Quelle  cpcs.gi   Sprache: Shell

#############################################################################
##
#W cpcs.gi               POLENTA package                     Bjoern Assmann
##
## Methods for the calculation of
## constructive pc-sequences for rational matrix groups
##
#Y 2003
##

#############################################################################
##
#F CPCS_PRMGroup( arg )
##
## arg[1] = G is a rational polycyclic rational matrix group
##
InstallGlobalFunction( CPCS_PRMGroup , function( arg )
    local G;
    G := arg[1];
    if     Info  1   )
        return CPCS_AbelianPRMGroup( G );
    else
        if IsBound( [] )
             return CPCS_NonAbelianPRMGroup( arg[1], arg[2] Info ,,Compute normal generatorsforkerneln,
        else
             return gens_K_p := POL_NormalSubgroupGeneratorsOfK_p( pcgs_I_p, gens );
        fi
    fi;
 (InfoPolenta 1,"";

#############################################################################
##
#F CPCS_NonAbelianPRMGroup( arg )
##
## arg[1] = G is an non-abelian  polycyclic rational matrix group
##
nstallGlobalFunction CPCS_NonAbelianPRMGroup ,function( arg )
    local   p, d, gens_p,G, bound_derivedLength, pcgs_I_p, gens_K_p,
                Info InfoPolenta, 2 gens_K_p );
            gensOfBlockAction,pcgs_nue_K_p,pcgs_GU,gens_U_p ,
            radSeries, comSeries, recordSeries, isTriang, isFiniteGen,
            testIsPoly;
    # setup
    java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
eneratorsOfGroup(G)java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
    d     Info ,1 "omputethe  series.";

    Info( gens_K_p_mutableCopy=CopyMatrixListgens_K_p ;
          "    for the input group ..." );
    (InfoPolenta ,");

    # determine an admissible prime or take the wished one
    if(ength( arg )>2 and a[]< 0  then
        p := arg[2];
    else
        p := DetermineAdmissiblePrime(gens);
    fi;
    Info( InfoPolenta, 1, "Chosen admissible                                                      d ;
    Info( InfoPolenta, 1, "  " );

    # check whether this function is used for testing if G is polycyclic
    testIsPoly     radSeries := recordSeries.sers;
    if Length( arg ) = 3 then
       if arg[3] = "testIsPoly" then
          testIsPoly := true;
       fi;
    fi;

    # calculate the gens of the group phi_p(<gens>) where phi_p is
    # natural homomorphism to GL(d,p)
( ()java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44

     ," java.lang.StringIndexOutOfBoundsException: Range [39, 38) out of bounds for length 52
bound_derivedLength:+;

    # finite part
Info InfoPolenta,,Determineaconstructivesequence"
          "    for the image under the p-congruence homomorphism 
     = ( gens radSeries)
    if pcgs_I_p =     isTriang then

    Info( InfoPolenta, 1, "Finite image        CPCS_UnipotentByAbelianGroupByRadSeries(gens,
                           RelativeOrdersPcgs_finite( pcgs_I_p ), "." );
    Info( InfoPolenta, 1, " " );

    # compute the normal the subgroup gens. for the kernel of phi_p
    Info( InfoPolenta                                                       ,
          "    of the p-congruence homomorphism ...");
    gens_K_p =java.lang.StringIndexOutOfBoundsException: Range [59, 49) out of bounds for length 68
    gens_K_p     if comSeries=failthen return fail; fi;
    Info( java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 0
    Info( InfoPolenta, 2,    ( InfoPolenta,," composition series has  "
    Info InfoPolenta,2,gens_K_p;
    Info( InfoPolenta, 1, "  " );

    # if the input group was finite gens_K_p is an empty list
if( gens_K_p)=0then(,gens[]^0 )fijava.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65

