Obj FuncKURATOWSKI_OUTER_PLANAR_SUBGRAPH(Obj self, Obj digraph) {
Obj res = boyers_planarity_check(digraph, EMBEDFLAGS_OUTERPLANAR, true);
return (ELM_PLIST(res, 1) == False ? ELM_PLIST(res, 2) : Fail);
}
UInt RNamNameWithLen(const Char * name, UInt len)
{
Obj rnam; /* record name (as imm intobj) */
UInt pos; /* hash position */
Char namx [1024]; /* temporary copy of <name> */
Obj string; /* temporary string object <name> */
Obj table; /* temporary copy of <HashRNam> */
Obj rnam2; /* one element of <table> */
UInt i; /* loop variable */
UInt sizeRNam;
if (len > 1023) {
// Note: We can't pass 'name' here, as it might get moved by garbage collection
ErrorQuit("Record names must consist of at most 1023 characters", 0, 0);
}
/* start looking in the table at the following hash position */
const UInt hash = HashString( name, len );
#ifdef HPCGAP
HPC_LockNames(0); /* try a read lock first */
#endif
/* look through the table until we find a free slot or the global */
sizeRNam = LEN_PLIST(HashRNam);
pos = (hash % sizeRNam) + 1;
while ( (rnam = ELM_PLIST( HashRNam, pos )) != 0
&& !EqString( NAME_RNAM( INT_INTOBJ(rnam) ), name, len ) ) {
pos = (pos % sizeRNam) + 1;
}
if (rnam != 0) {
#ifdef HPCGAP
HPC_UnlockNames();
#endif
return INT_INTOBJ(rnam);
}
#ifdef HPCGAP
if (!PreThreadCreation) {
HPC_UnlockNames(); /* switch to a write lock */
HPC_LockNames(1);
/* look through the table until we find a free slot or the global */
sizeRNam = LEN_PLIST(HashRNam);
pos = (hash % sizeRNam) + 1;
while ( (rnam = ELM_PLIST( HashRNam, pos )) != 0
&& !EqString( NAME_RNAM( INT_INTOBJ(rnam) ), name, len ) ) {
pos = (pos % sizeRNam) + 1;
}
}
if (rnam != 0) {
HPC_UnlockNames();
return INT_INTOBJ(rnam);
}
#endif
/* if we did not find the global variable, make a new one and enter it */
/* (copy the name first, to avoid a stale pointer in case of a GC) */
memcpy( namx, name, len );
namx[len] = 0;
string = MakeImmString(namx);
const UInt countRNam = PushPlist(NamesRNam, string);
rnam = INTOBJ_INT(countRNam);
SET_ELM_PLIST( HashRNam, pos, rnam );
/* if the table is too crowded, make a larger one, rehash the names */
if ( sizeRNam < 3 * countRNam / 2 ) {
table = HashRNam;
sizeRNam = 2 * sizeRNam + 1;
HashRNam = NEW_PLIST( T_PLIST, sizeRNam );
SET_LEN_PLIST( HashRNam, sizeRNam );
#ifdef HPCGAP
/* The list is briefly non-public, but this is safe, because
* the mutex protects it from being accessed by other threads.
*/
MakeBagPublic(HashRNam);
#endif
for ( i = 1; i <= (sizeRNam-1)/2; i++ ) {
rnam2 = ELM_PLIST( table, i );
if ( rnam2 == 0 ) continue;
string = NAME_RNAM( INT_INTOBJ(rnam2) );
pos = HashString( CONST_CSTR_STRING( string ), GET_LEN_STRING( string) );
pos = (pos % sizeRNam) + 1;
while ( ELM_PLIST( HashRNam, pos ) != 0 ) {
pos = (pos % sizeRNam) + 1;
}
SET_ELM_PLIST( HashRNam, pos, rnam2 );
}
}
#ifdef HPCGAP
HPC_UnlockNames();
#endif
/* return the record name */
return INT_INTOBJ(rnam);
}
Obj FuncPLANAR_EMBEDDING(Obj self, Obj digraph) {
Obj res = boyers_planarity_check(digraph, EMBEDFLAGS_PLANAR, true);
return (ELM_PLIST(res, 1) == True ? ELM_PLIST(res, 2) : Fail);
