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costab.c
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costab.c
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/****************************************************************************
**
** This file is part of GAP, a system for computational discrete algebra.
**
** 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 functions of for coset tables.
*/
#include "costab.h"
#include "bool.h"
#include "error.h"
#include "gvars.h"
#include "integer.h"
#include "io.h"
#include "lists.h"
#include "modules.h"
#include "plist.h"
/****************************************************************************
**
*V declaration of static variables
*/
static Obj objRel; // handle of a relator
static Obj objNums; // handle of parallel numbers list
static Obj objTable; // handle of the coset table
static Obj objTable2; // handle of coset factor table
static Obj objNext;
static Obj objPrev;
static Obj objFactor;
static Obj objTree; // handle of subgroup gens tree
static Obj objTree1; // first tree component
static Obj objTree2; // second tree component
static Obj objExponent; // handle of subgroup order
static Obj objWordValue; // handle of word value
static Int treeType; // tree type
static Int treeWordLength; // maximal tree word length
static Int firstDef;
static Int lastDef;
static Int firstFree;
static Int lastFree;
static Int minGaps; // switch for marking mingaps
static Int nrdel;
static Int dedfst; // position of first deduction
static Int dedlst; // position of last deduction
static Int dedgen [40960]; // deduction list keeping gens
static Int dedcos [40960]; // deduction list keeping cosets
static Int dedSize = 40960; // size of deduction list buffers
static Int dedprint; // print flag for warning
static Int wordList [1024]; // coset rep word buffer
static Int wordSize = 1023; // maximal no. of coset rep words
/* clean out global Obj-type variables to avoid hogging memory*/
static void CleanOut( void )
{
objRel = (Obj) 0;
objNums = (Obj) 0;
objTable = (Obj) 0;
objTable2 = (Obj) 0;
objNext = (Obj) 0;
objPrev = (Obj) 0;
objFactor = (Obj) 0;
objTree = (Obj) 0;
objTree1 = (Obj) 0;
objTree2 = (Obj) 0;
objExponent = (Obj) 0;
objWordValue = (Obj) 0;
}
/****************************************************************************
**
*F FuncApplyRel( <self>, <app>, <rel> ) apply a relator to a coset in a TC
**
** 'FuncApplyRel' implements the internal function 'ApplyRel'.
**
** 'ApplyRel( <app>, <rel> )'
**
** 'ApplyRel' applies the relator <rel> to the application list <app>.
**
** ... more about ApplyRel ...
*/
static Obj FuncApplyRel(Obj self,
Obj app, // handle of the application list
Obj rel) // handle of the relator
{
Int lp; // left pointer into relator
Int lc; // left coset to apply to
Int rp; // right pointer into relator
Int rc; // right coset to apply to
Int tc; // temporary coset
// check the application list
RequirePlainList(0, app);
if ( LEN_PLIST(app) != 4 ) {
ErrorQuit("<app> must be a list of length 4 not %d",
(Int)LEN_PLIST(app), 0);
}
// get the four entries
lp = INT_INTOBJ( ELM_PLIST( app, 1 ) );
lc = INT_INTOBJ( ELM_PLIST( app, 2 ) );
rp = INT_INTOBJ( ELM_PLIST( app, 3 ) );
rc = INT_INTOBJ( ELM_PLIST( app, 4 ) );
// get and check the relator (well, only a little bit)
RequirePlainList(0, rel);
// fix right pointer if requested
if ( rp == -1 )
rp = lp + INT_INTOBJ( ELM_PLIST( rel, 1 ) );
// scan as long as possible from the right to the left
while ( lp < rp
&& 0 < (tc = INT_INTOBJ(ELM_PLIST(ELM_PLIST(rel,rp),rc))) )
{
rc = tc; rp = rp - 2;
}
// scan as long as possible from the left to the right
while ( lp < rp
&& 0 < (tc = INT_INTOBJ(ELM_PLIST(ELM_PLIST(rel,lp),lc))) )
{
lc = tc; lp = lp + 2;
}
// copy the information back into the application list
SET_ELM_PLIST( app, 1, INTOBJ_INT( lp ) );
SET_ELM_PLIST( app, 2, INTOBJ_INT( lc ) );
SET_ELM_PLIST( app, 3, INTOBJ_INT( rp ) );
SET_ELM_PLIST( app, 4, INTOBJ_INT( rc ) );
// return 'true' if a coincidence or deduction was found
if ( lp == rp+1
&& INT_INTOBJ(ELM_PLIST(ELM_PLIST(rel,lp),lc)) != rc )
{
return True;
}
else
return False;
