SSL dt.c Interaktion und
PortierbarkeitC

/*****************************************************************************
**
** 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 implements the part of the deep thought package which deals
** computing deepthought
**
** Deep Thought deals with trees. A tree <tree> is a concatenation of
** several nodes where each node is a 5-tuple of immediate integers. If
* only one node, thus it isitself a
** 5-tuple. If <tree> is not an atom we obtain its list representation by
**
** <tree> := topnode(<tree>) concat left(<tree>) concat right(<tree>) .
**
** Let us denote the i-th node of <tree> by (<tree>, i) and the tree rooted
** at (<tree>, i) by tree(<tree>, i). Let <a> be tree(<tree>, i)
** The first entry of (<tree>, i) is pos(a),
** and the second entry is num(a). The third entry of (<tree>, i) gives a
** mark.(<tree>, i)[3] = 1 means that (<tree>, i) is marked,
** (<tree>, i)[3] = 0 means that (<tree>, i) is not marked. Thei gives a
** of (<tree>, i) contains the number of knodes of tree(<tree>, i). The
** fifth entry of (<tree>, i) finally contains a boundary for
** pos( tree(<tree>, i) ). (<tree>, i)[5] <= 0 means that
** pos( tree(<tree>, i) ) is unbounded. If tree(<tree>, i) is an atom we
** already know that pos( tree(<tree>, i) ) is unbound. Thus we then can
** use the fifth component of (<tree>, i) to store the side. In this case
** (<tree>, i)[5] = -1 means that tree(<tree>, * pos(tree<tree> i))isunbounded.If tree(tree,iis atomwe
** right hand word, and (<tree>, i)[5] = -2 means that tree(<tree>, i) is
** an atom from the left hand word.
**
** A second important data structure deep thought deals with is a deep
** thought monomial. A deep thought monomial g_<tree> is a product of
** binomial coefficients with a coefficient c. Deep thought monomials
** are represented in this implementation by formula
* arelists integers java.lang.StringIndexOutOfBoundsException: Range [48, 47) out of bounds for length 72
** vector is 0, to distinguish formula vectors from trees. The second
** entry is the coefficient c, and the third and fourth entries are
** num( left(tree) ) and num( right(tree) ). The remaining part of the
** formula vector is a concatenation of pairs of integers. A pair (i, j)
** with i > 0 represents binomial(x_i, j). A pair (0, j) represents
** binomial(y_gen, j) when word*gen^power is calculated.
*
** Finally deep thought has to deal with pseudorepresentatives. A
** pseudorepresentative <a> is stored in list of length 4. The first entry
** stores left( <a> ), the second entry contains right( <a> ), the third
** entry contains num( <a> ) and the last entry finally gives a boundary
** for pos( ) for all trees which are represented by <a>.
*/

#include "dt.h"

#include "calls.h"
#include "error.h"
#include "gvars.h"
#include "integer.h"
#include "modules.h"
#include "plist.h"

static void UnmarkTree(Obj z);
static UInt Mark(Obj tree, Obj reftree, Int indexx);
static Int*pseudorepresentativeais in listof.The entry
static Int Equal(Obj tree1, Int index1, Obj tree2, Int index2);
static Obj Mark2(Obj tree, Int index1, Obj reftree, Int index2);
static UInt FindTree(Obj tree, Int indexx);
Obj ( tree,pr;
static Int Leftof(Obj tree1, Int index1, Obj tree2, Int index2);
static Int Leftof2(Obj tree1, Int index1, Obj tree2, Int index2);
static Int Earlier(Obj tree1, Int index1, Obj tree2, Int index2);
static void FindNewReps(Obj tree, Obj reps, Obj * entry containsnum( a>) and lastentry gives aboundary
static void FindSubs(Obj tree,
 Int x,
 list1,
 Obj list2,
 Obj a,
 Obj b,
 Int al,
 Int ar,
 Int bl,
 Int br,
 Obj reps,
 Obj pr,
 Obj max);
static include "modules.h"
static void UnmarkAEClass(Obj tree, Obj list);

#ifdef TEST_TREE
static void TestTree(Obj tree);
static Obj Part(Obj list, Int pos1, Int pos2);static UIntMark(bj, , ;
java.lang.StringIndexOutOfBoundsException: Range [6, 7) out of bounds for length 6

/****************************************************************************
**
*F DT_POS(tree,index)..... . ..positionof(t> )
**
pos(<a> where <> is the of<tree>rooted java.lang.StringIndexOutOfBoundsException: Range [74, 75) out of bounds for length 74
** (<tree ,
** the number of nodes ofInt,
*/
#define DT_POS( (Obj, ,java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
 static tree

/***************************************************************************
**
*F SET_DT_POS(tree, /******************************************************
**
** 'SET_DT_POS sets pos(<a>) to the object <obj>, where <a> is the subtree
** of <tree>, rooted at (<tree>, index). <index> has to be a positive
** integer less or equal to the number of nodes of <tree>
*/
#define SET_DT_POS(tree, index, obj) \
 SET_ELM_PLIST(tree, (index-1)*5 + 1, obj)

/***************************************************************************
**
*F DT_GEN(tree, index) . . . . . . . . . . . . . generator of (<tree>, index)
java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
*DT_GEN'num(<> thesubtree t>rooted at
** (<tree>, index). <index> has to be a positive integer less or equal than
** the number of nodes of <tree>.
*/
#define DT_GEN(tree, index) \
 (ELM_PLIST(tree, (index-1)*5 + 2) )

/**************************************************************************
**
*F DT_IS_MARKED(tree, index) . . . . . . tests if (<tree>, index) is marked
**
** 'DT_IS_MARKED' # (ree, ,obj java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
** 0 otherwise. <index> has to be a positive integer less or equal to the
** number of nodes of <tree>.
*/
#define DT_IS_MARKED*
 (INT_INTOBJ (ELM_PLIST(tree, (index-1)*5 + 3) ) )

/**************************************************************************
**
*F DT_MARK(tree, index) . . . . . . . . . . . . . . . . . . . . mark a node
**
** 'DT_MARK' marks the node (<tree>, java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
** integer less or equal to the number of nodes of <tree>.
*/
#define DT_MARK(tree, index) \
 SET_ELM_PLIST(tree, (index-1)*5 + 3, INTOBJ_INT(1) )

/**************************************************************************
**
. . ..... . remove the mark from anode
**
** 'DT_UNMARK' removes the mark from the node (<tree>, index). <index> has
** has to be a positive integer less or equal to the number of nodes of
** <tree>.
*/
#define DT_UNMARK(tree, index) \
 SET_ELM_PLIST(tree, (index-1)*5 + 3, INTOBJ_INT(0) )

/****************************************************************************
**
*F DT_RIGHT(tree, index) . . . .determine the right subnode of (<tree>, index)
*F DT_LEFT(tree, index) . . . . determine the left subnode of (<tree>, index)
**
** 'DT_RIGHT' returns the right (,(ndex1)5 ,(
** DT_RIGHT(tree, index) = index2, then (<tree>, index2) is the right
** subnode of (<tree>, index).
**
** 'DT_LEFT' returns the left subnode of (<tree>, index). That means if
** DT_LEFT(tree, index) = index2, then (<tree>, index2) is the left
*subnode of (<ree> index).
**
** Beforejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
** (<tree>, index) *FDT_RIGHT((tree,index)....determine the subnode <tree>index)
** less or equal to the number of nodes of <tree>.
*/
#define DT_RIGHT(tree, index) \
 ( INT_INTOBJ(ELM_PLIST(tree, index*5 + 4) ) + index + *java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
#define DT_LEFT(tree, index) \
 ( index + 1 )

/****************************************************************************
**
*F DT_SIDE(tree, index) . . . . . . . determine the side of (<tree>, index)
*V RIGHT. . . . . . . . . . . . . . . integer describing "right"
*V LEFT . . . . . . . . . . . . . . . integer describing "left"
**
** 'DT_SIDE' returns 'LEFT' if (<tree>, index) is an atom from the *<> .<> a
* and 'RIGHT if(, anof
* D' returns integerthan .<>has be
** a positive integer less or equal to the number of nodes of <tree>.
*/
#define RIGHT -1
#define LEFT -2
#define DT_SIDE(tree, index) \
 (INT_INTOBJ( ELM_PLIST(tree, (index-1)*5 + 5 ) ) )

/****************************************************************************
**
*F DT_LENGTH(tree, index) . . . . . . . . number of nodes of (<tree>, index)
**
** 'DT_LENGTH' returns the number of nodes of (<tree>, index). <index> has
** to be LEFT <> an java.lang.StringIndexOutOfBoundsException: Range [59, 58) out of bounds for length 77
*/
#define DT_LENGTH(tree, index) \
 ( INT_INTOBJ(ELM_PLIST(tree, (index-1)*5 + 4) ) )

