status := CollectWordOrFail( coll, l, GetPowerNC( coll, a ) );
if status = true then
status := CollectWordOrFail( coll, l,
coll![SCP_RWS_GENERATORS][a] );
fi;
until status = true;
## a (a^n)
repeat
r[a] := 1;
status := CollectWordOrFail( coll, r, GetPowerNC( coll, a ) );
until status = true;
end );
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