}
/****************************************************************************
**
*F CompressDeductionList() . . . . removes unused items from deduction list
**
** 'CompressDeductionList' tries to find and delete deduction list entries
** which are not used any more.
**
** 'dedgen', 'dedcos', 'dedfst', 'dedlst', 'dedSize' and 'objTable' are
** assumed to be known as static variables.
*/
static void CompressDeductionList ( void )
{
Obj * ptTable; // pointer to the coset table
Int i;
Int j;
// check if the situation is as assumed
if ( dedlst != dedSize ) {
ErrorQuit("invalid call of CompressDeductionList", 0, 0);
}
// run through the lists and compress them
ptTable = BASE_PTR_PLIST(objTable) - 1;
j = 0;
for ( i = dedfst; i < dedlst; i++ ) {
if ( INT_INTOBJ(ELM_PLIST(ptTable[dedgen[i]],dedcos[i])) > 0
&& j < i )
{
dedgen[j] = dedgen[i];
dedcos[j] = dedcos[i];
j++;
}
}
// update the pointers
dedfst = 0;
dedlst = j;
// check if we have at least one free position
if ( dedlst == dedSize ) {
if ( dedprint == 0 ) {
Pr("#I WARNING: deductions being discarded\n", 0, 0);
dedprint = 1;
}
dedlst--;
}
}
/****************************************************************************
**
*F HandleCoinc( <cos1>, <cos2> ) . . . . . . . . handle coincidences in a TC
**
** 'HandleCoinc' is a subroutine of 'FuncMakeConsequences' and handles the
** coincidence cos2 = cos1.
*/
static void HandleCoinc (
Int cos1,
Int cos2 )
{
Obj * ptTable; // pointer to the coset table
Obj * ptNext;
Obj * ptPrev;
Int c1;
Int c2;
Int c3;
Int i;
Int firstCoinc;
Int lastCoinc;
Obj * gen;
Obj * inv;
// is this test necessary?
if ( cos1 == cos2 ) return;
// get some pointers
ptTable = BASE_PTR_PLIST(objTable) - 1;
ptNext = BASE_PTR_PLIST(objNext) - 1;
ptPrev = BASE_PTR_PLIST(objPrev) - 1;
// take the smaller one as new representative
if ( cos2 < cos1 ) { c3 = cos1; cos1 = cos2; cos2 = c3; }
// if we are removing an important coset update it
if ( cos2 == lastDef )
lastDef = INT_INTOBJ( ptPrev[lastDef ] );
if ( cos2 == firstDef )
firstDef = INT_INTOBJ( ptPrev[firstDef] );
// remove <cos2> from the coset list
ptNext[INT_INTOBJ(ptPrev[cos2])] = ptNext[cos2];
if ( ptNext[cos2] != INTOBJ_INT( 0 ) )
ptPrev[INT_INTOBJ(ptNext[cos2])] = ptPrev[cos2];
// put the first coincidence into the list of coincidences
firstCoinc = cos2;
lastCoinc = cos2;
ptNext[lastCoinc] = INTOBJ_INT( 0 );
// <cos1> is the representative of <cos2> and its own representative
ptPrev[cos2] = INTOBJ_INT( cos1 );
// while there are coincidences to handle
while ( firstCoinc != 0 ) {
// replace <firstCoinc> by its representative in the table
cos1 = INT_INTOBJ( ptPrev[firstCoinc] ); cos2 = firstCoinc;
for ( i = 1; i <= LEN_PLIST(objTable); i++ ) {
gen = BASE_PTR_PLIST(ptTable[i]) - 1;
// inv = ADDR_OBJ(ptTable[ ((i-1)^1)+1 ] );
inv = BASE_PTR_PLIST(ptTable[i + 2 * (i % 2) - 1]) - 1;
// replace <cos2> by <cos1> in the column of <gen>^-1
c2 = INT_INTOBJ( gen[cos2] );