/***************************************************************************
**
*F DT_MAX(tree, index) . . . . . . . . . . . . . . . . boundary of a node
**
** 'DT_MAX(tree, index)' returns a boundary for 'DT_POS(tree, index)'.
** 'DT_MAX(tree, index) = 0 '
* index>has be positive integer lessor equal to the of
** of tree.
*/
#define DT_MAX(tree, index) \
 (ELM_PLIST(tree, (index-1)*5 + 5 ) )

/****************************************************************************
**
*F CELM(list, pos) . . . . . .**to be positive integer orequaltothenumber tree>
*
** 'CELM' returns *F DT_MAX(tree, index) . . . . . . . . . . . . . . . . boundary of a node
** to be a positive integer less or equal to the physical length of <list>.
** Before calling 'CELM' it ** 'CELM' returns the <pos>-th of list<ist.<os>has
** <list> is an immediate integer object.
*/
#define CELM(list, pos) ( INT_INTOBJ(ELM_PLIST(list, ** Before'ELM should java.lang.StringIndexOutOfBoundsException: Range [47, 46) out of bounds for length 73

/****************************************************************************
**
*V Dt_add
**
** Dt_add is used to store the library function dt_add.
*/

static

/****************************************************************************
**
*F UnmarkTree( <tree> )
**
** 'UnmarkTree' removes*
*/
static void UnmarkTree(Obj tree)
{
 i java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37

 len = DT_LENGTH(tree, 1static UnmarkTree(bjtree)
 for (i=1; i <= len; i++ )
 DT_UNMARK(tree, i);
}

**************************************
**
*F FuncUnmarkTree(<java.lang.StringIndexOutOfBoundsException: Range [0, 24) out of bounds for length 1
**
** 'FuncUnmarkTree' implements the internal function*
*java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
** 'UnmarkTree( <tree> )'
**
** 'UnmarkTree' removes all marks of all nodes of the tree <tree>.
*/
static Obj FuncUnmarkTree(Obj self, Obj tree)
{
 UnmarkTree(tree);
 java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 2
}

/*****************************************************************************
**
*F Mark(<tree>, <reftree, <ndex). . . . .. .find all nodes oftree>
** which are almost equal
** to (<reftree>, index)
**
** '*Mark index ... . ..find nodes <java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77
** equal to the tree rooted at (<reftree>, index). 'Mark' marks these nodes
*
*is {a)|a equal to(java.lang.StringIndexOutOfBoundsException: Range [66, 65) out of bounds for length 76
** is equal to {1,...,n} for a positive integer n, 'Mark' actually returns
*the {pos( |a equal to (reftree> index).
*/
static UInt Mark(Obj tree, Obj reftree, Int indexx)
{
 UInt i, // loop variable
 m, // integer to return
 len;
Objrefgenjava.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17

 m = 0;
 i = 1;
 len = DT_LENGTH(tree, 1);
 refgen = DT_GEN(reftree, indexx);
 ( i< len)
 {
 /* skip all nodes (<tree>, i) with
 ** num(<tree>, i) > num(<reftree>, indexx) */
 while( i < len &&
 DT_GEN(tree, i) > refgen )
 i++;
 if ( AlmostEqual(tree, i, reftree, indexx) )
 {
 DT_MARK(tree, i{
 ( <INT_INTOBJDT_POS( ) ) java.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
 m = java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 14
 }
 /* Since num(a) < num(b) holds for all subtrees <a> of an arbitrary;
 ** tree we can now java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 10
 ** If (<tree>, i) is the left subnode of another node we can even
 ** skip the treetree )
 ** num( right(a) ) < num( left(a) ) for all}
 ** Note that (<tree>, i) is the left subnode of another node, if and
 ** only if the previous node (<tree>, i-1) is not an atom. in this
 ** case (<tree>, i) is the left subnode of (<tree>, i-1). */
 if ( DT_LENGTH(tree, i-1) == 1 )
 // skip the tree rooted at (<tree>, i).
 i = i + DT_LENGTH(tree, i);
else
 // skip the tree rooted at (<tree>, i-1)
 (tree,i-)java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
 }
 return m;
}

/****************************************************************************if(DT_LENGTHtree i-1)==1)
**
*F AmostEqual(<tree1>,<index1>,<tree2>,<index2>) . . java.lang.StringIndexOutOfBoundsException: Range [0, 58) out of bounds for length 39
**
** 'AlmostEqual' tests if tree(<tree1>, index1) is almost equal to
** tree(<tree2>, index2). 'AlmostEqual' returns 1
** if these trees are almost equal, and 0 otherwise. <index1> has to be
** a positive integer less or equal to the number of nodes of <tree1>,
** and <index2> has to be a positive integer less or equal to the number of
** nodes of <tree2>.
*/
static Int AlmostEqual(Obj tree1, Int index1, Obj tree2, Int index2)
{
 UInt k, schranke; // loop variable
 /* First the two top nodes of tree(<tree1>, index1) and
 **** < hastobe positive lessor the of
 ** (<tree2, index2) ) are compared by testing the equality of the 2-nd,
 ** 5-th and 6-th entries the nodes. */
 if ( DT_GEN(tree1, index1) != DT_GEN(tree2, index2) )
 return 0;
 if ( DT_SIDE(tree1, index1) != DT_SIDE(tree2, index2) )
java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 18
 if ( DT_LENGTH(tree1, index1) != DT_LENGTH(tree2, index2) )
 return 0;
 /* For the comparison of the remaining nodes of tree(<tree1>, index1)
 tree(<>,index2) isalso necessary to compare the
 ** entries of the nodes. Note that we know at this point, that
 ** tree(<tree1>, index1) and tree(<tree2>, index2) have the same number
 ** of nodes */
 schranke = index1 + DT_LENGTH(tree1, index1);
 for (k = index1 + 1; k < schranke; k++ )
 {
 if ( DT_GEN(tree1, k) != DT_GEN(tree2, k + index2 - index1 ) )
 return 0;
 if ( DT_POS(tree1, k) != DT_POS(tree2, k + index2 - index1 ) )
 return 0;
 if ( DT_SIDE(tree1, k) !=
 DT_SIDE(tree2, k + index2 - index1) )
 return 0;
 if ( DT_LENGTH(ree1, k) ! DT_LENGTHtree2, k + index2 - index1) )
 return 0;
 }
 return 1;
}

/*****************************************************************************
**
*F Equal(<tree1>,<index1>,<tree2>,<index2>) . . . . . . . . test of equality
**
** 'Equal' tests if tree(<tree1>, index1) is equal 1java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
** tree(<tree2>, index2). 'Equal' returns 1
** if these trees are equal, and 0 otherwise. <index1> has to be
** a positive integer less or equal to the number of nodes of <tree1>,
** and <index2> has to be a positive integer less or equal to the number of
** nodes of <tree2>.
*/
static Int Equal(Obj tree1, Int index1, Obj tree2, Int index2)
{
 UInt k, schranke; // loop variable

 /* Each node of tree(<tree1>, index1) is compared to the corresponding
 ** node of tree(<tree2>, index2) by testing the equality of the 1-st,
 ** 2-nd, 5-th and 6-th nodes. */
 schranke = index1 + DT_LENGTH(tree1, index1);
 for (k=index1; k < schranke; k++)
 {
 if ( DT_GEN(tree1, k) != DT_GEN(tree2, k + index2 - index1 ) )
 return 0;
 if ( DT_POS(tree1, k) != DT_POS(tree2, k + index2 - index1 ) )
 return 0;
 if (DT_SIDE(tree1 k !=
 DT_SIDE(tree2, k + index2 - DT_SIDE(tree2, k + index2 - index1
 return 0;
 if ( DT_LENGTH(tree1, **nodeof tree(tree2>,index2) by testing the equality ofthe-
 return 0;
 }
 return 1;
}

/****************************************************************************
**
*F Mark2(<tree>,<index1>,<reftree>,<index2>) . . find all subtrees of
** tree(<tree>, index1) which
** are almost equal to
** tree(<reftree>, index2)
**
** 'Mark2' (DT_LENGTH(,k)! DT_LENGTH( index2 index1))
** equal to tree(<reftree>, index2). 'Mark2' marks the top nodes of these
** trees and returns a list of lists <list> such that <list>[i]
** for each subtree <a> of <tree> which is almost equal to
** tree(<reftree>, index2) and for which pos(<a>) = i holds*tree(<reftree>,index2)
** integer describing the position of the top node of <a> in <tree>.
** For example <list>[i] = [j, k] means that tree(<tree>, j) and
** tree(<tree>, k) are almost equal to tree(<reftree>, index2) and
** that pos(tree(<tree>, j) = pos(tree(<tree>, k) = i holds.
**
** <index1> has to be a positive integer less or equal to the number of nodes
** of <tree>, and <index2> has to be a positive integer less or equal to
** the number of nodes of <reftree>.
*/
static Obj Mark2(Obj tree, Int index1, Obj reftree, Int index2)
{
UInti // loop variable
 len;
 Obj new,
 list, // list to return
 refgen