}
/****************************************************************************
**
*F ProdVectorMatrix(<vecL>,<vecR>) . . . . product of a vector and a matrix
**
** 'ProdVectorMatrix' returns the product of the vector <vecL> and the matrix
** <vecR>. The product is the sum of the rows of <vecR>, each multiplied by
** the corresponding entry of <vecL>.
**
** 'ProdVectorMatrix' is an improved version of 'ProdListList', which does
** not call 'PROD' and also accumulates the sum into one fixed vector
** instead of allocating a new for each product and sum.
*/
Obj ProdVecFFEMatFFE (
Obj vecL,
Obj matR )
{
Obj vecP; /* handle of the product */
Obj * ptrP; /* pointer into the product */
FFV * ptrV; /* value pointer into the product */
FFV valP; /* one value of the product */
FFV valL; /* one value of the left operand */
Obj vecR; /* one vector of the right operand */
Obj * ptrR; /* pointer into the right vector */
FFV valR; /* one value from the right vector */
UInt len; /* length */
UInt col; /* length of the rows in matR */
UInt i, k; /* loop variables */
FF fld; /* the common finite field */
FF * succ; /* the successor table */
/* check the lengths */
len = LEN_PLIST(vecL);
col = LEN_PLIST(ELM_PLIST(matR, 1));
if (len != LEN_PLIST(matR)) {
matR = ErrorReturnObj(
"<vec>*<mat>: <vec> (%d) must have the same length as <mat> (%d)",
(Int)len, (Int)col,
"you can replace matrix <mat> via 'return <mat>;'");
return PROD(vecL, matR);
}
/* check the fields */
vecR = ELM_PLIST(matR, 1);
fld = FLD_FFE(ELM_PLIST(vecL, 1));
if (FLD_FFE(ELM_PLIST(vecR, 1)) != fld) {
/* check the characteristic */
if (CHAR_FF(fld) == CHAR_FF(FLD_FFE(ELM_PLIST(vecR, 1))))
return ProdListList(vecL, matR);
matR = ErrorReturnObj(
"<vec>*<mat>: <vec> and <mat> have different fields",
0L, 0L,
"you can replace matrix <mat> via 'return <mat>;'");
return PROD(vecL, matR);
}
/* make the result list by multiplying the first entries */
vecP = ProdFFEVecFFE(ELM_PLIST(vecL, 1), vecR);
/* to add we need the successor table */
succ = SUCC_FF(fld);
/* convert vecP into a list of values */
/*N 5Jul1998 werner: This only works if sizeof(FFV) <= sizeof(Obj) */
/*N We have to be careful not to overwrite the length info */
ptrP = ADDR_OBJ(vecP);
ptrV = ((FFV*)(ptrP + 1)) - 1;
for (k = 1; k <= col; k++)
ptrV[k] = VAL_FFE(ptrP[k]);
/* loop over the other entries and multiply */
for (i = 2; i <= len; i++) {
valL = VAL_FFE(ELM_PLIST(vecL, i));
vecR = ELM_PLIST(matR, i);
ptrR = ADDR_OBJ(vecR);
if (valL == (FFV)1) {
for (k = 1; k <= col; k++) {
valR = VAL_FFE(ptrR[k]);
valP = ptrV[k];
ptrV[k] = SUM_FFV(valP, valR, succ);
}
} else if (valL != (FFV)0) {
for (k = 1; k <= col; k++) {
valR = VAL_FFE(ptrR[k]);
valR = PROD_FFV(valL, valR, succ);
valP = ptrV[k];