if ( c2 > 0 ) {
c1 = INT_INTOBJ( gen[cos1] );
// if the other entry is empty copy it
if ( c1 <= 0 ) {
gen[cos1] = INTOBJ_INT( c2 );
gen[cos2] = INTOBJ_INT( 0 );
inv[c2] = INTOBJ_INT( cos1 );
if ( dedlst == dedSize )
CompressDeductionList( );
dedgen[dedlst] = i;
dedcos[dedlst] = cos1;
dedlst++;
}
// otherwise check for a coincidence
else {
inv[c2] = INTOBJ_INT( 0 );
gen[cos2] = INTOBJ_INT( 0 );
if ( gen[cos1] <= INTOBJ_INT( 0 ) ) {
gen[cos1] = INTOBJ_INT( cos1 );
if ( dedlst == dedSize )
CompressDeductionList( );
dedgen[dedlst] = i;
dedcos[dedlst] = cos1;
dedlst++;
}
// find the representative of <c1>
while ( c1 != 1
&& INT_INTOBJ(ptNext[INT_INTOBJ(ptPrev[c1])]) != c1 )
{
c1 = INT_INTOBJ(ptPrev[c1]);
}
// find the representative of <c2>
while ( c2 != 1
&& INT_INTOBJ(ptNext[INT_INTOBJ(ptPrev[c2])]) != c2 )
{
c2 = INT_INTOBJ(ptPrev[c2]);
}
// if the representatives differ we got a coincindence
if ( c1 != c2 ) {
// take the smaller one as new representative
if ( c2 < c1 ) { c3 = c1; c1 = c2; c2 = c3; }
// if we are removing an important coset update it
if ( c2 == lastDef )
lastDef = INT_INTOBJ(ptPrev[lastDef ]);
if ( c2 == firstDef )
firstDef = INT_INTOBJ(ptPrev[firstDef]);
// remove <c2> from the coset list
ptNext[INT_INTOBJ(ptPrev[c2])] = ptNext[c2];
if ( ptNext[c2] != INTOBJ_INT( 0 ) )
ptPrev[INT_INTOBJ(ptNext[c2])] = ptPrev[c2];
// append <c2> to the coincidence list
ptNext[lastCoinc] = INTOBJ_INT( c2 );
lastCoinc = c2;
ptNext[lastCoinc] = INTOBJ_INT( 0 );
// <c1> is the rep of <c2> and its own rep.
ptPrev[c2] = INTOBJ_INT( c1 );
}
}
}
// save minimal gap flags
else if ( minGaps != 0 && c2 == -1 ) {
if ( gen[cos1] <= INTOBJ_INT( 0 ) ) {
gen[cos1] = INTOBJ_INT( -1 );
}
gen[cos2] = INTOBJ_INT( 0 );
}
}
// move the replaced coset to the free list
if ( firstFree == 0 ) {
firstFree = firstCoinc;
lastFree = firstCoinc;
}
else {
ptNext[lastFree] = INTOBJ_INT( firstCoinc );
lastFree = firstCoinc;
}
firstCoinc = INT_INTOBJ( ptNext[firstCoinc] );
ptNext[lastFree] = INTOBJ_INT( 0 );
nrdel++;
}
}
/****************************************************************************
**
*F FuncMakeConsequences( <self>, <list> ) find consqs of a coset definition
*/
static Obj FuncMakeConsequences(Obj self, Obj list)
{
Obj hdSubs;
Obj objRels;
Obj * ptRel; // pointer to the relator bag
Obj * ptNums; // pointer to this list
Int lp; // left pointer into relator
Int lc; // left coset to apply to
Int rp; // right pointer into relator
Int rc; // right coset to apply to
Int tc; // temporary coset
Int i; // loop variable
Obj hdTmp; // temporary variable
RequirePlainList(0, list);
objTable = ELM_PLIST( list, 1 );
objNext = ELM_PLIST( list, 2 );
objPrev = ELM_PLIST( list, 3 );
firstFree = INT_INTOBJ( ELM_PLIST( list, 6 ) );
lastFree = INT_INTOBJ( ELM_PLIST( list, 7 ) );
firstDef = INT_INTOBJ( ELM_PLIST( list, 8 ) );
lastDef = INT_INTOBJ( ELM_PLIST( list, 9 ) );
minGaps = INT_INTOBJ( ELM_PLIST( list, 12 ) );
nrdel = 0;