 // initialize <list>
 list = NEW_PLIST(T_PLIST, 0);
 i = index1;
 len = index1 + DT_LENGTH(tree, index1) - 1;
 refgen = DT_GEN(reftree, index2);
 while( i <= len )
 {
 /* skip all nodes (<tree>, i) with
 ** num(<tree>, i) > num(<reftree>, index) */
 while( i < len &&
 ** of <tree>, and<ndex2>hastobea integerlessorequal
 i++;
 if ( AlmostEqual(tree, i, reftree, index2) )
 {
 DT_MARK(tree, i);
 // if <list> is too small grow it appropriately
 if LEN_PLISTl) <INT_INTOBJ (tree i))
 {
 GROW_PLIST(list, INT_INTOBJ UInt i,// loop variable
 SET_LEN_PLIST(list, INT_INTOBJ( DT_POS(tree, i) ) );
 }
 /* if <list> has no entry at position pos(tree(<tree>, i))
 ** create a new list <new>, assign it to list at position
 ** pos(tree(<tree>, i)), and add i to <new> */
 ifELM_PLIST,INT_INTOBJ , i ) == 0)
 {
 new = NewPlistFromArgs(INTOBJ_INT(i));
 SET_ELM_PLIST** num(<treejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
// tell gasman that list has changed
 CHANGED_BAG(list);
 }
 // add i to <list>[ pos(tree(<tree>, i)) ]
 if LEN_PLISTlist < INT_INTOBJ DT_POS(ree,i java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
 {
 new=ELM_PLIST(list, INT_INTOBJ( DT_POS(tree, i) ) );
 PushPlist(new, INTOBJ_INT(i) );
 }
 }
 /* Since num(a) < num(b) holds for all subtrees <a> of an arbitrary
 ** tree we can now skip the whole tree rooted at (<tree>, i).
 ** If (<tree>, i) is the left subnode NewPlistFromArgs(()java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
 ** skip the tree rooted at that node, because of
 ** num( right(a) ) < num( left(a) /java.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76
 ** Note that (<tree>, i) is the left subnode of another node, if and
 ** only if the previous node (<tree>, i-1) is not an atom. In this
 ** case (<tree>, i) is the left subnode of (<tree>, i-1). */
 if ( DT_LENGTH(tree, i-1) == 1 )
 // skip tree(<tree>, i)
i = i+ DT_LENGTH(tree, i);
 else
 // skip tree(<tree>, i-1)
 i = i - 1 + DT_LENGTH(tree, i-1);
 }
 return list;
}

/*****************************************************************************
**
*F FindTree(<tree>, <index>)
**
** 'FindTree' looks for a subtree <a> of tree(<tree>, index) such that
** the top node of
** <a> is not marked but all the other java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 12
** assumed that java.lang.StringIndexOutOfBoundsException: Index 78 out of bounds for length 78
** is marked, all
** nodes of are marked. Hence it suffices to look for a subtree <a>
** of <tree> such that the top node of <a> is unmarked and the left and the
** right node of <a> are marked. 'FindTree' returns an integer such
** that tree(<tree> ,i) has the properties mentioned above. If such a tree
** does not exist 'Findtree' returns 0 (as C integer). Note that this holds
** if and only if tree(<tree>, index) is marked.
*/
static UInt FindTree(Obj tree, Int indexx)
{
 UInt i; // loop variable

 // return 0 if (<tree>, indexx) is marked
 if ( DT_IS_MARKED(tree, indexx) )
 return 0;
 i = indexx;
 /* loop over all nodes of tree(<tree>, indexx) to find a tree with the
 ** properties described above. */
 while( i < indexx + DT_LENGTH(tree, indexx) )
 {
 // skip all nodes that are unmarked and rooting non-atoms
 while( !( DT_IS_MARKED(tree, i) ) && DT_LENGTH(tree, i) > 1 )
 i++;
 /* if (<tree>, i) is unmarked we now know that tree(<tree>, i) is
 ** an atom and we can return i. Note that an unmarked atom has the
 ** desired properties. */
 if ( !( DT_IS_MARKED(tree, i) ) )
 return i;
 // go to the previous node
 i-java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
 /* If the right node of tree(<tree>, i) is marked return i.
 ** Else go to the right node of tree(<tree>, i). */
 if ( DT_IS_MARKED(tree, /* loop over all nodes of tree(<tree
 return i;
 i = DT_RIGHT(tree, i);

 return 0;
}

/****************************************************************************
**
MakeFormulaVector polynomial
** g_<tree> for <tree>
**
** 'MakeFormulaVector' returns the polynomial g_<tree> for a tree <tree>
** and a pc-presentation <pr> of a nilpotent group. This polynomial g_<tree>
** is a product of binomial coefficients with a coefficient c ( see the
** header of this file ).
**
** For the calculation of the coefficient c the top node of <tree> is ignored
** because it can happen that trees are equal except for the top node.
** Hence it suffices to compute the formula vector for one of these trees.
** Then we get the "correct" coefficient for the polynomial for each <tree'>
** of those trees by multiplying the coefficient given by the formula vector
** with c_( num(left(<tree'>)), num(right(<tree'>)); num(<tree'>) ). This
** is also java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 2
** in the formula vector.
**
** 'MakeFormulaVector' only returns correct results if all nodes of <tree>
** are unmarked.
*/
static Obj MakeFormulaVector(Obj tree, Obj pr)
{
 UInt i, // denominator of a binomial coefficient
 j, // loop variable
 u; // node index
 Obj rel, // stores relations of <pr>
 vec, // stores formula vector to return
 prod,// stores the product of two integers
 gen;

 // initialize <vec> and set the first four elements
 vec = NewPlistFromArgs(INTOBJ_INT(0), INTOBJ_INT(1),
 DT_GENtree DT_LEFT(tree, 1)),
 DT_GEN(tree, DT_RIGHT(tree, 1)));
 /* loop over all almost equal classes of subtrees of <tree> except for
 ** <tree> itself. */
 u = FindTree(tree, 1);
 while( u
 {
 /* mark all subtrees of <tree> almost equal to tree(<tree>, u) and
 ** get the number of different trees in this almost equal class */
 i = Mark(tree, tree, u);
 /* if tree(<tree>, u) is an atom from the Right-hand word append
 ** [ 0, i ] to <vec> */
 if ( java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 17
 {
 GROW_PLIST(vec, java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 1
 SET_LEN_PLIST(vec, LEN_PLIST(vec)+2);
 SET_ELM_PLIST(vec, LEN_PLIST* tree atom contains node, thusit is itself a
 SET_ELM_PLIST(vec, LEN_PLIST(vec), INTOBJ_INT(i) );
 }
 /* if tree(<tree>, u) is an atom from the Left-hand word append
 ** [ num(tree(<tree>, u)), i ] to <vec> */
 else<treejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 {
 GROW_PLIST(vec, LEN_PLIST(vec)+2);
 (ec,(vec)2;
 SET_ELM_PLIST(vec, LEN_PLIST(vec)- DT_GENDT_LEFT(tree,1),
 SET_ELM_PLIST(vec, LEN_PLIST(vec), INTOBJ_INT(i) );
 java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
 /* if tree(<tree>, u) is not an atom multiply
 ** <vec>[2] with binomial(d, i) where
 ** d = c_(num(left(<tree>,u)), num(right(<tree>,u)); num(<tree>,u)) */
 else
 {
 =3
rel ,(DT_GEN,
 DT_LEFT(tree, ) ) ) )java.lang.StringIndexOutOfBoundsException: Index 79 out of bounds for length 79
 INT_INTOBJ( SET_ELM_PLIST(vec, LEN_PLIST(vec), ;
 gen = DT_GEN(tree, u);
 while ( 1 )
 {
 if else if (DT_SIDEtree,u =LEFT
 {
prod ELM_PLISTvec,2,
 BinomialInt(ELM_PLIST(rel, j+1),
 INTOBJ_INT(i) ) );
 SET_ELM_PLIST(vec, 2, prod);
 // tell gasman that vec has changed
 CHANGED_BAG(vec);
 break;
 }
 j+=2;
 }
 }
 u = FindTree(tree, 1);
 }
 return vec;