ptrV[k] = SUM_FFV(valP, valR, succ);
}
}
}
/* convert vecP back into a list of finite field elements */
/*N 5Jul1998 werner: This only works if sizeof(FFV) <= sizeof(Obj) */
/*N We have to be careful not to overwrite the length info */
for (k = col; k >= 1; k--)
ptrP[k] = NEW_FFE(fld, ptrV[k]);
/* return the result */
return vecP;
}
extern inline Obj NAME_RNAM(UInt rnam)
{
return ELM_PLIST(NamesRNam, rnam);
}
Obj FuncAddRowVectorVecFFEsMult( Obj self, Obj vecL, Obj vecR, Obj mult )
{
Obj *ptrL;
Obj *ptrR;
FFV valM;
FFV valS;
FFV valL;
FFV valR;
FF fld;
FFV *succ;
UInt len;
UInt xtype;
UInt i;
if (TNUM_OBJ(mult) != T_FFE)
return TRY_NEXT_METHOD;
if (VAL_FFE(mult) == 0)
return (Obj) 0;
xtype = KTNumPlist(vecL, (Obj *) 0);
if (xtype != T_PLIST_FFE && xtype != T_PLIST_FFE + IMMUTABLE)
return TRY_NEXT_METHOD;
xtype = KTNumPlist(vecR, (Obj *) 0);
if (xtype != T_PLIST_FFE && xtype != T_PLIST_FFE + IMMUTABLE)
return TRY_NEXT_METHOD;
/* check the lengths */
len = LEN_PLIST(vecL);
if (len != LEN_PLIST(vecR)) {
vecR = ErrorReturnObj(
"AddRowVector: vector lengths differ <left> %d, <right> %d",
(Int)len, (Int)LEN_PLIST(vecR),
"you can replace vector <right> via 'return <right>;'");
return CALL_3ARGS(AddRowVectorOp, vecL, vecR, mult);
}
/* check the fields */
fld = FLD_FFE(ELM_PLIST(vecL, 1));
if (FLD_FFE(ELM_PLIST(vecR, 1)) != fld) {
/* check the characteristic */
if (CHAR_FF(fld) == CHAR_FF(FLD_FFE(ELM_PLIST(vecR, 1))))
return TRY_NEXT_METHOD;
vecR = ErrorReturnObj(
"AddRowVector: vectors have different fields",
0L, 0L,
"you can replace vector <right> via 'return <right>;'");
return CALL_3ARGS(AddRowVectorOp, vecL, vecR, mult);
}
/* Now check the multiplier field */
if (FLD_FFE(mult) != fld) {
/* check the characteristic */
if (CHAR_FF(fld) != CHAR_FF(FLD_FFE(mult))) {
mult = ErrorReturnObj(
"AddRowVector: <multiplier> has different field",
0L, 0L,
"you can replace <multiplier> via 'return <multiplier>;'");
return CALL_3ARGS(AddRowVectorOp, vecL, vecR, mult);
}
/* if the multiplier is over a non subfield then redispatch */
if ((DEGR_FF(fld) % DegreeFFE(mult)) != 0)
return TRY_NEXT_METHOD;
/* otherwise it's a subfield, so promote it */
valM = VAL_FFE(mult);
if (valM != 0)
valM = 1 + (valM - 1) * (SIZE_FF(fld) - 1) / (SIZE_FF(FLD_FFE(mult)) - 1);
} else
valM = VAL_FFE(mult);
succ = SUCC_FF(fld);
ptrL = ADDR_OBJ(vecL);
ptrR = ADDR_OBJ(vecR);
/* two versions of the loop to avoid multipling by 1 */
if (valM == 1)
for (i = 1; i <= len; i++) {
valL = VAL_FFE(ptrL[i]);
valR = VAL_FFE(ptrR[i]);
valS = SUM_FFV(valL, valR, succ);
ptrL[i] = NEW_FFE(fld, valS);
}
else
for (i = 1; i <= len; i++) {
valL = VAL_FFE(ptrL[i]);
valR = VAL_FFE(ptrR[i]);
valS = PROD_FFV(valR, valM, succ);
valS = SUM_FFV(valL, valS, succ);
ptrL[i] = NEW_FFE(fld, valS);