// initialize the deduction queue
dedprint = 0;
dedfst = 0;
dedlst = 1;
dedgen[ 0 ] = INT_INTOBJ( ELM_PLIST( list, 10 ) );
dedcos[ 0 ] = INT_INTOBJ( ELM_PLIST( list, 11 ) );
// while the deduction queue is not empty
while ( dedfst < dedlst ) {
// skip the deduction, if it got irrelevant by a coincidence
hdTmp = ELM_PLIST( objTable, dedgen[dedfst] );
hdTmp = ELM_PLIST( hdTmp, dedcos[dedfst] );
if ( INT_INTOBJ(hdTmp) <= 0 ) {
dedfst++;
continue;
}
// while there are still subgroup generators apply them
hdSubs = ELM_PLIST( list, 5 );
for ( i = LEN_LIST( hdSubs ); 1 <= i; i-- ) {
if ( ELM_PLIST( hdSubs, i ) != 0 ) {
objNums = ELM_PLIST( ELM_PLIST( hdSubs, i ), 1 );
ptNums = BASE_PTR_PLIST(objNums) - 1;
objRel = ELM_PLIST( ELM_PLIST( hdSubs, i ), 2 );
ptRel = BASE_PTR_PLIST(objRel) - 1;
lp = 2;
lc = 1;
rp = LEN_LIST( objRel ) - 1;
rc = 1;
// scan as long as possible from the right to the left
while ( lp<rp && 0 < (tc=INT_INTOBJ(ELM_PLIST(ptRel[rp],rc))) ) {
rc = tc; rp = rp - 2;
}
// scan as long as possible from the left to the right
while ( lp<rp && 0 < (tc=INT_INTOBJ(ELM_PLIST(ptRel[lp],lc))) ) {
lc = tc; lp = lp + 2;
}
// if a coincidence or deduction has been found, handle it
if ( lp == rp + 1 ) {
if ( INT_INTOBJ(ELM_PLIST(ptRel[lp],lc)) != rc ) {
if ( INT_INTOBJ( ELM_PLIST(ptRel[lp],lc) ) > 0 ) {
HandleCoinc( INT_INTOBJ( ELM_PLIST(ptRel[lp],lc) ), rc );
}
else if ( INT_INTOBJ( ELM_PLIST(ptRel[rp],rc) ) > 0 ) {
HandleCoinc( INT_INTOBJ( ELM_PLIST(ptRel[rp],rc) ), lc );
}
else {
SET_ELM_PLIST( ptRel[lp], lc, INTOBJ_INT( rc ) );
SET_ELM_PLIST( ptRel[rp], rc, INTOBJ_INT( lc ) );
if ( dedlst == dedSize )
CompressDeductionList();
dedgen[ dedlst ] = INT_INTOBJ( ptNums[lp] );
dedcos[ dedlst ] = lc;
dedlst++;
}
}
// remove the completed subgroup generator
SET_ELM_PLIST( hdSubs, i, 0 );
if ( i == LEN_PLIST(hdSubs) ) {
while ( 0 < i && ELM_PLIST(hdSubs,i) == 0 )
--i;
SET_LEN_PLIST( hdSubs, i );
i++;
}
}
// if a minimal gap has been found, set a flag
else if ( minGaps != 0 && lp == rp - 1 ) {
SET_ELM_PLIST( ptRel[lp], lc, INTOBJ_INT( -1 ) );
SET_ELM_PLIST( ptRel[rp], rc, INTOBJ_INT( -1 ) );
}
}
}
// apply all relators that start with this generator
objRels = ELM_PLIST( ELM_PLIST( list, 4 ), dedgen[dedfst] );
for ( i = 1; i <= LEN_LIST( objRels ); i++ ) {
objNums = ELM_PLIST( ELM_PLIST(objRels,i), 1 );
ptNums = BASE_PTR_PLIST(objNums) - 1;
objRel = ELM_PLIST( ELM_PLIST(objRels,i), 2 );
ptRel = BASE_PTR_PLIST(objRel) - 1;
lp = INT_INTOBJ( ELM_PLIST( ELM_PLIST(objRels,i), 3 ) );
lc = dedcos[ dedfst ];
rp = lp + INT_INTOBJ( ptRel[1] );
rc = lc;
// scan as long as possible from the right to the left
while ( lp<rp && 0 < (tc=INT_INTOBJ(ELM_PLIST(ptRel[rp],rc))) ) {
rc = tc; rp = rp - 2;
}
// scan as long as possible from the left to the right
while ( lp<rp && 0 < (tc=INT_INTOBJ(ELM_PLIST(ptRel[lp],lc))) ) {
lc = tc; lp = lp + 2;
}
// if a coincidence or deduction has been found, handle it