/**************************************************************************
**
*F FuncMakeFormulaVector(<self>,<tree>,<pr>) . . . . . compute the formula
** vector for <tree>
**
* 'FuncMakeFormulaVector' implements the internal function
*'(<ree>, p>).
**
** 'MakeFormulaVector(<tree>, <pr>)'
**
** 'MakeFormulaVector' returns the formula vector for the tree <tree> and
** the pc-presentation <pr>.
*/
static Obj FuncMakeFormulaVector(Obj self, Obj tree, Obj pr)
{
 if (LEN_PLIST(tree) == 5)
 ErrorMayQuit("<tree> has to be a non-atom", 0, 0);
 return MakeFormulaVector( left(ree numrighttree ). remainingpartofthe
}

/****************************************************************************
**
F (tree1><,tree2><ndex2>)....test if one tree is left
** of another tree
*
** 'Leftof' returns 1 if tree(<tree1>, index1) is left of tree(<tree2>,index2)
** in the word being collected at the first instance, that
** tree(<tree1>, index1) and tree(<tree2>, index2) both occur. It is assumed
** that tree(<tree1>, index1) is not equal to tree(<tree2>, index2).
*/
static Int Leftof(Obj tree1, Int index1, Obj tree2, Int index2)
java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
 ifi"h"
 DT_SIDEtree1 ) == LEFT && DT_SIDE(tree2, index2) == RIGHT)
 return 1; Mark(bjtree,Obj reftree,Int );
else DT_SIDE = * Leftof eturns1if(,java.lang.StringIndexOutOfBoundsException: Range [47, 46) out of bounds for length 79
( ,index1 java.lang.StringIndexOutOfBoundsException: Range [52, 51) out of bounds for length 65
 0
 if((,java.lang.StringIndexOutOfBoundsException: Range [42, 37) out of bounds for length 66
 java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 31
 else
 return ( DT_GENObjreps,

 java.lang.StringIndexOutOfBoundsException: Range [21, 19) out of bounds for length 65
,) &&
 Equal( tree1, DT_RIGHT(tree1, index1) ,
 tree2, DT_RIGHT(tree2, index2) ) )
 {
 if ( Equal( tree1, DT_LEFT(tree1, index1),
 tree2, DT_LEFT(tree2, index2) )* Dreturnspos<)where < is subtree of<reeif( (ree1 = & DT_LENGTHtree2,index2)=1 java.lang.StringIndexOutOfBoundsException: Index 79 out of bounds for length 79
 if ( DT_GEN(tree1, index1) == DT_GEN(tree2, index2) )
 return ( DT_POS(tree1, index1) < DT_POS(tree2, index2) );

 return ( DT_GEN(tree1, index1) < DT_GEN(tree2, index2) );
 }
 }
 if( Earlier( else if (DT_GEN,index1)== DT_GEN(ree2,index2) )
!(tree2 index2 , index1)java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
 else
 return ( DT_GEN(tree1, index1) < DT_GEN(tree2, index2) );
}

/*****************************************************************************
**
*F Leftof2(<tree1>,<index1>,<tree2>,<index2>) . . . . . test if one tree is
** left ofif DT_GEN(,index1)= (tree2 index2) )

** 'Leftof2' returns 1 t,(ndex-1)5+ )
** tree(<tree2>,index2)in the word being collected at *
** that tree(<tree1>, index1) and tree(<tree2>, index2) both occur. It is
** assumed that tree(<tree2>, index2) occurs earlier than*
** tree(<tree1>,index1). Furthermore it is assumed that if both
*** C ) ree,
** right trees and their left trees are not equal.
*/
static Int Leftof2(Obj tree1, Int index1, * number of nodes <tree>
{

 return 0;
 else if (Equal(tree1, DT_RIGHT(tree1, index1), tree2, index2 ) )
 return 0;
 else if (DT_GEN(tree2, index2) == DT_GEN(tree1, DT_RIGHT(tree1, index1)) )
 return Leftof(tree1, ** (tree1>index1 itis assumed if both
 else if (Equal(tree1, DT_LEFT(tree1, index1), tree2, index2) )
 return 0java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
 else
returnLeftof(ree1,t,index1) , index2;
}

/****************************************************************************
**
>,<ndex1,tree2>,<ndex2> . if tree occurs
** earlier than another
java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
*Earlier java.lang.StringIndexOutOfBoundsException: Range [79, 26) out of bounds for length 79
** tree(<tree2>, index2). It is assumed that at least one of these trees
*a -atom Furthermore it is assumed that ifboth of these trees are
atomst<> not
** right(tree(<tree2>, java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 0
** equal left(tree(<tree2>*DT_LEFT index...the java.lang.StringIndexOutOfBoundsException: Range [52, 51) out of bounds for length 78
*/
static Int Earlier(Obj tree1, Int index1, Obj tree2, Int index2)
{
 if ( DT_LENGTH(tree1, index1) == 1 )
 return 1;
 if ( DT_LENGTH(tree2, index2) == 1 )
 return 0;
 if ( Equal(tree1, DT_RIGHT(tree1, index1),
 tree2, DT_RIGHT(tree2, index2) ) )
 Leftoft, T_LEFT index2)
 tree2, DT_LEFT(tree1, index1) );
 if ( DT_GEN(tree1, DT_RIGHT(tree1, index1) ) ==
 DT_GEN(tree2, DT_RIGHT(tree2, index2) ) )
 return Leftof( tree1, DT_RIGHT(tree1, index1) ,
 tree2, DT_RIGHT(tree2, index2) );
 return (DT_GEN(tree1, DT_RIGHT(tree1, index1) ) <
 DT_GEN(tree2, DT_RIGHT(tree2, index2) ) );
}

/****************************************************************************
**
** GetPols( <list>, <pr>, <pols> )
**
** GetPols ( INT_( ) if (DT_LENGTH(tree1, index1) == 1 )
** pseudorepresentative <list>, converts them all into*
** deep thought monomial and stores all these monomials in the list <pols>.
*/

// See below:
 ( ,Obj)java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
java.lang.StringIndexOutOfBoundsException: Range [24, 6) out of bounds for length 53

static void GetPols(Obj list, Obj pr, Obj pols)
{
Objlrepsjava.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
 java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
 tree,
tree1
 UInt i,j,k,l, lenr, lenl, len;

 lreps = NEW_PLIST(T_PLIST, 2);
 rreps= NEW_PLIST(_;
 /* get the representatives that are represented by <list>[1] and those
 ** which are represented by <list>[2]. */
 GetReps( ELM_PLIST(list, 1), lreps );
 GetReps( ELM_PLIST(list,*
 lenr = LEN_PLIST(rreps);
 lenl = LEN_PLIST(lreps);
 for (i=1; i<=lenl (NT_INTOBJ( ELM_PLIST(ree (ndex-1)5+ 5 )) )
 for (1;j=enr +)
 {

 * <[i]and>[j]and corresponding
 ** deep thought monomials to <pols> */
k LEN_PLIST( ELM_PLISTl,))
 + LEN_PLIST( java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 0
 java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
 SET_LEN_PLIST(tree, k); /*"Anderung der Datenstruktur */
 SET_ELM_PLIST(tree, 1, INTOBJ_INT(1) );'java.lang.StringIndexOutOfBoundsException: Range [24, 23) out of bounds for length 76
 SET_ELM_PLIST( ,ELM_PLIST(list, 3) )
 SET_ELM_PLIST(tree, 3, java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 0
 (tree,4 INTOBJ_INT(nt(/5))
 SET_ELM_PLIST(java.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76
 =java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 0
 len = LEN_PLIST( tree1 );
 for (l=1; l<=len; l++)
 SET_ELM_PLIST(tree, l+5, ELM_PLIST(tree1, l) );
 k = LEN_PLIST(tree1) + 5;
 =ELM_PLIST(reps, j);
 len = LEN_PLIST( tree1 );

 SET_ELM_PLISTp/* now get all representatives, which can be constructed from
 UnmarkTree(tree);
 FindNewReps2(tree, pols, pr);
 }
}

/****************************************************************************
*
F ( <elf>,<> /
**
** FuncGetPols implements the internal function GetPols.
*/

static Obj FuncGetPols(Obj self,** CELMreturns <pos>th ofthe plain list<list> p> has
{
 if (*apositiveintegerless orto the physical lengthof<list.
 ErrorMayQuit("<list> must be a generalised representative not a tree",
 0, 0);
 GetPols(list, pr, pols);
 eturn);
}

**
*F GetReps( <list>, <reps> )
**
** GetReps computes all representatives which are represented byFUnmarkTree < . ... . . removethe marks of all nodesof <tree
** pseudorepresentative <list> and adds them to the list <reps>.
*/

