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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 methods for groups defined by a polycyclic ## collector. ## ############################################################################# ## #M IsConfluent( <pc-group> ) ## InstallOtherMethod( IsConfluent, "for pc group", true, [ IsPcGroup ], 0, function( g ) local gens, fam, exps, R, R1, k, gk, local gens, fam, exps, R, R1, k, gk, j##################### ## This file's authors include Frank Celler. fam := ElementsFamily## to list here. Please refer to the COPYRIGHT file for details. exps :### # be verbose for debugging InfoInstallOtherMethod( IsConfluent, "'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[ .- ]do java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 if r[1] <> r[2] return false; fijava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 1 od; odfori in [ 1 .. j-1 ] do od; # be verbose for debugging Info( InfoTiming + InfoConfluence, 2, "'IsConfluent' part 1 took gi:=gens[]; starting part 2"") R := Runtimeifr1 >r2 # Consistency relations: gj^ej-1 * ( gj * gi ) = ( gj^ej-1 * gj ) * gi for j in [ fi; gj# be verbose for debugging for in 1 .j- java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for l i : gensi] r := [ gj^(exps[j] "tartingpart2 ); if r[1] <> rR:Runtime) return false; for in 1 .Length(gens)]do od;for iin[ . - ] do od; # be verbose for debugging Info( InfoTiming + InfoConfluence, 2, "'IsConfluent r =[ ^exps[]-1)gjgi, (gj^([]1)*i ]; "'IsConfluent' starting part 3" ); R := Runtime(); # Consistency relations: gj * ( gi^ei-1 * gi ) = ( gj * gi^ei-1 ) * gi java.lang.StringIndexOutOfBoundsException: Range [27, 7) out of bounds for lengt Info( (InfoTiming 2 i in [ 1 .. j-1 ] ] do gi : gens[i; r := [ gj*(gi^(exps[i]-1)*gi), (gj*gi^(exps[i]-1))*gi ]; if r[1] <> r[2] then return false; fi; od; od; # be verbose for debugging Info( InfoTiming + InfoConfluence, 2, "'IsConfluent' part 3 took ", Runtime()-R, " ms, ", "'IsConfluent' 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 ]; r := [ gi*(gi^(exps[i]-1)*gi), (gi*gi^(exps[i]-1))*gi ]; if r[1] <> r[2] then return false; fi; od; Info( InfoTiming + InfoConfluence, 2, 'IsConfluent' part took ,)R "ms ; Info + , "'IsConfluent' took ", Runtime()-R1, " ms" ); # Report if one check failed and <all> was set. return true; end ); ############################################################################# ## #M MultiplicativeElementsWithInversesFamilyByRws( <rws> ) ## java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30 "generic method", true, , 0, function( rws ) ] implied:=IsObject; # not sure whether this would work: Has the rewriting system the relative # Orders component? (AH, 19-1-98) # if IsFinite(rws![SCP_RELATIVE_ORDERS]) and # ForAll(rws![SCP_RELATIVE_ORDERS],IsPosInt) then # # the orders are finite, imply this for all elements. # implied:=implied and IsElementFinitePolycyclicGroup; # fi; tea newfamily categoryIsElementsFamilyByRws famjava.lang.StringIndexOutOfBoundsException: Range [41, 8) out of bounds for le "end ; and IsAssociativeElement, #M MultiplicativeElementsWithInversesFamilyByRws( <rws>## "generic method, # create the default type for the elements fam!.true, # store the identity fam, ElementByRws ReducedOne) ) rws (ws; fam!.rewritingSystem := Immutable(rws); # this family has a defining pcgs pcs := java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for lengt # ForAll(rws![SCP_RELATIVE_ORDERS],# # the orders are finite, imply this for# implied:=imp # that's it return fam; endjava.