if ( lp == rp+1 && INT_INTOBJ(ELM_PLIST(ptRel[lp],lc)) != rc ) {
if ( INT_INTOBJ( ELM_PLIST(ptRel[lp],lc) ) > 0 ) {
HandleCoinc( INT_INTOBJ( ELM_PLIST(ptRel[lp],lc) ), rc );
}
else if ( INT_INTOBJ( ELM_PLIST(ptRel[rp],rc) ) > 0 ) {
HandleCoinc( INT_INTOBJ( ELM_PLIST(ptRel[rp],rc) ), lc );
}
else {
SET_ELM_PLIST( ptRel[lp], lc, INTOBJ_INT( rc ) );
SET_ELM_PLIST( ptRel[rp], rc, INTOBJ_INT( lc ) );
if ( dedlst == dedSize )
CompressDeductionList();
dedgen[ dedlst ] = INT_INTOBJ( ptNums[lp] );
dedcos[ dedlst ] = lc;
dedlst++;
}
}
// if a minimal gap has been found, set a flag
else if ( minGaps != 0 && lp == rp - 1 ) {
SET_ELM_PLIST( ptRel[lp], lc, INTOBJ_INT( -1 ) );
SET_ELM_PLIST( ptRel[rp], rc, INTOBJ_INT( -1 ) );
}
}
dedfst++;
}
SET_ELM_PLIST( list, 6, INTOBJ_INT( firstFree ) );
SET_ELM_PLIST( list, 7, INTOBJ_INT( lastFree ) );
SET_ELM_PLIST( list, 8, INTOBJ_INT( firstDef ) );
SET_ELM_PLIST( list, 9, INTOBJ_INT( lastDef ) );
// clean out
CleanOut();
return INTOBJ_INT( nrdel );
}
/****************************************************************************
**
*F FuncMakeConsequencesPres( <self>, <list> ) . . . . . . find consequences
**
** This is a special version of `FuncMakeConsequences' for the subgroup
** presentation routines.
*/
static Obj FuncMakeConsequencesPres(Obj self, Obj list)
{
Obj objDefs1; // handle of defs list part 1
Obj objDefs2; // handle of defs list part 2
Obj objRels;
Obj * ptRel; // pointer to the relator bag
Obj * ptNums; // pointer to this list
Int ndefs; // number of defs done so far
Int undefined; // maximal of undefined entreis
Int apply; // num of next def to be applied
Int ndefsMax; // maximal number of definitions
Int coset; // coset involved in current def
Int gen; // gen involved in current def
Int lp; // left pointer into relator
Int lc; // left coset to apply to
Int rp; // right pointer into relator
Int rc; // right coset to apply to
Int tc; // temporary coset
Int i; // loop variable
RequirePlainList(0, list);
objTable = ELM_PLIST( list, 1 );
objDefs1 = ELM_PLIST( list, 2 );
objDefs2 = ELM_PLIST( list, 3 );
undefined = INT_INTOBJ( ELM_PLIST( list, 4 ) );
ndefs = INT_INTOBJ( ELM_PLIST( list, 5 ) );
// check the definitions lists
if ( ! ( IS_PLIST(objDefs1) && IS_PLIST(objDefs2) &&
LEN_PLIST(objDefs1) == LEN_PLIST(objDefs2) ) ) {
ErrorQuit("inconsistent definitions lists", 0, 0);
}
ndefsMax = LEN_PLIST(objDefs1);
apply = 1;
// while the deduction queue is not worked off
while ( apply <= ndefs ) {
// apply all relators that start with this generator
coset = INT_INTOBJ( ELM_PLIST( objDefs1, apply ) );
gen = INT_INTOBJ( ELM_PLIST( objDefs2, apply ) );
objRels = ELM_PLIST( ELM_PLIST( list, 6 ), gen );
for ( i = 1; i <= LEN_LIST( objRels ); i++ ) {
objNums = ELM_PLIST( ELM_PLIST(objRels,i), 1 );
ptNums = BASE_PTR_PLIST(objNums) - 1;
objRel = ELM_PLIST( ELM_PLIST(objRels,i), 2 );
ptRel = BASE_PTR_PLIST(objRel) - 1;
lp = INT_INTOBJ( ELM_PLIST( ELM_PLIST(objRels,i), 3 ) );