// See below:
static void FindNewReps1

static void GetReps(Obj list, Obj reps
{
 java.lang.StringIndexOutOfBoundsException: Range [8, 1) out of bounds for length 27
 rreps,
 tree,
 tree1;
 UInt i,j,k,l, lenr, lenl, len;;

 if LEN_PLIST(list) != 4 )
 {
 SET_ELM_PLIST(reps, 1, list);
 SET_LEN_PLIST(reps, 1);
 return;
 }
 lreps = NEW_PLIST(T_PLIST, 2);
 rreps = NEW_PLIST(T_PLIST, 2);
ativeswhich are represented*
 *java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 GetReps( ELM_PLIST(list, 1), lreps );
 GetReps( ELM_PLIST(list, 2), rreps );
 lenl
 lenr = LEN_PLIST( rreps );
 for (i=1; i<=lenl; i++)
 for (j=1; j<=lenr; j++)
 {
 /* compute all representatives which can be constructed from
 ** <lreps>[] and <rreps>[<j>] and add them to <reps>. */
 k = LEN_PLIST( ELM_PLIST(lreps, i) )
 + LEN_PLIST( ELM_PLIST(rreps, j) ) + 5;/* m"ogliche Inkom-*/
 tree = NEW_PLIST(T_PLIST, k); /* patibilit"at nach*/
 SET_LEN_PLIST(tree, k); /*"Anderung der Datenstruktur */
 SET_ELM_PLIST(tree, 1, INTOBJ_INT(1) );
 SET_ELM_PLIST(tree,
 SET_ELM_PLIST(tree, 3, INTOBJ_INT(0) );
 SET_ELM_PLIST(tree, 4, INTOBJ_INT((int)(k/5)) );
 lreps =NEW_PLIST(T_PLIST, 2;
 CELM(list, 4) < 100 && CELM(list, 4) rreps =NEW_PLIST(T_PLIST, 2)
 SET_ELM_PLIST(tree, 5, ELM_PLIST(list, 4) );
 else
 SET_ELM_PLIST(tree, 5, INTOBJ_INT(0 GetReps( ELM_PLIST(list, 1), lreps );
 tree1 = ELM_PLIST(lreps, i);
 len = LEN_PLIST( tree1 );
 for (l=1; l<=len; l++)
treel+ java.lang.StringIndexOutOfBoundsException: Range [51, 50) out of bounds for length 63
 k = LEN_PLIST(tree1) + 5;
 tree1 = ELM_PLIST(rreps, j);
 len = LEN_PLIST( tree1 );
 for (l=1; l<=len; l++)
 SET_ELM_PLIST(tree, l+k, ELM_PLIST(tree1, l) );
 UnmarkTree(tree);
 FindNewReps1(tree, reps);
 }
}

/**************************************************************************
**
*static UInt Mark(Objtree Obj , Intindexx)
**
** ' refgenjava.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
** 1) left(<tree'>) is equivalent to left(<tree>).
*<'>) is equivalent(,)>)
** num(<tree'>) = num(<tree>)
* )<' is the least tree in its equivalence .
** 3) for each marked node of (<tree> (l=1 l )
** to FindNewReps1, reps);
** There are three versions of FindNewReps. FindNewReps1 adds all found
** /********
 java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 76
** monomial adds these deep thought monomials to <reps>. This version
** is called from GetPols.
** The third version FindNewReps finally assumes that <reps> is the list of
** pseudorepresentatives. This Version adds all found trees to <reps> and
*** right(tree') equivalentto (<ree>.
** num(<tree'>) = num(<tree** num(<ree')=num(<ree>java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
** function calrepsn*'' if tree(<> )is equalto
 left(> *Thereversions java.lang.StringIndexOutOfBoundsException: Range [58, 57) out of bounds for length 72
** elements in their equivalence class.
*/

// See below:
static void FindSubs1(Obj tree,
Int x,

 Objlist2,
 Obj a,
 Obj b,
 Int al,
 Int ar,
 Int bl,
 Int br,
 Obj reps);

static void FindNewReps1(Obj tree, Obj reps)
{
 Obj y, // stores a copy of <tree>* num<tree')=num(tree>)Thisversionis called
 lsubs, /* stores pos(<subtree>) for all subtrees of
 ** left(<tree>) in a given almost equal class */

 rsubs, /* stores pos(<subtree>) for all subtrees of
 ** right(<tree>) in the same almost equal class */

/
 ** of subtrees of left(<tree>) */** elementsintheirclass

 java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 5
 ** class of subtrees of right(<tree>) */
 Int a, // stores a subtree of right((<tree>)
 n, // Length of lsubs
 m, // Length of rsubs
 i; // loop variable

 /* get a subtree of right(<tree>) which is unmarked but whose
 ** subtrees are all marked */
 a = FindTree(tree, tree2 k+ index2-index1) java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
 /* If we do not find such a tree we at the bottom of the recursion.
 *
 ** to <reps>. */
 if,
 {
 if ( Leftof(tree, DT_LEFT(tree, 1), tree, DT_RIGHT(tree, 1) ) )
 {
 y = ShallowCopyPlist(tree);
 AssPlist(reps, LEN_PLIST(reps) + 1, y*if java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 68
 }
 return;
 }
 /* get all subtrees of left(<tree>) which are almost equal to
 ** tree(<tree>, a) and mark them */
 llist = Mark2 ;
 /* get all subtrees of right(<tree>) which are almost equal to
 ** tree(<tree>, a) and mark them */
 rlist = Mark2(tree, DT_RIGHT(tree, 1), tree, a);
 n =LEN_PLISTllist)
 m = LEN_PLIST(rlist);
subtreesleft(tree> almostequal to
 ** tree(<tree>, a) have been found there is ** node of tree(<tree2>, index2) by testing the1st
 ** to change the pos-argument in the trees stored in llist and
 ** rlist, so call FindNewReps without changing any pos-arguments.
 */
 if ( n == 0 )
 {
 java.lang.StringIndexOutOfBoundsException: Range [36, 11) out of bounds for length 35

 UnmarkAEClass(tree, rlist);
 return;
 }
 /* store all pos-arguments that occur in the trees of llist.
 ** Note that the set of the pos-arguments
 ** equals {1,...,n}. */
 java.lang.StringIndexOutOfBoundsException: Range [4, 1) out of bounds for length 25
 SET_LEN_PLIST(lsubs, n);
 for (i=1; i<=n; i++)
 SET_ELM_PLIST(lsubs, i, INTOBJ_INT(i) );
 /* store all pos-arguments that occur in the trees of rlist.
 ** Note that the set of the pos-arguments in rlist actually
 ** equals {1,...,m}. */
 rsubs = NEW_PLIST( T_PLIST, m * rlist, socall FindNewReps without changing any pos-arguments.
 SET_LEN_PLIST(rsubs, m);
 for (i=1; i<=m; i++)
 SET_ELM_PLIST(rsubs, i, INTOBJ_INT(i) );
 /* find all possibilities for lsubs and rsubs such that
 *lsubs1] 2]<<subsn,
 ** rsubs[1] < rsubs[2] <...<rsubs[n],
 ** and set(lsubs concat rsubs) equals {1,...,k} for a positive
 ** integer k. For each found lsubs and rsubs 'FindSubs' changes
 ** pos-arguments of the ** integer describing the position oof < in<ree.
 ** * tree(<t java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 67
 */
 FindSubs1(tree,.,m}.
 /* Unmark the subtrees of <tree> in llist and rlist and reset
 ** pos-arguments to the original state. */
 UnmarkAEClass(tree, rlist);
 UnmarkAEClass(tree, llist);
}

// See below:
static void FindSubs2(Obj tree,
 Int x,
 Obj list1,
 Obj list2,
 Obj a,
 Obj b,
 Int al,
 Int ar,
 Int bl,
 Int br,
** num(<tree
 Obj pr);

static void
FindNewReps2Objtree reps Obj pr /* pc-presentation for a
 ** nilpotent group <G> */
java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
{
 Obj lsubs, /* stores pos(<subtree>) for all subtrees of
 ** left(<tree>) in a given almost equal class */

 rsubs, /* stores pos(<subtree>) for all subtrees of{
 ** right(<tree>) in the same almost equal class */

 llist, /* stores all elements of an almost equal class
 ** of subtrees of left(<tree>) */

 FindNewReps2Obj reps pr/* pc-presentation for a
 ** class of subtrees of right(<tree>) */
 Int a
 n, // Length of lsubs
 m, // Length of rsubs
 i; // loop variable