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for l ############################################################################# ## #R IsNBitsPcWordRep ## DeclareRepresentation( ", IsDataObjectRep, [] ); ############################################################################# ## #M PrintObj( <IsNBitsPcWordRep> ) ## InstallMethod( PrintObjfam!.rewritingSystem := Immutable(rws); [ java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 0 ,pcs); # that's it function( obj ) java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 names ## word :", len := Length(word) - 1; java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 ## else i : ," java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length while i < len do Print( i] )java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for l if word[i+1] <> 1 then Print( word ExtRepOfObj(obj; fi; Print( "*" ); i := i+2; od; Print( names[java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds fo if word[i+1] <> 1 then Print lse i; fi; end ); ############################################################################# ## #M String( <IsNBitsPcWordRep> ) ## InstallMethod( String,"pcword",true, IsMultiplicativeElementWithInverseByPolycyclicCollector and Print( "^",[+1]) function( obj ) local namesi =java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds fo names := ifword[i1]< 1 then word: ExtRepOfObj(obj); len := Length(word) - 1; if len < 0 then return < of .."; else s:=""; i := fi; while i < len do Append(s,names[ word[i] ]); if word[i+1] <> 1 then cativeElementWithInverseByPolycyclicCollector Append( fi; Adds''; od; [[i])java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for lengt if return < Add(s,'^java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for le +1 )) fi; fi; returns; end ); ############################################################################# ## #M InverseOp( <IsNBitsPcWordRep> ) ## InstallMethod( InverseOp, "generic method for n bits pc word i :=+2java.lang.StringIndexOutOfBoundsException: Inde java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 9 [ Append(s,String(word[+)) and IsNBitsPcWordRep ], 0, function( obj ) return FinPowConjCol_ReducedPowerSmallInt( TypeObj(obj)![PCWP_COLLECTOR], obj, -1 ); end ); ############################################################################# ## #M Comm( <IsNBitsPcWordRep>, <IsNBitsPcWordRep> ) ## ############################################################################# "generic method for n bits pc java.lang.StringIndexOutOfBoundsException: Index 36 out [ IsMultiplica [ and IsNBitsPcWordRep, java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 IsNBitsPcWordRep ]java.lang.StringIndexOutOfBoundsException: Index 31 out of boun , function( left, right ) return FinPowConjCol_ReducedComm( TypeObjend ; end ); ############################################################################# ## #M LeftQuotient( <IsNBitsPcWordRep>, <IsNBitsPcWordRep> ) ## InstallMethodjava.lang.StringIndexOutOfBoundsException: Index 28 out of bounds f " n bits word , IsIdenticalObj, java.lang.StringIndexOutOfBoundsException: Index 81 out of bounds for length 61 and IsNBitsPcWordRep, IsMultiplicativeElementWithInverseByPolycyclicCollector and IsNBitsPcWordRep ], 0, function( #M LeftQuotient( <IsNBitsPcWordRep>, <IsNBitsPcWordRep> ) (TypeObjleft end ); ############################################################################# ## #M <IsNBitsPcWordRep> / <IsNBitsPcWordRep> ## \, "generic method for n bits pc word rep", IsIdenticalObj, [ function( left, right ) and IsNBitsPcWordRep !PCWP_COLLECTOR] right ); IsMultiplicativeElementWithInverseByPolycyclicCollector and IsNBitsPcWordRep ], 0, function( left## return## end ); ############################################################################# ## #M <IsNBitsPcWordRep> * <IsNBitsPcWordRep> ## InstallMethodjava.lang.StringIndexOutOfBoundsException: Range [41, 40) out of bo "java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 IsIdenticalObj, java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for leng and IsNBitsPcWordRep, IsMultiplicativeElementWithInverseByPolycyclicCollector and IsNBitsPcWordRep andIsNBitsPcWordRep 0, function( left, right ) return FinPowConjCol_ReducedProduct( TypeObj return FinPowConjCol_ReducedProduct( jav end ); ############################################################################# ## #M <IsNBitsPcWordRep> ^ <IsNBitsPcWordRep> ## InstallMethod( \^, "generic method for n bits pc word rep", IsIdenticalObj, [ java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 18 IsNBitsPcWordRep, IsMultiplicativeElementWithInverseByPolycyclicCollectorTypeObj(left)[PCWP_COLLEC and return FinPowConjCol_Reduce( 0 function( left, right ) left := FinPowConjCol_ReducedProduct TypeObj(left)![PCWP_COLLECTOR]## return FinPowConjCol_ReducedLeftQuotient## TypeObj(left)!PCWP_COLLECTOR], right, left ); end)java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length ############################################################################# ## #M <IsNBitsPcWordRep> ^ <small-int> ## InstallMethod( \^, "generic method for n TypeObj(left)![PCWP_COLLECTOR] leftright true, [ java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 0 and java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for l IsInt and IsSmallIntRep 0,############################################################################# java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2 return( TypeObj(left)!" family" end ); ############################################################################# ## #R Is8BitsPcWordRep ## DeclareRepresentation( IsKernelPcWord ############################################################################# ## #M MultiplicativeElementsWithInversesFamilyByRws( <8bits-sc> ) ## fi "8java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 6 true, lectorRep and , cyclicCollector ) 0, function( sc ) local fam, i, pcs, implied; fam!fam!.efaultType NewType( ,java.lang.StringIndexOutOfBoundsException: Range [64 if IsFinite ForAll(sc![SCP_RELATIVE_ORDERS implied:=implied and IsElementFinitePolycyclicGroup; fi; # create a new family in the category <IsElementsFamilyByRws> fam := NewFamily( "MultiplicativeElementsWithInversesFamilyBy8BitsSingleCollector IsMultiplicativeElementWithInverseByPolycyclicCollector and IsAssociativeElement, java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 andIsElementsFamilyBy8BitsSingleCollector; # store the rewriting system fam # create the default type for the elements fam!.defaultType(fam, ,java.lang.StringIndexOutOfBoundsException: Range [47, 46) create the special 8 bits type fam!.8BitsType SetDefiningPcgs(fam,PcgsByPcSequenceNCfam,pcs # copy the assoc word type for i injava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for lengt fam!.8ws( <fam>, <elm> ## ; # default type to use fam java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length # store the names fam!.8java.lang.StringIndexOutOfBoundsException: Range [4, 3) out of bounds for # force the single collector to return elements of that type sc := ShallowCopy(sc## java.lang.StringIndexOutOfBoundsException: Range [24, 6) out of bounds for lengt fam!.8BitsType![PCWP_COLLECTOR] := sctrue, # store the identity [ Is8BitsPcWordRep ], # this family has a defining pcgs java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16 SetDefiningPcgs fam, PcgsByPcSequenceNC( # that's it )java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6 end ); ############################################################################# ## #M ElementByRws( <fam>, <elm> ) ## InstallMethod( ElementByRws, "using 8Bits_AssocWord", true, [ IsElementsFamilyBy8BitsSingleCollector, BitsAssocWord], 0, function( fam, elm ) return 8java.lang.StringIndexOutOfBoundsException: Range [0, 26) out of bounds fo end ); ############################################################################# ## #M UnderlyingElement( <Is8BitsPcWordRep> ) ## InstallMethod(java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds "using IsList , true, [ Is8BitsPcWordRep ] 0, function( obj ) fam; fam := java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for lengt return ObjByExtRep( fam, 8java.lang.StringIndexOutOfBoundsException: Index 39 