lc = coset;
rp = lp + INT_INTOBJ( ptRel[1] );
rc = lc;
// scan as long as possible from the right to the left
while ( lp<rp && 0 < (tc=INT_INTOBJ(ELM_PLIST(ptRel[rp],rc))) ) {
rc = tc; rp = rp - 2;
}
// scan as long as possible from the left to the right
while ( lp<rp && 0 < (tc=INT_INTOBJ(ELM_PLIST(ptRel[lp],lc))) ) {
lc = tc; lp = lp + 2;
}
// if a deduction has been found, handle it
if ( lp == rp+1 && INT_INTOBJ(ELM_PLIST(ptRel[rp],rc)) <= 0 ) {
SET_ELM_PLIST( ptRel[lp], lc, INTOBJ_INT( rc ) );
undefined--;
if ( INT_INTOBJ(ELM_PLIST(ptRel[rp],rc)) <= 0 ) {
SET_ELM_PLIST( ptRel[rp], rc, INTOBJ_INT( lc ) );
undefined--;
}
ndefs++;
if ( ndefs > ndefsMax ) {
ErrorQuit("inconsistent definitions lists", 0, 0);
}
SET_ELM_PLIST( objDefs1, ndefs, INTOBJ_INT( lc ) );
SET_ELM_PLIST( objDefs2, ndefs, ptNums[lp] );
if ( undefined == 0 ) {
return INTOBJ_INT( 0 );
}
}
}
apply++;
}
// clean out
CleanOut();
return INTOBJ_INT( undefined );
}
/****************************************************************************
**
*F FuncStandardizeTableC(<self>,<table>,<stan>) . . . . . . standardize CT
**
** This is the kernel routine for standardizing a coset table. It is called
** by the GAP routine 'StandardizeTable'. The user should not call the
** kernel routine but only the GAP routine.
**
** If <stan> = 1 the table is standardized using the (old) semilenlex
** standard.
** If not <stan> = 1 the table is standardized using the (new) lenlex
** standard (this is the default).
*/
static Obj FuncStandardizeTableC(Obj self, Obj table, Obj stan)
{
Obj * ptTable; // pointer to table
UInt nrgen; // number of rows of the table / 2
Obj * g; // one generator list from table
Obj * h; // generator list
Obj * i; // and inverse
UInt acos; // actual coset
UInt lcos; // last seen coset
UInt mcos;
UInt c1, c2; // coset temporaries
Obj tmp; // temporary for swap
UInt j, k, nloop; // loop variables
RequirePlainList(0, table);
// get the arguments
objTable = table;
ptTable = BASE_PTR_PLIST(objTable) - 1;
nrgen = LEN_PLIST(objTable) / 2;
for ( j = 1; j <= nrgen*2; j++ ) {
if ( ! IS_PLIST(ptTable[j]) ) {
ErrorQuit(
"<table>[%d] must be a plain list (not a %s)",
(Int)j,
(Int)TNAM_OBJ(ptTable[j]) );
}
}
if (stan == INTOBJ_INT(1)) {
// use semilenlex standard
nloop = nrgen;
}
else {
// use lenlex standard
nloop = nrgen*2;
}
// run over all cosets
acos = 1;
lcos = 1;
while ( acos <= lcos ) {
// scan through all columns of acos
for ( j = 1; j <= nloop; j++ ) {
k = ( nloop == nrgen ) ? 2*j - 1 : j;
g = BASE_PTR_PLIST(ptTable[k]) - 1;
// if we haven't seen this coset yet
if ( lcos+1 < INT_INTOBJ( g[acos] ) ) {
// swap rows lcos and g[acos]
lcos = lcos + 1;
mcos = INT_INTOBJ( g[acos] );
for ( k = 1; k <= nrgen; k++ ) {
h = BASE_PTR_PLIST(ptTable[2 * k - 1]) - 1;
i = BASE_PTR_PLIST(ptTable[2 * k]) - 1;
c1 = INT_INTOBJ( h[lcos] );
c2 = INT_INTOBJ( h[mcos] );
if ( c1 != 0 ) i[c1] = INTOBJ_INT( mcos );
if ( c2 != 0 ) i[c2] = INTOBJ_INT( lcos );