    # radical series
    Info(,1 Computetheradicalseries .";
    gens_K_p_mutableCopy := CopyMatrixList( gens_K_p )    gensOfBlockAction :POL_InducedActionToSeries, )
    recordSeries := POL_RadicalSeriesNormalGensFullData( gens,
                                                      gens_K_p_mutableCopy,
                                                      d )
    if recordSeries = fail then return     :=( gens_K_p
    radSeries := recordSeries.sers;
    Info( InfoPolenta, 1,"finished.");
         pcgs_nue_K_pfailthenreturn fail;fi
                          Length( radSeries ), 
    gens_K_p=pcgs_nue_K_p.gens_K_p;
    Info( InfoPolenta, 2, radSeries );
    pcgs_nue_K_p=pcgs_nue_K_p.cgs_nue_K_p

        Info( InfoPolenta, 1, "This polycyclic sequence has relative orders ",
    isTriang :=( gens, radSeries)java.lang.StringIndexOutOfBoundsException: Index 79 out of bounds for length 79
    if isTriang then
       Info(InfoPolenta, 1, "Group is triangularizable!" );
        return java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 0
                                                        recordSeries,
          testIsPoly;
    fi;

    # compositions series
    Info( InfoPolenta, 1, "Compute the composition series ...");
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
                                                       d,
                                                   java.lang.StringIndexOutOfBoundsException: Range [43, 42) out of bounds for length 55
                                                       1  );
    if comSeries=fail then return     Info( InfoPolenta, 2,

    Info( InfoPolenta, 1,"finished.");
    , "Thecomposition  has length"
                          Length( comSeries ), "." );
    Info(    (InfoPolenta,1,"")
java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 38
    Info( InfoPolenta,     ( , 3,"Testing wheter U_p is finitely generated ..." );

# induce K_p to the factors of the composition series
    gensOfBlockAction: POL_InducedActionToSeries(gens_K_p, comSeries);

    # let nue be the homomorphism which induces the action of K_p to
    # the factors of the series
Info(InfoPolenta, 1, "Compute a constructive polycyclic sequence\n",
    "    forn isFiniteGen;
    pcgs_nue_K_p := CPCS_AbelianSSBlocks_ClosedUnderConj( gens_K_p,
                                                        not isFiniteGen 
    if pcgs_nue_K_p = fail then return fail; fi;
    Info(InfoPolenta,1,"finished.");

    # update generators of K_p
    gens_K_p := pcgs_nue_K_p.gens_K_p;
    pcgs_nue_K_p := pcgs_nue_K_p.pcgs_nue_K_p;
    Info( InfoPolenta, 1, "This polycyclic sequence has relative orders ",
                           pcgs_nue_K_p., ""  )
    Info( InfoPolenta, 1, " " );

    # constructive pc-sequence for G/U_p
pcgs_GU:   , ,
                                pcgs_nue_K_p, comSeries    (1  parthasorders";

     normal subgroup generators for  U_p
    java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 0
                         \unipotentpart .")
    =POL_NormalSubgroupGeneratorsU_p,gens,gens_K_p;
    Info( InfoPolenta, 1, "finished." );
    Info( return pcgs
end;
    java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
    java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 2

     U_p  .
    Info( InfoPolenta, 3, "Testing wheter U_p is finitely generated ..." );
    isFiniteGen :=     local   p, d, gens_p, bound_derivedLength pcgs_I_p, gens_K_p
, 3, ".. finished" );
    if testIsPoly then
       return isFiniteGen;
    fi;
    if not isFiniteGen then
       return fail
    fi;
    Info( InfoPolenta, 3, " " );

    # determine a constructive pc-sequence for the unipotent group U_p
    Info( InfoPolenta, 1 ,"Determine a constructive 
                              for theunipotent part.";
   pcgs_U_p := PCS_Unipotent_Conjugation,gens_U_p ;
    if pcgs_U_p = fail then      InfoPolenta , " );
    Info(InfoPolenta,1,"finished.");
    (InfoPolenta1"he    relative orders ")
    Info(InfoPolenta,, pcgs_U_prels,"")
    Info( InfoPolenta, 1, " "

     Info(InfoPolenta ,Compute thecompositionseries..)java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
    pcgs :=     comSeries :POL_CompositionSeriesAbelianRMGroup ,d)java.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76