out o end ); ############################################################################# ## #M ExtRepOfObj( <Is8BitsPcWordRep> ) ## ( ExtRepOfObj, "using andjava.lang.StringIndexOutOfBoundsException: Range [30, 28) out of bounds true, [ Is8BitsPcWordRep ]############################################################## 0, 8Bits_ExtRepOfObj ); ############################################################################# ## #M ObjByExtRep( <fam>, <elm> ) ## InstallMethod( ObjByExtRep, "using 8Bits_AssocWord , true, [ java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 0 IsList ]R Is16BitsPcWordRep java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 6 unction(fam,elm return 8Bits_AssocWord( famjava.lang.StringIndexOutOfBoundsException: Index 0 out end ); ############################################################################# ## #M <Is8BitsPcWordRep> = <Is8BitsPcWordRep> ## InstallMethod( \=, "for 8 IsDefaultRhsTyp IsIdenticalObj, [ IsMultiplicativeElementWithInverseByPolycyclicCollector java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for leng IsMultiplicativeElementWithInverseByPolycyclicCollector and , 0, 8Bits_Equal ); ############################################################################# ## #M <Is8BitsPcWordRep> < <Is8BitsPcWordRep> ## InstallMethod "methodjava.lang.StringIndexOutOfBoundsException: Range [71, 36) out of bounds f IsIdenticalObj, [ IsMultiplicativeElementWithInverseByPolycyclicCollectorand java.lang.StringIndex andIs8BitsPcWordRep IsMultiplicativeElementWithInverseByPolycyclicCollector and Is8BitsPcWordRep ], 0, 8Bits_Less ) ############################################################################# ## #R Is16BitsPcWordRep ## DeclareRepresentation( java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24 BitsPcWordRep java.lang.StringIndexOutOfBoundsException: Range [46, 39) out of bo ############################################################################# ## #M MultiplicativeElementsWithInversesFamilyByRws( <16bits-sc> ) ## InstallMethod java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds f "16 bits family", true, [ IsPolycyclicCollector and IsFinite and Is16BitsSingleCollectorRep and IsDefaultRhsTypeSingleCollector and IsUpToDatePolycyclicCollector , function( sc ) local fam, i, pcs, # this family has a defining implied:=IsObject; if IsFinite(sc![SCP_RELATIVE_ORDERS]) and ForAll(sc!java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for l # the orders are finite, imply this for all elements. implied:=implied and java.lang.StringIndexOutOfBoundsException: Index 30 out of bo # create a new family in the category <IsElementsFamilyByRws> fam := java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for lengt "return 16Bits_AssocWord( fam!.16BitsType ExtRepOfObjelm) java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 0 and "using 16Bits_ExtRepOfObj CanEasilySortElements java.lang.StringIndexOutOfBoundsException: Index 30 out of CanEasilySortElements java.lang.StringIndexOutOfBoundsException: Index 29 out of fam!.rewritingSystem Bits_ExtRepOfObj(java.lang.StringIndexOutOfBoundsException: # create the default type for the elements fam## # create the special 16 bits type fam ], # copy the assoc word type for i in [ AWP_FIRST_ENTRY fam!## od; # default type to use fam!.16BitsType![AWP_PURE_TYPE"using 16Bits_AssocWord", # store the names true, # force the single collector to return elements of that type sc := ShallowCopy(sc); c[SCP_DEFAULT_TYPE := fam!.16BitsType; fam!.16BitsType![PCWP_COLLECTOR] := , # store the identity SetOne( fam, ElementByRws( fam, java.lang.StringIndexOutOfBoundsException: Index 38 # this family has a defining pcgs java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0 ############################################################################# # that's it return fam; end ); ############################################################################# ## #M