tmp = h[lcos];
h[lcos] = h[mcos];
h[mcos] = tmp;
if ( i != h ) {
c1 = INT_INTOBJ( i[lcos] );
c2 = INT_INTOBJ( i[mcos] );
if ( c1 != 0 ) h[c1] = INTOBJ_INT( mcos );
if ( c2 != 0 ) h[c2] = INTOBJ_INT( lcos );
tmp = i[lcos];
i[lcos] = i[mcos];
i[mcos] = tmp;
}
}
}
// if this is already the next only bump lcos
else if ( lcos < INT_INTOBJ( g[acos] ) ) {
lcos = lcos + 1;
}
}
acos = acos + 1;
}
// shrink the table
for ( j = 1; j <= nrgen; j++ ) {
SET_LEN_PLIST( ptTable[2*j-1], lcos );
SET_LEN_PLIST( ptTable[2*j ], lcos );
}
// clean out
CleanOut();
return 0;
}
/****************************************************************************
**
*F InitializeCosetFactorWord() . . . . . . . initialize a coset factor word
**
** 'InitializeCosetFactorWord' initializes a word in which a new coset
** factor is to be built up.
**
** 'wordList', 'treeType', 'objTree2', and 'treeWordLength' are assumed to
** be known as static variables.
*/
static void InitializeCosetFactorWord ( void )
{
Obj * ptWord; // pointer to the word
Int i; // integer variable
// handle the one generator MTC case
if ( treeType == 1 ) {
objWordValue = INTOBJ_INT(0);
}
// handle the abelianized case
else if ( treeType == 0 ) {
ptWord = BASE_PTR_PLIST(objTree2) - 1;
for ( i = 1; i <= treeWordLength; i++ ) {
ptWord[i] = INTOBJ_INT(0);
}
}
// handle the general case
else {
wordList[0] = 0;
}
}
/****************************************************************************
**
*F TreeEntryC() . . . . . . . . . . . . returns a tree entry for a rep word
**
** 'TreeEntryC' determines a tree entry which represents the word given in
** 'wordList', if it finds any, or it defines a new proper tree entry, and
** then returns it.
**
** Warning: It is assumed, but not checked, that the given word is freely
** reduced and that it does not contain zeros, and that the tree type is
** either 0 or 2.
**
** 'wordList' is assumed to be known as static variable.
**
*/
static Int TreeEntryC ( void )
{
Obj * ptTree1; // ptr to first tree component
Obj * ptTree2; // ptr to second tree component
Obj * ptWord; // ptr to given word
Obj * ptFac; // ptr to old word
Obj * ptNew; // ptr to new word
Obj objNew; // handle of new word
Int treesize; // tree size
Int numgens; // tree length
Int leng; // word length
Int sign; // sign flag
Int i, k; // integer variables
Int gen; // generator value
Int u, u1, u2; // generator values
Int v, v1, v2; // generator values
Int t1, t2; // generator values
Int uabs, vabs; // generator values
// Get the tree components
ptTree1 = BASE_PTR_PLIST(objTree1) - 1;
ptTree2 = BASE_PTR_PLIST(objTree2) - 1;
treesize = LEN_PLIST(objTree1);
numgens = INT_INTOBJ( ELM_PLIST( objTree, 3 ) );
// handle the abelianized case
if ( treeType == 0 )
{
ptWord = BASE_PTR_PLIST(objTree2) - 1;
for ( leng = treeWordLength; leng >= 1; leng-- ) {
if ( ptWord[leng] != INTOBJ_INT(0) ) {
break;
}
}
if ( leng == 0 ) {
return 0;
}