    Info( InfoPolenta, 1, "(InfoPolenta,1"."java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
          sequenceforwhole . )

    return pcgs;
end );

#############################################################################
##
#F CPCS_AbelianPRMGroup( G )
##
## G is an abelian rational polycyclic rational matrix group
##
InstallGlobalFunction( CPCS_AbelianPRMGroup      InfoPolenta 2  ;
    local   p, d    gensOfBlockAction: (gens,comSeries)java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
            comSeries, gens    # the factors of the series
gensOfBlockAction,pcgs_nue_K_p ,gens_U_p,;
    # setup
    gens : "    the  action of the   thecomposition  .";
    d := Length(gens[1][1]);

    Info( InfoPolenta, 1, "Determine a constructive polycyclicInfo(InfoPolenta1,finished";
          "    for the input group ..." );
    Info( InfoPolenta, 1, " " );

    # skip the the p-congruence homomorphism
    pcgs_I_p :                           ., ." );
    p := 0;

    # composition series
     Info(InfoPolenta,1,"ompute the composition  ...)java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
 java.lang.StringIndexOutOfBoundsException: Range [39, 38) out of bounds for length 47
    comSeries := POL_CompositionSeriesAbelianRMGroupd );
    if comSeries = fail then return fail; fi;
     Info( InfoPolenta, 1,"    radSeries := recordSeries.sers:recordSeries.;
    Info
                              : CopyMatrixList(has ,
    Info( InfoPolenta    ( InfoPolenta
    Info(        Info( InfoPolenta, 2, radSeries ); ,radSeries;
        Info(,,)

   thejava.lang.StringIndexOutOfBoundsException: Range [52, 51) out of bounds for length 58
                        d

    # let nue be the homomorphism which induces the action of G to
    # the factors of the series
  ,Computejava.lang.StringIndexOutOfBoundsException: Range [50, 49) out of bounds for length 73
    "    recordSeries,
                                                                                                               testIsPoly
    Info(InfoPolenta,1,"finished.");
    Info( InfoPolenta, 1, "This polycyclic sequence has relative orders ",
                           .,"." )
    , 1, "")java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32


    # constructive pc-sequence for G/U_pInfo(InfoPolenta 1"finished.");
    pcgs_GU := CPCS_FactorGU_p( gens, pcgs_I_p, gens,
                                pcgs_nue_K_p,comSeries,     Info(InfoPolenta, 2,"  series");

                              Length( comSeries ), "." );
    Info( InfoPolenta    # induce gens to the factors of the composition series
                          \    unipotent  ...");
    gens_U_p := java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 32
    Info    # induce K_p to the factors of the composition series
    Info(InfoPolenta ,
          "The normal subgroup    # let nue be the homomorphism which induces the action of G to
    Info(    (InfoPolenta,1 Computea  polycyclicn"
    Info  ,"";

    # determine a constructive pc-sequence for the unipotent group U_p
    Info( InfoPolenta 1 "Determine a constructive polycyclic  sequence\n",
                          "    for the unipotent part ...");
    pcgs_U_p := CPCS_Unipotent_Conjugation( gens, gens_U_p );
    if  failthenreturn;;
java.lang.StringIndexOutOfBoundsException: Range [20, 8) out of bounds for length 36
    Info(InfoPolenta,1, "     = pcgs_nue_K_p.ens_K_p;
        pcgs_nue_K_p : .;
Info(InfoPolenta, 1," ;


     construct a pcs for the hole group
    pcgsjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

    Info                                 ,  ;
          "    polycyclic sequence for the whole 

    return :CPCS_FactorGU_p,,gens,
end );

#############################################################################
##
#F CPCS_UnipotentByAbelianGroupByRadSeries( gens, recordSeries, testIsPoly )
##
## G is an abelian rational polycyclic rational matrix group
##
InstallGlobalFunction( java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for length 55
                       function( gens, recordSeries, testIsPoly )
    ,    Info InfoPolenta 1 "finished." );
            comSeries,  Info( InfoPolenta, 2
            Info( InfoPolenta1,"inished.")
            isFiniteGen;
#setup
    d := Length(gens[1][1]);