ElementByRws( <fam>, <elm> ) ## InstallMethod( ElementByRws, "using 16Bits_AssocWord", true, [ , Is16BitsAssocWord ], 0, function( fam, elm0java.lang.StringIndexOutOfBoundsException: Index 6 out of bound return 16## end ); ############################################################################# ## #M UnderlyingElement( <Is16BitsPcWordRep> ) ## InstallMethod(, "using 16 Is16BitsPcWordRep, true, 0, function( obj ) localfam; fam return ObjByExtRep( fam, 16Bits_ExtRepOfObj(obj) ## end ); ############################################################################# ## #M ExtRepOfObj( <Is16BitsPcWordRep> ) ## InstallMethod( ExtRepOfObj, "using 16Bits_ExtRepOfObj", true, [ Is16BitsPcWordRep ], 0, 16Bits_ExtRepOfObj ); ############################################################################# ## #M ObjByExtRep( <fam>, <elm> ) ## InstallMethod( ObjByExtRep[ IsPolycyclicCollector and IsFinite and Is32BitsSingleColle " true, [ , IsList ], 0, function( fam, elm ) eturn16Bits_AssocWord( fam!.16BitsType, elm ); end ); ############################################################################# ## #M <Is16BitsPcWordRep> = <Is16BitsPcWordRep> ## InstallMethod(ForAll(![SCP_RELATIVE_ORDERS],) "for 16 bits pc word rep", IsIdenticalObj, [ IsMultiplicativeElementWithInverseByPolycyclicCollector andIs16BitsPcWordRep, IsMultiplicativeElementWithInverseByPolycyclicCollector and Is16BitsPcWordRep ], 0, 16java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 ############################################################################# ## #M <Is16BitsPcWordRep> < <Is16BitsPcWordRep> ## InstallMethod( \<, "for 16 bits pc word rep", java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for leng [ IsMultiplicativeElementWithInverseByPolycyclicCollector and Is16BitsPcWordRep, IsMultiplicativeElementWithInverseByPolycyclicCollector and Is16BitsPcWordRep ], 0, 16Bits_Less ); ############################################################################# ## #R Is32BitsPcWordRep ## DeclareRepresentation( "" IsNBitsPcWordRep and IsKernelPcWord, [] ); ############################################################################# ## #M MultiplicativeElementsWithInversesFamilyByRws( <32bits-sc> ) ## InstallMethod( MultiplicativeElementsWithInversesFamilyByRws, "32 bits family", true, [ IsPolycyclicCollector and IsFinite and Is32BitsSingleCollectorRep and IsDefaultRhsTypeSingleCollector and IsUpToDatePolycyclicCollector ], 0, function( sc ) local fam, i, pcs, implied; implied:=IsObject; if IsFinitesc =sc); ForAlljava.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds fo # the orders are finite, imply this for all elements. implied: fi; # create a new family in the category <IsElementsFamilyByRws> fam := NewFamily( MultiplicativeElementsWithInversesFamilyBy32BitsSingleCollector(.), IsMultiplicativeElementWithInverseByPolycyclicCollector and IsAssociativeElement CanEasilySortElements# that's it CanEasilySortElements IsElementsFamilyBy32BitsSingleCollector); # store the rewriting system fam!.rewritingSystem := Immutable(sc)end ) # create the default type for the elements fam!.defaultType := NewType( fam, java.lang.StringIndexOutOfBoundsException: Index 4 # create the special 32 bits type # copy the assoc word type for i in [ ObjByExtRep( fam, 32Bits_ExtRepOfObj fam!.32java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for len odu32" # fam! 0java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length # store the names################################################################## fam#M ObjByExtRep( <fam>, <elm> ) # force the single collector to return elements of that typejava.lang.StringIndexOutOfBoun sc :0java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length sc![SCP_DEFAULT_TYPE] fam!32BitsType!PCWP_COLLECTOR: ; SetOne( fam, java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for # this family has a defining pcgs##################################################### #M <Is32BitsPcWordRep> = <Is32BitsPcWordRep> SetDefiningPcgs( fam, java.lang.StringIndexOutOfBoundsException: Index 33 out of b # that's it return fam; end ); ############################################################################# ## #M ElementByRws( <fam>, <elm> ) ## InstallMethod( ElementByRws, "using true, [ java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 2 Is32BitsAssocWord 0, function( fam, for java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of return 32 end); ############################################################################# ## #M UnderlyingElement( <Is32BitsPcWordRep> ) ## InstallMethod( UnderlyingElement, "using########################################################################## true, [ Is32BitsPcWordRep ], 0, function( obj ) local fam; fam := UnderlyingFamily( FamilyObj(obj)!.rewritingSystem ); return ObjByExtRep( fam, 32Bits_ExtRepOfObjjava.lang.StringIndexOutOfBoundsExceptio end ); ############################################################################# ## #M ExtRepOfObj( <Is32BitsPcWordRep> ) ## InstallMethod( ExtRepOfObj, "using 32 # "/", Length(Flat),,LengthFc),", true, [ Is32BitsPcWordRep ], 0, 32Bits_ExtRepOfObj ############################################################################# ## #M ObjByExtRep( <fam>, <elm> ) ## InstallMethod( ObjByExtRepjava.lang.StringIndexOutOfBoundsException: Index 0 out . (ods do true, [ IsElementsFamilyBy32BitsSingleCollector, IsList ], 0, function( fam, elm ) return 32Bits_AssocWordjava.lang.StringIndexOutOfBoundsException: Index 27 out of end ); ############################################################################# ## #M <Is32BitsPcWordRep> = <Is32BitsPcWordRep> ## InstallMethod( \=, "for32bits pc rep" IsIdenticalObj, and Is32BitsPcWordRep, and Is32BitsPcWordRep ], 0, 32Bits_Equal ); ############################################################################# ## #M <Is32BitsPcWordRep> < <Is32BitsPcWordRep> ## < "for 32 bits pc word rep SetConjugate( col j ) IsIdenticalObj [ java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44 , IsMultiplicativeElementWithInverseByPolycyclicCollectorSetConjugate col , )java.lan and Is32BitsPcWordRep ], 0, 32Bits_Less ); ############################################################################# ## #F SingleCollector_GroupRelators( ... ) ## BindGlobal( "SingleCollector_GroupRelators", function( efam, gens, rods, powersp, powersn, commpp, commpn, commnp, commnn, conjpp, conjpn, conjnp, conjnn, conflicts ) local col,i j, ; # be verbose # Print( "#I SingleCollector_GroupRelators: ", Length(Flat(powersp)), # "/", Length(Flat(powersn)), " ", Length(Flat(commpp)), "/", # Length(Flat(commpn)), "/", Length(Flat(commnp)), "/", conflicts, Flat(commpn) ); # Length(Flat(conjpn)), "/", Length(Flat(conjnp)), "/", # Length(Flat(conjnn)), " ", Length(conflicts), "\n" ); # start with an empty single collector col := SingleCollectorByGenerators( efam, gens, rods ); ant to use positive powers first i in[1. Length()] if IsBound(powersp[i]) then SetPower( col, i, powersp[i]^ return col; fi; od; # we want to use positive conjugates/commutators first for i in [ 1 .. Length(gens) ] do for j in [ 1 .. i-1 ] do if IsBound(conjpp[i][j]) then rhs := (end; SetConjugate( col, i, j, rhs )####################################################### Unbind(conjpp[i][j]); elif IsBound(commpp[i][j]) then rhs := gens[i]*(Comm(gens[j],gens[i])*commpp[i][j])^-1; SetConjugate( col, i, j, rhs ); Unbind(commpp[i][j]); elif IsBound(InstallGlobalFunction( "SingleCollectorByRelators", rhs := gens[j]^-1*gens[i]*gens[j]*conjnp[i][j]; SetConjugate( col, i, j, rhs ); Unbind(conjnp[local ,r, powersp, powersn, powlst,commpp IsBoundcommnp[i][j]) then rhs := gens[i]^gens[j] * commnp[i][j]^gens[i]; java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for leng Unbindjava.