}
return (Obj) 0;
}
Obj FuncMultRowVectorVecFFEs( Obj self, Obj vec, Obj mult )
{
Obj *ptr;
FFV valM;
FFV valS;
FFV val;
FF fld;
FFV *succ;
UInt len;
UInt xtype;
UInt i;
if (TNUM_OBJ(mult) != T_FFE)
return TRY_NEXT_METHOD;
if (VAL_FFE(mult) == 1)
return (Obj) 0;
xtype = KTNumPlist(vec, (Obj *) 0);
if (xtype != T_PLIST_FFE &&
xtype != T_PLIST_FFE + IMMUTABLE)
return TRY_NEXT_METHOD;
/* check the lengths */
len = LEN_PLIST(vec);
fld = FLD_FFE(ELM_PLIST(vec, 1));
/* Now check the multiplier field */
if (FLD_FFE(mult) != fld) {
/* check the characteristic */
if (CHAR_FF(fld) != CHAR_FF(FLD_FFE(mult))) {
mult = ErrorReturnObj(
"MultRowVector: <multiplier> has different field",
0L, 0L,
"you can replace <multiplier> via 'return <multiplier>;'");
return CALL_2ARGS(MultRowVectorOp, vec, mult);
}
/* if the multiplier is over a non subfield then redispatch */
if ((DEGR_FF(fld) % DegreeFFE(mult)) != 0)
return TRY_NEXT_METHOD;
/* otherwise it's a subfield, so promote it */
valM = VAL_FFE(mult);
if (valM != 0)
valM = 1 + (valM - 1) * (SIZE_FF(fld) - 1) / (SIZE_FF(FLD_FFE(mult)) - 1);
} else
valM = VAL_FFE(mult);
succ = SUCC_FF(fld);
ptr = ADDR_OBJ(vec);
/* two versions of the loop to avoid multipling by 0 */
if (valM == 0) {
Obj z;
z = NEW_FFE(fld, 0);
for (i = 1; i <= len; i++) {
ptr[i] = z;
}
} else
for (i = 1; i <= len; i++) {
val = VAL_FFE(ptr[i]);
valS = PROD_FFV(val, valM, succ);
ptr[i] = NEW_FFE(fld, valS);
}
return (Obj) 0;
}
UInt RNamName (
const Char * name )
{
Obj rnam; /* record name (as imm intobj) */
UInt pos; /* hash position */
UInt len; /* length of name */
Char namx [1024]; /* temporary copy of <name> */
Obj string; /* temporary string object <name> */
Obj table; /* temporary copy of <HashRNam> */
Obj rnam2; /* one element of <table> */
const Char * p; /* loop variable */
UInt i; /* loop variable */
/* start looking in the table at the following hash position */
pos = 0;
len = 0;
for ( p = name; *p != '\0'; p++ ) {
pos = 65599 * pos + *p;
len++;
}
pos = (pos % SizeRNam) + 1;
if(len >= 1023) {
// Note: We can't pass 'name' here, as it might get moved by garbage collection
ErrorQuit("Record names must consist of less than 1023 characters", 0, 0);
}
/* look through the table until we find a free slot or the global */
while ( (rnam = ELM_PLIST( HashRNam, pos )) != 0
&& strncmp( NAME_RNAM( INT_INTOBJ(rnam) ), name, 1023 ) ) {
pos = (pos % SizeRNam) + 1;
}
/* if we did not find the global variable, make a new one and enter it */
/* (copy the name first, to avoid a stale pointer in case of a GC) */
if ( rnam == 0 ) {
CountRNam++;
rnam = INTOBJ_INT(CountRNam);
SET_ELM_PLIST( HashRNam, pos, rnam );
strlcpy( namx, name, sizeof(namx) );
C_NEW_STRING_DYN(string, namx);
GROW_PLIST( NamesRNam, CountRNam );