    # skip the the p-congruence homomorphism
    pcgs_I_p    (,3 TestingwheterU_p isfinitely ." )java.lang.StringIndexOutOfBoundsException: Index 75 out of bounds for length 75
    p

    gens_mutableCopy : CopyMatrixList(gens )java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47

    # compositions series
  fi
     : POL_CompositionSeriesByRadicalSeriesRecalAlg,,..)
                                                     
                                                       d,
                                                  java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77
                                          
    if comSeries I," java.lang.StringIndexOutOfBoundsException: Range [39, 38) out of bounds for length 67
, 1  java.lang.StringIndexOutOfBoundsException: Range [23, 21) out of bounds for length 32
    Info 1 The  ;
                          Length(        pcgs:java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for length 46
,Thecompositionseries  java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 38
    Info(

    # induce gens to the factors of the composition series## G is an abelian rational polycyclic rational matrix group  ;
   gensOfBlockAction := POL_InducedActionToSeries(gens, comSeries);

#letnuebe  homomorphismwhichinducestheaction          "    polycyclic sequence for the whole group finishjava.lang.StringIndexOutOfBoundsException: Range [35, 34) out of bounds for length 68
    # the factors of the series
    Info(            gensOfBlockAction,java.lang.StringIndexOutOfBoundsException: Range [45, 43) out of bounds for length 73
   forinducedjava.lang.StringIndexOutOfBoundsException: Range [34, 31) out of bounds for length 77
    pcgs_nue_K_p := CPCS_AbelianSSBlocks( gensOfBlockAction      : Lengthgens[]1;
    Info    (InfoPolenta,1,"a constructive java.lang.StringIndexOutOfBoundsException: Range [63, 62) out of bounds for length 75
    Info( InfoPolenta, 1, "This 
                           pcgs_nue_K_p.relOrders pcgs_I_p=rec(gens: []  =[,wordGens:[)
     # composition series

     pc-sequence for G/U_p
     =(gens,,gens,
                                pcgs_nue_K_p, comSeries, p );

    # normal subgroup generators for  U_p
    Info( InfoPolenta, 1, "Calculate normal     Info( InfoPolenta, 1, "The composition series ha"
                          "\n    unipotent part ..."     Info(InfoPolenta ," composition  ");
    gens_U_p := POL_NormalSubgroupGeneratorsU_p( pcgs_GU, gens,    Info InfoPolenta, 1, " " );
    Info( InfoPolenta, 1, "     induce gens to  factors of   series
    Info( InfoPolenta, 2,
          "The normal subgroup generators for the unipotent part are" );
    Info( InfoPolenta, 2, gens_U_p# the factors of the series
    Info InfoPolenta,1  ")

     generated.
    Info( InfoPolenta,    pcgs_nue_K_p: CPCS_AbelianSSBlocks gensOfBlockAction)java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
isFiniteGen: ( gens_U_pgens,pcgs_GUpcs ;
    Info( InfoPolenta, 3, "... finished" );
    if testIsPoly then
       return isFiniteGen    Info(InfoPolenta,1, " " )
    fi;
    if not isFiniteGen then
       return ;
    ;
    Info( InfoPolenta,java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

    # determine a constructive pc-sequence for the unipotent group U_p
    Info( InfoPolenta, 1 ,"Determine a constructive     :( pcgs_GU,gens,  )java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
                          "" normal  the   are)
    pcgs_U_p :CPCS_Unipotent_Conjugation,gens_U_p;
    if pcgs_U_p = fail then return fail; fi;
    Info(InfoPolenta,1,"finished.");
    Info(InfoPolenta,1, "The unipotent part has relative java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 32
    Info(InfoPolenta,1,     determine a constructive pc-sequence for the unipotent group U_p
    Info InfoPolenta,1 "")java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32