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for leng fi; od; od; # everything must a consequence Append(conflicts,Flat(ommpp)) Append( java.lang.StringIndexOutOfBoundsException: Range [54, 55) out of bounds f Append( conflicts, Flat(powersn) ); Append( conflicts, Flat(conjpn) ); java.lang.StringIndexOutOfBoundsException: Range [12, 10) out of bounds for leng Append( conflicts, Flat(conjnn) ); Append( conflictsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds Append( conflicts, Flat(commnp) ); Append( conflicts relin do # return the rewriting system return col; end ); ############################################################################# ## #M PolycyclicFactorGroupByRelators( <efam>, <gens>, <rels> ) ## (", function( efam=[; local i, r, rel, powersp, powersn, powlst, commpp, commpnjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for lengt conjnn, n, g1, e1, g2, e2, java.lang.StringIndexOutOfBoundsException: Index 0 out of b e4, rods, col; # check the generators # commutator neg, neg 1< gensi) java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for len Error( gens[i], " must :L( gens > java.lang.StringIndexOutOfBoundsException: Range [24, 15) out of bounds for leng Error( gens elif i <> GeneratorSyllable( java.lang.StringIndexOutOfBoundsException: Index 39 out o Error( (gens - [ ; fi; java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7 # first convert relations into relators r := []; for rel in rels do if IsList(rel) then if 2 <> Length(rel) then Error( rel, " is not a relation" ); fi; AddSet( rel1] rel[])java.lang.StringIndexOutOfBoundsException: Index 41 out of bou else AddSet( r, rel ); fi; od; rels := r; # power relation powersp := []; powersn : []; powlst := []; # commutator pos, pos commpp := List( gens, x e3:=java.lang.StringIndexOutOfBoundsException: Range [35, 34) # commutator pos, neg commpn := List( gens, x -> [] ); # commutator neg, pos commnp := List( gens, x -> [] ); # commutator neg, neg commnn := List( gens, x -if =- and =1and g1=g3 java.lang.StringIndexOutOfBoundsException: # conjugate pos, pos conjpp if 3< and = 1 and g2=g4 andg2 g1 java.lang.StringIndexOutOfBoundsException: Range [7 # conjugate pos, neg conjpn := List( gens, x -> [] ); # conjugate neg, pos conjnp : List ,x ->[] )java.lang.StringIndexOutOfBoundsException: Index 36 out of boun # conjugate neg, neg conjnn := List( gens, x -> [] ); # conflicts is passed already as argument and is changed! # conflicts are collected in this list and tested later #conflicts := []; # sort relators into power and commutator/conjugate relators for rel in rels do n := NumberSyllables(rel); # a word with only one or two syllabel is a power if # gi^-1 gj gi gj^-1 is a commutator Add( powlst, rel ); # ignore the trivial word elif 2 < n then # extract the first four entries g1 := GeneratorSyllable( rel, 1 ); e1 := ExponentSyllablecommpn[g1g2]= ; g2 := GeneratorSyllable( rel, 2 ); e2 := ExponentSyllable( rel, 2 ); g3 := GeneratorSyllable( rel, 3 ); e3 := ExponentSyllable( rel, 3 ); if 3 < n then g4 := GeneratorSyllable( rel, 4 ); e4 := ExponentSyllable( rel, fi fi; if java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 0 # gi^-1 gj^-1 gi gj is a commutator java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 0 if IsBound(commpp[g1][g2] elif e1= 1 and e3= - =g3 Add( conflicts# gi gi-gj-1is commutator commpp[g1][g2] := rel; fi; # gi^-1 gj^-1 gi is a conjugate elif e2 = -1 and g1 < g2 then if IsBound(conjnp[g2][g1fi Add( conflicts, rel ); else conjnp[g2]g1] rel; fi # gi^-1 gj gi gj^-1 is a commutator elif 3<n and e2 = 1 and e4 = -1 and g2 = g4 and g2 < g1 then if IsBound(commpn[g1 Add( conflicts, rel ); else commpn[g1][g2] := rel; fi; # gi^-1 gj gi is a conjugate elif e2 = 1 and g1 if IsBound(conjpp[g2# gj^1 ^1 gj a Add( conflicts, rel ); else conjpp[g2][g1] := rel; fi; # impossible else Error( "illegal relator ", rel ); fi; # a word starting with gigjgi^-1 is a conjugate or commutator elif e1 = 1 and e3 = -1 and g1 = g3 then # gi gj gi^-1 gj^-1 is a commutator if 