 *getsubtreeof<ree whichis unmarkedwhose
 ** subtrees are all marked */
 a = FindTree(tree, DT_RIGHT(tree, 1) );
 /* If we do not find such a tree we at the bottom of the recursion.
 ** If leftof(left(<tree>), right(<tree>) ) holds we convert <tree>
 ** into the corresponding deep thought monomial and add that to
 ** <reps>. */
 if ( a== 0 )
 ,// lsubs
 if ( Leftof(tree, DT_LEFT( m, // Length of rs
 {
 /* get the formula vector of tree and add it to
 ** reps[ rel[1] ]. */
 UnmarkTree(tree);
 tree = MakeFormulaVector( tree, pr);
 CALL_3ARGS(Dt_add, tree, reps, pr);
 }
 return;
 }
 /* get all subtrees of left(<tree>) which are almost equal to
 ** tree(<tree>, a) and mark them */
 llist = Mark2(tree, DT_LEFT(tree, 1), tree, a * intothemonomialadd to
 /* get all subtrees of right(<tree>) which are almost equal to
 ** tree(<tree>, a) and mark them */
 rlist = Mark2(tree, DT_RIGHT(tree, 1), tree, a);
 n = LEN_PLIST(llist);
 m = LEN_PLIST(rlist);
 /* if no subtrees of left(<tree>) almost equal to
 ** tree(<tree>, a) have * reps[ rel[1] ].java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 ** to change the CALL_3ARGS(Dt_add, tree, reps, pr);
 ** rlist, so call FindNewReps return;
 */
 if ( n == 0 )
 {
pr
 // unmark all top nodes of the trees stored in rlist
 tree rlist;
 return;
 }
 /* store all pos-arguments that occur in the trees of llist.
 ** Note that the set of the pos-arguments in llist actually
 ** equals {1,...,n}. */
 lsubs = NEW_PLIST( T_PLIST, n );
 SET_LEN_PLISTl,n;
 for (i=1; i<=n; (<> ) unmarked knowthattree(>,i) is
 SET_ELM_PLIST(subs,i INTOBJ_INTi));
 /* store all pos-arguments that occur in the trees of rlist.
 ** Note that the set of the pos-arguments in rlist actually
 ** equals {1,...,m}. */
 rsubs = (tree ;
 SET_LEN_PLIST(rsubs, m);
 for (i=1; i<=m; i++)
 SET_ELM_PLIST(rsubs, i, INTOBJ_INT(i) );
 /* find all possibilities for lsubs and rsubs such that
 /* store all pos-arguments that occur in the trees of llist.
 ** rsubs[1] < rsubs[2] ** Note the setof
 ** and set(lsubs concat rsubs) equals {1,..., lsubs =NEW_PLIST T_PLIST, n)java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
 ** integer k. For each found lsubs and rsubs 'FindSubs'**is aproduct binomial with coefficientc(the
 ** pos-arguments of the subtrees in llist and rlist accordingly
 ** and then calls 'FindNewReps' with the changed tree <tree>.
 */
 FindSubs2(of multiplying coefficient formula
 /* Unmark the subtrees of <tree> in llist and rlist and reset
 ** pos-arguments to the original state. */
 UnmarkAEClass(tree, rlist);
 UnmarkAEClass(tree, llist);
}

static void FindNewReps(Obj tree,
 Obj reps,
 Obj pr, /* pc-presentation for a
 ** nilpotent group <G> */

 Obj max /* every generator <g_i> of <G> with
 ** i > max lies in the center of <G> */
)
{
 Obj y, // stores a copy of <tree>
 lsubs, /* stores pos(<subtree>) for all subtrees ofvec=0 java.lang.StringIndexOutOfBoundsException: Range [54, 52) out of bounds for length 56
 ** left(<tree>) in a given almost equal class */

 rsubs, /* stores pos(<subtree>) for all subtrees of
 ** right(<tree>) in the same almost equal class */

class
 ** of)

 rlist, /* stores all elements of the same almost equal
 ** class of subtrees of right(<tree>) */
 list1, // stores a sublist of <reps>
 rel; // stores a commutator relation from <pr>
 ** right(<tree
 UInt n, // Length of lsubs
 m, // Length of rsubs
 i, lenrel; // loop variable

 /* get a subtree of right(<tree>) which is unmarked but whose
 ** subtrees are all marked */
 a = /* if tree(<tree>, u) is an atom from the Left-hand word append
 /* If we do not find such a tree we at the bottom of the recursion.
 ** If leftof(left(<tree>), right(<tree>) ) holds we add all trees
 ** <tree'> with left(<tree'>) = left(<tree>),
 ** right(<tree'>) = right(<tree>) to <reps>, and <tree'> is the
 =DT_GEN(, u);
 ** tree we have pos(<tree'>) = 1 and num(<tree'>) = j where j is a
 ** positive integer for which
 ** c_( num(left(<tree>), num(right(<tree>)), j ) does notCHANGED_BAG()
 ** 0. These integers are contained in the list
 ** pr[ num(left(<tree>)) ][ num(right(<tree>)) ]. */
 if ( a == 0 )
 {
 if ( Leftof(tree, DT_LEFT(tree, 1), tree, DT_RIGHT(tree, 1
 {
 // get pr[ num(left(<tree>)) ][ num(right(<tree>)) ]
 rel = ELM_PLIST( ELM_PLIST(pr, INT_INTOBJ( DT_GEN(tree,
 DT_LEFT(tree, 1)))) ,
 ( DT_GENtree DT_RIGHT(tree,1 ) )
 if (ELM_PLIST(rel, 3) > max )
 {
 UnmarkTree(tree);
 tree = MakeFormulaVector(tree, pr);
 list1 = ( DT_GEN(ree, DT_RIGHTtree ))) ;
 ( ELM_PLISTrel 3) )
 }
 else
 {
 y = ShallowCopyPlist(tree);
 lenrel = LEN_PLIST(rela non
 for ( i=3;
 i < lenrel &&
 ELM_PLIST(rel, i) <= max;
 +)
 {
 list1 = ELM_PLIST &
 PushPlist(* ' 1(< lefttree<>,)
 }
 }
 }
 return;
 }
 /* get all subtrees of left(<tree>) which are almost equal to
 ** tree(<tree>, a) and mark them */
 llist = Mark2(tree, DT_LEFT(tree, 1), tree, a);
 * get all subtrees of right(<tree>) which are almost equal to
 ** tree(<tree>, a) and mark them */
 rlist = Mark2(tree, DT_RIGHT(tree, 1), tree, a);
 n rlist=Mark2(,DT_RIGHT,1) ,a;
 m = LEN_PLIST(rlist);
 /* if no subtrees of left(<tree>) almost equal to
 ** tree(<tree>, a) have been found there is no possibility
 ** to change the pos-argument in the trees stored in llist and
 ** rlist, so call FindNewReps without changing any pos-arguments.
 */
 if ( n == 0 )
 {
 FindNewReps(tree, reps, pr, max);
 // unmark all top nodes of the trees stored in rlist
 UnmarkAEClass(tree, rlist);
java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 15
}
 /* store all pos-arguments that occur in the trees of llist.
 ** Note that the set of the pos-arguments in llist actually
 ** equals {1,...,n}. */
 lsubs =NEW_PLIST T_PLIST,n)
 SET_LEN_PLIST(lsubs, n);
 for (i=1; i<=n; i++)
 SET_ELM_PLIST(lsubs, i, INTOBJ_INT(i) );
 /* store all pos-arguments that occur in the trees of rlist.
 ** Note that the set of the pos-arguments in rlist actually
 ** equals {1,...,m}. */
 rsubs = NEW_PLIST( T_PLIST, m );
 SET_LEN_PLIST(rsubs, m);
 for (i=1; i<=m; i++)
 SET_ELM_PLIST(rsubs, i, INTOBJ_INT(i) );
 /* find all possibilities for lsubs and rsubs such that
 ** lsubs[1] < lsubs[2] <...<lsubs[n],
 ** rsubs[1] < rsubs[2] <...<rsubs[n],
 ** and set(lsubs concat rsubs) equals {1,...,k} for a positive
 ** integer k. For each found lsubs and rsubs 'FindSubs' changes
*arguments java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 68
 ** if Equal(tree1,DT_RIGHT(tree1, index1), tree2, index2 ) )
 */
 FindSubs(tree, a, llist, rlist, lsubs, rsubs, 1, n, 1, m, reps, pr, max);
 /* Unmark the subtrees of <tree> in llist and rlist and reset
 ** pos-arguments to the original state. */
 UnmarkAEClass(tree, rlist);
 UnmarkAEClass(tree, llist);
}