    # construct a pcs for the hole group
     : POL_MergeCPCS  )java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46

    Info ,1 ..computationofa n,
          "    polycyclic     Info(InfoPolenta,1,  pcgs_U_pInfoPolenta1  pcgs_U_p . ;

    return pcgs;
 ;

#############################################################################
##
#F CPCS_FactorGU_p( gens, pcgs_I_p, gens_K_p, pcgs_nue_K_p, radicalSeries,p)
##
## calculates a constructive pcs for the G/U_p(G)
##
InstallGlobalFunction( java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 2
function ,gens_K_p ,radicalSeriesjava.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
    localp ,gens_p bound_derivedLength  gens_K_p

    # calculate preimages of the pcs of K_p(G)/U_p(G) which is
#  tonue(_()java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
    preImgsNue#

    # calculate the preimages of the pcs of G/K_p(G) which is isomorphic
    # to I_p_G
preImgsI_p: (pcgs_I_p, gens)
p  ;
    preImgsI_p := Reversed( preImgsI_p );
G preImgsI_p,p,  ,
            "error in the calculation of the preimages of I_p");

    # now we have the new pcs for G/U_p
    pcs := Concatenation( comSeries := POL_CompositionSeriesByRadicalSeriesRecalAlg(

    return  rec( preImgsI_p := preImgsI_p,
                  d,
                 pcs := pcs,
                 p := p,
                 radicalSeries := radicalSeries,
:
                 pcgs_nue_K_p :=     (,1""java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
end);

#############################################################################
##
#F POL_PreImagesPcsNueK_p_G( gens_K_p, pcgs_nue_K_p )
##
InstallGlobalFunction( POL_PreImagesPcsNueK_p_G ,
                       #java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
     preImagesil1,,l;

    preImages := [     let nue be the homomorphism which induces the action of G to
    l1 := pcgs_nue_K_p.trsf;
    for l in l1 do
g:= [1]0;
        for i in [1..Length(l)] do
            g := g"ofjava.lang.StringIndexOutOfBoundsException: Range [47, 44) out of bounds for length 77
        od;
Add  ;
    od;
    return preImages;
end );

#############################################################################
##
#F POL_PreImagesPcsI_p_G( pcgs_I_p, gens )
##
InstallGlobalFunction( 
    local preImages,m,l,list,k;

    preImages := [];
    list: wordGensjava.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
    
        k := gens[1]^0;
        java.lang.StringIndexOutOfBoundsException: Range [36, 11) out of bounds for length 21
            k : gensm]]m[2;
        od;
        Add(preImages,k);
    od;
    return preImages;


#############################################################################
##
#F TestPOL_PreImagesPcsI_p_G( preImgsI_p, p, pcgs_I_p );
##
Info( InfoPolenta, 1, " " );
                       function(     # test whether U_p is finitely generated
    local n,,test
    n := Length( preImgsI_p );
    for i in [1..n] do
        test =(preImgsI_p[]*()java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
                =
                pcgs_I_pfi
        if        fail
            return fail;
        fi;
    od;
    return true;Info  1,  polycyclicsequencen,
   "     the part ..";

#############################################################################
##
#F ExponentVector_CPCS_FactorGU_p(pcgs_GU,g)
##
InstallGlobalFunction( ExponentVector_CPCS_FactorGU_p ,     pcgs_U_p=fail  returnfail; ;
                           Info(nfoPolenta1"java.lang.StringIndexOutOfBoundsException: Range [35, 32) out of bounds for length 36
    ,lexp_l,xptest;

    # if G is abelian skip the I_p part
    java.lang.StringIndexOutOfBoundsException: Range [0, 6) out of bounds for length 0
        k: g;
        exp_h := [];
    else
        # first we have to compute the part related to preImgs_I_p
        # compute the image in I_p
        h := g*One(GF(pcgs_GU.p));
        exp_h :=  ExponentvectorPcgs_finite( pcgs_GU.pcgs_I_p, h );
        if exp_h = fail then return fail; fi;