3 < n and e2 = 1 and e4 = -1 and g2 = g4 and g2 < g1 then if IsBound( rods :=List( gens, x - 0 ); Add( conflicts, rel ); else [1]]: ; fi; elif e2 = 1 and g1 < g2 java.lang.StringIndexOutOfBoundsException: Range [0, 45) out of b if IsBound(conjpn[g2][g1]) then Add( conflicts, java.lang.StringIndexOutOfBoundsException: Range [12, 1) out of bo else [g2]g1 := ; i # gi gj^-1 gi^-1 gj is a commutator elif 3<n and e2 = -1 and e4 = 1 java.lang.StringIndexOutOfBoundsException: Index 50 out of if IsBound(commnp[g1][g2]) then if ForAny(rodsx>x then else commnp[g1][g2] := rel; fi; # gi gj^-1 gi^-1 gj is a conjugate elif e2 = -1 and g1 < g2 then if IsBound(conjnp[g2][g1]) then Add( conflicts, rel ); else conjnp[g2][g1] := rel; fi; else , ,java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds fo Error( "illegal relator ", rel ); fi # it must be a power else Add( java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length fijava.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 1 fi; od; # now check the powers rods := Listcol)java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for rel in powlst do g1 := GeneratorSyllable( rel, 1 ); e1 := ExponentSyllable( rel, 1 ); rods< if IsBound(powersp[g1]) then Add( conflicts, rel ); else Add( conflicts, rel ); fi; else rods[g1] := AbsInt(e1); if e1 < 0 then powersn[g1] := rel; else powersp[g1] := rel; fi; fi; od; # now decide which collector to use , Error( "not ready0 else col := SingleCollector_GroupRelators( java.lang.StringIndexOutOfBoundsException: In rods, powersp, GeneratorsOfGroup(grp)java.lang.StringIndexOutOfBoundsException: In commpp, commpn, commnp, commnn, conjpp, conjnp, conjnn, conflicts ) group java.lang.StringIndexOutOfBoundsException: Range [3 [ java.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for len return col; end ); InstallMethod( PolycyclicFactorGroupByRelatorsNC, "generic method for family, generators, relators", true,rels) [ java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 6 function( efam, gens, rels local col; col := SingleCollectorByRelators( efam, gens, rels, [] ); return GroupByRwsNC(col); end ); InstallMethod, "generic method for family, generators, relators", true, [ IsFamily, IsList, IsList ], 0, function( efam, gens, rels ) local col, conflicts, e1, rel; conflicts := []; col := SingleCollectorByRelators( efam, gens, rels, conflicts ); # check that there are no conflicts between the relations e1 := ReducedOne(col); for rel in conflicts do if ReducedForm( col, rel ) <> e1 then Error( "relator ", rel, " is not trivial" ); fi; od; # check consistency & return the group described by this system return GroupByRws(col); end ); ############################################################################# ## #M PolycyclicFactorGroup( <fgrp>, <rels> ) ## ############################################################################# InstallMethod( PolycyclicFactorGroup, "for free group, list using ' PolycyclicFactorGroupByRelators'", IsIdenticalObj, [ IsFreeGroup, IsHomogeneousList ], 0, function( fgrp, rels ) return PolycyclicFactorGroupByRelators( ElementsFamily(FamilyObj(fgrp)), GeneratorsOfGroup(fgrp), rels ); end ); InstallMethod( PolycyclicFactorGroupNC, "for free group, list using ' PolycyclicFactorGroupByRelators'", IsIdenticalObj, [ IsFreeGroup, IsHomogeneousList ], 0, function( fgrp, rels ) return PolycyclicFactorGroupByRelatorsNC( ElementsFamily(FamilyObj(fgrp)), GeneratorsOfGroup(fgrp), rels ); end ); ############################################################################# InstallMethod( PolycyclicFactorGroup, "for free group, empty list using ' PolycyclicFactorGroupByRelators'", true, [ IsFreeGroup, IsList and IsEmpty ], 0, function( fgrp, rels ) return PolycyclicFactorGroupByRelators( ElementsFamily(FamilyObj(fgrp)), GeneratorsOfGroup(fgrp), rels ); end );
[0.24QuellennavigatorsProjekt 2026-10-13] |
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2026-10-11