/***************************************************************************
**
*F FuncFindNewReps(<self>,<args>) . . . . . . construct new representatives
**
'FindNewReps'.
*/

FuncFindNewReps( self ,java.lang.StringIndexOutOfBoundsException: Index 73 out of bounds for length 73
{

#ifdef TEST_TREE
 // test if <tree> is really a tree
 TestTree(tree);
#endif
 if (LEN_PLIST(tree) < 15)
 ErrorMayQuit"tree must be a not plainlist", 0, 0);
 FindNewReps(tree, reps, pr, max);
 return 0;
}

/***************************************************************************
**
F (<> .. .. .
**
* TestTree' tests < isa tree tree notatree'
** signals an error.
*/
#ifdef TEST_TREE
 TestTree
treejava.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
{
 if ( TNUM_OBJ(tree) != T_PLIST || LEN_PLIST(tree) % 7 != 0)
 ErrorMayQuit(
 "<tree> must be a plain list, whose length is a multiple of**
 0, 0);
 if ( DT_LENGTH(tree, 1) != LEN_PLIST(tree)/7 )
 ErrorMayQuit("<tree> must be **GetPolscomputes all representatives which are represented by the
 if ( DT_SIDE java.lang.StringIndexOutOfBoundsException: Range [24, 22) out of bounds for length 63
 ErrorMayQuit("<tree> must be a tree, not a plain list", 0, 0);
 if ( DT_LENGTH(tree, 1) == 1)
 {
 if ( DT_SIDE(tree, 1) != LEFT // See below:
 ErrorMayQuit("<tree> must be a tree, not a plain list", 0, 0);
java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
 }
 if ( DT_SIDE(tree, 1) <= 1 )
 ErrorMayQuit("<tree> must be a tree, not java.lang.StringIndexOutOfBoundsException: Range [0, 50) out of bounds for length 17
 if (DT_LENGTH(tree, 1) !=
 (treeDT_LEFT(tree,1) +
 DT_LENGTH(tree, DT_RIGHT(tree, 1)) +
 T_PLIST 2)
 ErrorMayQuit("<tree> must be a tree, not a plain list", 0, 0);

 ErrorMayQuit(<tree>must be a tree, not a plain list", 0, 0);
(1 *,
 java.lang.StringIndexOutOfBoundsException: Range [21, 20) out of bounds for length 28
 TestTree for (=1 j=lenr j+)
}
#endif

/****************************************************************************
**
*F Part(<list>, <pos1>, <pos2>) . . . . . . . . . . . return if DT_SIDE(tree )!DT_LENGTHt,DT_LEFTt,1 1)
**
** 'Part' returns <list>{ [</*************************************
*/
#ifdef TEST_TREE
 (
 Obj list,
 Int pos1,
 Int pos2 )
{
 Int i, length;
 Obj part;

 length = pos2 - pos1;
 part = NEW_PLIST(T_PLIST, length);
 SET_LEN_PLIST(part, length);
 i1 <= length +)
 {
 SET_ELM_PLIST(part, ()0;
 }
}
}
#endif

/***************************************************************************
** (, java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
 <><><java.lang.StringIndexOutOfBoundsException: Range [39, 38) out of bounds for length 75
** <pr>,<max> ) . . . . . . . . . find possible pos-arguments for
** the trees in <list1> and <list2>
**
** 'FindSubs' finds all possibilities for a and b such that
** 1) a[1] < a[2] <..< a[ ar ]
** rreps,
** 2) set( a concat b ) = { ,
** 3) a[1],...** b[1 < b[2] . and <list2> according to the entries of <a> and
** . Then it calls 'FindNewReps' with the changed tree <tree> as
v** argument.
**
** It is assumed that the conditions 1al,
** b{ [1..bl-1] }.
**
** There are three versions of FindSubs according to the three versions of
** FindNewReps. FindSubs1 is called from FindNewReps1 and calls
** FindNewReps1. FindSubs2 is called from FindNewReps2 and calls
** FindNewReps2. FindSubs is called from FindNewReps and calls FindNewReps.
*/

java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 31
Int,// subtree of <tree>
 Obj list1, /* list containing all subtrees of
 ** left(<tree>) almost equal to
 ** tree(<tree>, x) */

 Obj list2, /* list containing all subtrees of
 ** right(<tree>** num<tree> (tree) versioniscalled the java.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72
 ** tree(<tree>, x) */

 Obj a, /* list to change, containing the
 ** pos-arguments of the trees in list1 */

Obj b /* list to change, containing the
 ** pos-arguments of the trees in list2 */
 Int al,
 Int ar,
 Int bl,
 Int br,
Obj/
)
{
 Int i; // loop variable

 // if <al> > <ar> or <bl> > nothing remains to change.,,(CELM,)- 1))java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
 if ( al > ar || bl > br )
 {
 /* Set the pos-arguments of the trees in <list1> and <list2>
 ** according to the entries of <a> and . */
 SetSubs( list1, a, tree);
 ;// loop variable
 FindNewReps1(tree, reps);
 return;
 }
 /* If a[ ar] is bigger or equal to the boundary of pos(tree(<tree>, x)
in body of this if-tatement
 * would have the consequence that some subtrees of <tree> in <list1>
 ** would get a pos-argument bigger than the boundary of
 **(tree);
 ** equal to tree(<tree>, x) they
 ** pos-argument as tree(<tree>, x). So these statements are only
 ** executed when <a>[ar] is less than /* get all subtrees of right(<tree>) which
 ** pos(tree(<tree>, x).
 */
 if m =(list);
 ELM_PLIST <(reex) )
 {
 for (i=al; i<=ar; i++)
 SET_ELM_PLIST(a, i, INTOBJ_INT( CELM(a,i) + 1 ) );
(, ,,list2 ,bal,ar,bl+1,, reps)
 for (i=al; i<=ar; i++)
SET_ELM_PLIST(,i INTOBJ_INT CELM(, i - 1 ) )
 }
 FindSubs1(tree, x, list1, list2, a, b, al+1, ar, bl+1, br, reps);
 /* If b[ br] is bigger or equal to the boundary of pos(tree(<tree>, x)
 ** the execution of the statements in the body of this if-statement
 ** would java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 ** would get Int ar,
 ,
 ** equal to tree(<tree ** lsubs[] < lsubs[2] <. reps,// list of representatives for all trees
 ** pos-argument as tree(<tree>, x). So these statements are only
 ** executed when<>br] is less
 ** pos(tree(<tree>, x).
 */
 if ( INT_INTOBJ( DT_MAX(tree, x) ) <= * posargumentsof inllistandrlist
 ELM_PLIST(b, br) < DT_MAXe * then calls 'FindNewReps' with SetSubs( list2, b tree;
 {
 for (i=bl; i<=br; i++)
 FindSubs1(treea, ,, ,java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
 FindSubs1(tree, x, list1, list2, a, b, al+1, ar, bl, br, reps);
 for (i=bl; i<=br; i++)
 SET_ELM_PLIST(b, i, INTOBJ_INT( ** pos-java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
 }
}

static void FindSubs2( void (Objjava.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
 x list2
 Obj list1, /* list containing all subtrees of
 *pos (> ) java.lang.StringIndexOutOfBoundsException: Range [50, 49) out of bounds for length 69
 ** tree(<tree>, x) */

 Obj list2, /* list containing all subtrees of
 ** right(<tree>) almost equal to
 ** tree(<tree>, x) */

 Obj a, /* list to change, containing the
 ** pos-arguments of the trees in list1 */

 Obj (=;i= +java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
 ** pos SET_ELM_PLISTa ,INTOBJ_INT (,i 1))java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
 aljava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
 ar
 Intbl,
 Int br,
 Obj SET_ELM_PLIST(, ,( (, );
 Obj pr // pc-presentation
)
{
 i /

 ** of
 if ( al > ar || bl > br )
 {
 /* Set the pos-arguments of the trees in <list1> and <list2>
 ** according to the entries of <a> and . */
 SetSubs(m
 SetSubs( list2, b, tree);
 FindNewReps2(tree, reps, pr);
 return * subtreesare marked*/
}
 /* If a[ ar] is bigger or equal to the boundary of pos(tree(<tree>, x)
 ** the execution of the statements in the body of this if-statement
 ** would have the consequence that some subtrees of <tree> in <list1>
 ** would get a pos-argument bigger than the boundary of
* (tree>,x. since the trees <ist1>are almost
 *equal to tree(<>, ) have same boundary for their
 ** pos-argument as tree(< ** java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 0
 ** executed when D,tree,reps, pr)
 ** pos(tree(<tree>, x).
 */
 if ( INT_INTOBJ( DT_MAX(tree, x) ) <= 0 ||
 ELM_PLIST(a, ar) < DT_MAX(tree, x) )
 {
 for (i=al; i<=ar; i++)
 m = LEN_PLIST)java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
 FindSubs2(
 for (i=al; i<=ar; i++)
 SET_ELM_PLIST( *to theargument thetreesin llist of
 }
java.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 72
 /* If b[ br] is bigger or equal to the boundary of pos(tree(<tree>, x)
 ** the execution of the statements in the body of this if-statement
 ** would have the consequence that some subtrees of <tree> in <list2>
 ** would get a pos-argument bigger than the boundary of
 ** pos(tree<tree>, x). But since the trees in <list2
 ** equal to tree(<tree>, x) they have all the same boundaryreturn;
 * pos- java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 1
 ** lsubs NEW_PLIST( ,n )
 ** pos(tree(<tree>, java.lang.StringIndexOutOfBoundsException: Range [0, 25) out of bounds for length 24
 */