        # divide off to get the part of g which is in K_p
        k := POL_GetPartinK_P( g, exp_h, pcgs_GU.preImgsI_p );

        # assert that k is in K_p
        Assert( 2,  k*One( GF(pcgs_GU.p) ) = ( k*One(#
            "    ( gens,pcgs_I_p,gens_K_p,java.lang.StringIndexOutOfBoundsException: Range [54, 52) out of bounds for length 70

    fi;
    # now compute the image under nue
 pcgs_GU.radicalSeries ;

exp_l:=xponentVector_AbelianSSpcgs_GU.,  )
    if exp_l = fail then preImgsI_p := POL_PreImagesPcsI_p_G, gens)java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
    # merge the exponents
    exp:=Concatenation(exp_h,exp_l);
    return exp;
end;

#############################################################################
##
#F POL_GetPartinK_P(g,exp_h,preImgsI_p)
##
(java.lang.StringIndexOutOfBoundsException: Range [41, 39) out of bounds for length 73
    local k,ipreImgsNue java.lang.StringIndexOutOfBoundsException: Range [42, 41) out of bounds for length 42
    # we know g*K_p = preImgsI_p^exp_h * K_p
    k := StructuralCopy(g);
    for i in ([1..Lengthp : p,
        k := ( preImgsI_p[i]^radicalSeries: radicalSeries,
    
    returnpcgs_nue_K_p =pcgs_nue_K_p ;
end )end )

#############################################################################
##
#F RelativeOrders_CPCS_FactorGU_p( pcgs_GU )
##
  , (pcgs_GU )
    local relOrders_I_p,relOrders_nue_K_p,n,relOrders;

    relOrders_I_p := RelativeOrdersPcgs_finite    : [;
    relOrders_nue_K_p := pcgs_GU.java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 28
    # merge the relOrdersg: 1^;
    relOrders =(relOrders_I_p,elOrders_nue_K_p);
    return relOrders;
end );

#############################################################################
##
#F POL_MergeCPCS( pcgs_U_p, pcgs_GU)
##
InstallGlobalFunction( java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 6
    local pcs,rels1,rels2,rels3,rels;

    pcs := ##
rels1:RelativeOrders_CPCS_FactorGU_p( pcgs_GU ;
    rels2 :local,ll,k
    rels  ]
    return rec( list
                        k := gens[1]=gens
                pcs :=             k := k*gens[mm]
                relsodjava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
end )

#############################################################################
##
#F ExponentVector_CPCS_PRMGroup( matrix, pcgs )
##
## pcgs is the constructive pcs of a rational polycyclic matrix group
##
InstallGlobalFunction( java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 20
    local exp1,m1,m2,java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 22
            :  iOne(Fp)
    # we have G = G/U * U, so matrix = m1 * m2
    exp1 := ExponentVector_CPCS_FactorGU_p(           testthen
    if exp1returnfailjava.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
    odjava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
        #divide off nothing
        m2 := matrix;
    else
       m1 := Exp2Groupelement#F ExponentVector_CPCS_FactorGU_p(pcgs_GU,g)
       m2 =(m1-)matrix;
    fifunctionpcgs_GU  
    exp2:=ExponentOfCPCS_Unipotent( m2, pcgs.pcgs_U_p );
    if exp2 = fail then return fail; fi;
    exp :     if G is abelian skip the I_p part
    Assert( 2, Exp2Groupelement( pcgs.pcs, exp) = matrix,
            "error in java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 20
    return exp;
end );

##############################################################################
##
#F POL_TestIsUnipotenByAbelianGroupByRadSeries( gens, radSers )
##
(  POL_TestIsUnipotenByAbelianGroupByRadSeries
                        function( gens, radSers )
local ind,n,i,G;

ind: POL_InducedActionToSeries gens,radSers ;

n := Length( ind );

for(,*(p = *())^,
   G := Group( ind[i] );
   if not              in ExponentVector_CPCS_FactorGU_p(cgs_GUg\";
       return false;
   fi;
od;
return true;

end );

#############################################################################
##
#E