for ( k = 1; k <= leng; k++ ) {
if ( ptWord[k] != INTOBJ_INT(0) ) {
break;
}
}
sign = 1;
if ( INT_INTOBJ( ptWord[k] ) < 0 ) {
// invert the word
sign = - 1;
for ( i = k; i <= leng; i++ ) {
ptWord[i] = INTOBJ_INT( - INT_INTOBJ( ptWord[i] ) );
}
}
for ( k = 1; k <= numgens; k++ ) {
ptFac = BASE_PTR_PLIST(ptTree1[k]) - 1;
if ( LEN_PLIST(ptTree1[k]) == leng ) {
for ( i = 1; i <= leng; i++ ) {
if ( ptFac[i] != ptWord[i] ) {
break;
}
}
if ( i > leng ) {
return sign * k;
}
}
}
// extend the tree
numgens++;
if ( treesize < numgens ) {
treesize = 2 * treesize;
GROW_PLIST( objTree1, treesize );
CHANGED_BAG(objTree);
}
objNew = NEW_PLIST( T_PLIST, leng );
SET_LEN_PLIST( objNew, leng );
SET_ELM_PLIST( objTree, 3, INTOBJ_INT(numgens) );
SET_LEN_PLIST( objTree1, treesize );
SET_ELM_PLIST( objTree1, numgens, objNew );
CHANGED_BAG(objTree1);
// copy the word to the new bag
ptWord = BASE_PTR_PLIST(objTree2) - 1;
ptNew = BASE_PTR_PLIST(objNew) - 1;
while ( leng > 0 ) {
ptNew[leng] = ptWord[leng];
leng--;
}
return sign * numgens;
}
// handle the general case
// Get the length of the word
leng = wordList[0];
gen = ( leng == 0 ) ? 0 : wordList[1];
u2 = 0; // just to shut up gcc
for ( i = 2; i <= leng; i++ ) {
u = gen;
v = wordList[i];
while ( i ) {
// First handle the trivial cases
if ( u == 0 || v == 0 || ( u + v ) == 0 ) {
gen = u + v;
break;
}
// Cancel out factors, if possible
u1 = INT_INTOBJ( ptTree1[ (u > 0) ? u : -u ] );
if ( u1 != 0 ) {
if ( u > 0 ) {
u2 = INT_INTOBJ( ptTree2[u] );
}
else {
u2 = - u1;
u1 = - INT_INTOBJ( ptTree2[-u] );
}
if ( u2 == -v ) {
gen = u1;
break;
}
}
v1 = INT_INTOBJ( ptTree1[ (v > 0) ? v : -v ] );
if ( v1 != 0 ) {
if ( v > 0 ) {
v2 = INT_INTOBJ( ptTree2[v] );
}
else {
v2 = - v1;
v1 = - INT_INTOBJ( ptTree2[-v] );
}
if ( v1 == -u ) {
gen = v2;
break;
}
if ( u1 != 0 && v1 == - u2 ) {
u = u1;
v = v2;
continue;
}
}
// Check if there is already a tree entry [u,v] or [-v,-u]
if ( u < -v ) {
t1 = u;
t2 = v;
}
else {
t1 = -v;
t2 = -u;
}
uabs = ( u > 0 ) ? u : -u;
vabs = ( v > 0 ) ? v : -v;
k = ( uabs > vabs ) ? uabs : vabs;
for ( k++; k <= numgens; k++ ) {
if ( INT_INTOBJ(ptTree1[k]) == t1 &&
INT_INTOBJ(ptTree2[k]) == t2 )
{
break;
}
}
// Extend the tree, if necessary
if ( k > numgens ) {
numgens++;
if ( treesize < numgens ) {
treesize = 2 * treesize;
GROW_PLIST( objTree1, treesize );
GROW_PLIST( objTree2, treesize );
ptTree1 = BASE_PTR_PLIST(objTree1) - 1;
ptTree2 = BASE_PTR_PLIST(objTree2) - 1;
SET_LEN_PLIST( objTree1, treesize );
SET_LEN_PLIST( objTree2, treesize );
CHANGED_BAG(objTree);
}
ptTree1[numgens] = INTOBJ_INT( t1 );
ptTree2[numgens] = INTOBJ_INT( t2 );
SET_ELM_PLIST( objTree, 3, INTOBJ_INT(numgens) );
}
gen = ( u > - v ) ? -k : k;
break;
}
}
return gen;
}
/****************************************************************************
**
*F AddCosetFactor2( <factor> ) . add a factor to a coset representative word
**
** 'AddCosetFactor2' adds a factor to a coset representative word and