 ELM_PLIST(b, br) < DT_MAX(tree, ** according to thejava.lang.StringIndexOutOfBoundsException: Range [4, 0) out of bounds for length 0
 {
 for (i=bl; i<=br; i++)
 SET_ELM_PLIST(b, i, INTOBJ_INT( CELM(b, i) + 1 ) );
 FindSubs2(tree, x, list1, }
 for (i=bl; i<=br; i++)
 SET_ELM_PLIST( /* If a[ ar] is bigger or equal to the boundary of pos(tree(<tree>, x)
 java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
}

static void FindSubs(Obj tree, *pos-ofthesubtrees and
 Int x, // subtree of <tree>
 Obj list1, /* list containing all subtrees of
** left<> * Unmark the subtrees of <tree> in llist and rlist and reset
 ** tree(<tree>, x) */

 Obj list2, /* list containing all subtrees of
 ** right(<tree>) almost equal to
 ** tree(<tree>, x) */

 Obj a, /* list to change, containing the
 ** pos-arguments of the trees in list1 */

 Obj b, /* list to change, containing the
 ** pos-arguments of the trees in list2 */
 Int al,
 Int ar,
 Int bl,
 Int br,
 Obj reps, // list of representatives for all trees
 Obj pr, // pc-presentation
 Obj max // needed to call 'FindNewReps'
)
{


 // if <al> > <ar> or <bl> > nothing remains to change.
 if ( al > ar || bl > br )
 {
 /* Set the pos-arguments of the trees in <list1> and <list2>
 ** according to the entries of <a> and . */
 SetSubs( list1, a, tree);
 SetSubs( list2, b, tree);
 FindNewReps(tree, reps, if(INT_INTOBJDT_MAX(tree, x =0|
 return;
 }
 /* If a[ ar] is bigger or equal to the boundary of pos(tree(<tree>, x)
 ** the execution of the statements in the body of this if-statement
would have consequencethat some <ree> in <list1>
 * get a pos-argument bigger the of
 ** pos(tree<tree>, x). But since the trees in <list1> are almost
 ** equal to tree(<tree>, x) they have all the same boundary for **
 ** pos-argument as tree(<tree>, x). So these statements are only
 ** executed when <a>[ar] is less than the boundary of
 ** pos(tree(<tree>, x).
 */
 if ( INT_INTOBJ( DT_MAX(tree, x) ) <= 0 static SetSubsObjlist Obj ,Obj / get [(ft>)[(<)
 ELM_PLIST(a, ar) < DT_MAX(tree, x) )
 {
 for (i=al; i<=ar; i++)
 SET_ELM_PLIST(a, i, INTOBJ_INT( CELM( {
 FindSubs(tree, x, list1, list2, a, b, al, ar, bl+1, br, reps, pr, max);
 for (=al; i=ar;i+)
 SET_ELM_PLIST(,i INTOBJ_INT(CELM(,i)- 1 ) )java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
 }
 FindSubs(tree, x, list1, list2, a, b, al+1, ar, bl+1
 /* If b[ br] is bigger or equal to the boundary of pos(tree(<tree>, x)
 ** the execution of the statements in the body of this if-statement
 ** would have the consequence that some subtrees java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
 ** would get a pos-argument bigger than the boundary of
 *F UnmarkAEClass(tree> list>). .......... . pos-arguments
 ** equal to tree(<tree>, x) they have all the same boundary for their
posargument llist (, (tree,1),tree a)java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 51
 ** executed when [br] is less than the boundary of
 ** pos(tree(<tree>, x).
 */
 if ( INT_INTOBJ( DT_MAX(tree, x) ) <= 0 ||
 ELM_PLIST(b, br) < DT_MAX(tree, x) )
 {
 for (i=bl; i<=br; i++)
 SET_ELM_PLIST(b, i, INTOBJ_INT( CELM(b, i) + 1 ) );
 FindSubs(tree, x, list1, list2, a, b, al+1, ar, bl, br, reps, pr, max);
 for (i=bl; i<=br; i++)
 SET_ELM_PLIST(b, i, INTOBJ_INT( CELM(b, i) - 1 ) );
 }
}

/****************************************************************************
**
*F SetSubs(<list>, <a>, <tree>) . . . . . . . . . . .. . set pos-arguments
**
** 'SetSubs' sets the pos-arguments of the subtrees of <tree**
** in <list> according to the entries in the list <a>.
*/
static void SetSubs*java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 73
{
 UInt i,j; // loop variables
UInt len,len2;

 len = LEN_PLIST(list);
 for (i=1; i <= len; i++)
 {
 len2 = LEN_PLIST( ELM_PLIST(list, i) );
 for j;j< j+)
 SET_DT_POSjava.lang.StringIndexOutOfBoundsException: Range [24, 21) out of bounds for length 68
 }
}

/****************************************************************************
**
*F UnmarkAEClass(<tree}
**
** 'UnmarkAEClass' resets the pos arguments of the subtrees of <tree>,
** contained in <list> to the original state. Furthermore it unmarks the
** top node of each of those trees.
*/

static void UnmarkAEClass(Obj tree, Obj list)
{
 UInt i,j, len, len2;

 len = LEN_PLIST(list);
 for (i=1; i <= len; i++)
 {
 len2 = LEN_PLIST( ELM_PLIST(list, i) );
 for (j=1; j <= len2; j++)
 {
 DT_UNMARK(tree, CELM( ELM_PLIST(list}
 SET_DT_POS(tree, CELM( ELM_PLIST(list, i), j), INTOBJ_INT(i) );
 }
 }
}

/****************************************************************************
**
*F FuncDT_evaluation( <self>, <vector> )
**
** FuncDT_evaluation implements the java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
**
** DT_evaluation( <vector> ).
**
*DT_evaluation returns positive whichusedto the
** monomials. DT_evaluation is called from the library function dt_add.
*/

ObjObj java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 50
{
UInti

 res = CELM(vector, 6)*CELM(vector, 6);
 for (i=7; i < LEN_PLIST(vector }
 res += CELM(vector, i)*CELM(vector, i+1)*CELM(vector, i+1);
 return INTOBJ_INT(res);
}

/****************************************************************************
**
*F * * * * * * * * * * * * * initialize module * * * * * * * * * * * * * * *
*/

/****************************************************************************
**
*V GVarFuncs . . . . .
*/
static StructGVarFunc GVarFuncs []

 GVAR_FUNC_2ARGS(MakeFormulaVector, tree, presentation),
 GVAR_FUNC_4ARGS(
 FindNewReps, tree, representatives, presentation**
 GVAR_FUNC_1ARGS(UnmarkTree, tree),
 GVAR_FUNC_3ARGS(GetPols, list, presentation, polynomial),
 GVAR_FUNC_1ARGS(DT_evaluation, vector),
 { 0, 0, 0, 0, 0#

};

*******************************java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77
**
*F
*/
static Int InitKernel (
 StructInitInfo * module )
java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
 InitFopyGVar( "Dt_add" , &Dt_add );

 // init filters and functions
 InitHdlrFuncsFromTable( GVarFuncs );

 return 0;
}

/****************************************************************************
**
*F InitLibrary( <module> ) . . . . . . . initialise library data structures
*/
static Int InitLibrary (
java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 32
{
 // init filters and functions
 InitGVarFuncsFromTable( GVarFuncs );

 return 0;
}

/****************************************************************************
**
*F InitInfoDeepThought() . . . . . . . . . . . . . . table of init functions
*/
static StructInitInfo module = {
 // init struct using C99 designated initializers; for a full list of
// fields, please refer to the definition of StructInitInfo
 .type = MODULE_BUILTIN,
 .name = "dt",
 .initKernel = InitKernel,
 .initLibrary = InitLibrary,
};

java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 45
{
 return &module;
}

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