SET_LEN_PLIST( NamesRNam, CountRNam );
SET_ELM_PLIST( NamesRNam, CountRNam, string );
CHANGED_BAG( NamesRNam );
}
/* if the table is too crowed, make a larger one, rehash the names */
if ( SizeRNam < 3 * CountRNam / 2 ) {
table = HashRNam;
SizeRNam = 2 * SizeRNam + 1;
HashRNam = NEW_PLIST( T_PLIST, SizeRNam );
SET_LEN_PLIST( HashRNam, SizeRNam );
for ( i = 1; i <= (SizeRNam-1)/2; i++ ) {
rnam2 = ELM_PLIST( table, i );
if ( rnam2 == 0 ) continue;
pos = 0;
for ( p = NAME_RNAM( INT_INTOBJ(rnam2) ); *p != '\0'; p++ ) {
pos = 65599 * pos + *p;
}
pos = (pos % SizeRNam) + 1;
while ( ELM_PLIST( HashRNam, pos ) != 0 ) {
pos = (pos % SizeRNam) + 1;
}
SET_ELM_PLIST( HashRNam, pos, rnam2 );
}
}
/* return the record name */
return INT_INTOBJ(rnam);
}
/****************************************************************************
**
*F DiffVecFFEVecFFE(<vecL>,<vecR>) . . . . . . . . difference of two vectors
**
** 'DiffVecFFEVecFFE' returns the difference of the two vectors <vecL> and
** <vecR>. The difference is a new list, where each element is the
** difference of the corresponding elements of <vecL> and <vecR>.
**
** 'DiffVecFFEVecFFE' is an improved version of 'DiffListList', which does
** not call 'DIFF'.
*/
Obj DiffVecFFEVecFFE (
Obj vecL,
Obj vecR )
{
Obj vecD; /* handle of the difference */
Obj * ptrD; /* pointer into the difference */
FFV valD; /* one element of difference list */
Obj * ptrL; /* pointer into the left operand */
FFV valL; /* one element of left operand */
Obj * ptrR; /* pointer into the right operand */
FFV valR; /* one element of right operand */
UInt len, lenL, lenR; /* length */
UInt lenmin;
UInt i; /* loop variable */
FF fld; /* finite field */
FF * succ; /* successor table */
/* check the lengths */
lenL = LEN_PLIST(vecL);
lenR = LEN_PLIST(vecR);
if (lenR > lenL) {
len = lenR;
lenmin = lenL;
} else {
len = lenL;
lenmin = lenR;
}
/* check the fields */
fld = FLD_FFE(ELM_PLIST(vecL, 1));
if (FLD_FFE(ELM_PLIST(vecR, 1)) != fld) {
/* check the characteristic */
if (CHAR_FF(fld) == CHAR_FF(FLD_FFE(ELM_PLIST(vecR, 1))))
return DiffListList(vecL, vecR);
vecR = ErrorReturnObj(
"Vector -: vectors have different fields",
0L, 0L, "you can replace vector <right> via 'return <right>;'");
return DIFF(vecL, vecR);
}
/* make the result list */
vecD = NEW_PLIST((IS_MUTABLE_OBJ(vecL) || IS_MUTABLE_OBJ(vecR)) ?
T_PLIST_FFE : T_PLIST_FFE + IMMUTABLE, len);
SET_LEN_PLIST(vecD, len);
/* to subtract we need the successor table */
succ = SUCC_FF(fld);
/* loop over the elements and subtract */
ptrL = ADDR_OBJ(vecL);
ptrR = ADDR_OBJ(vecR);
ptrD = ADDR_OBJ(vecD);
for (i = 1; i <= lenmin; i++) {
valL = VAL_FFE(ptrL[i]);
valR = VAL_FFE(ptrR[i]);
valR = NEG_FFV(valR, succ);
valD = SUM_FFV(valL, valR, succ);
ptrD[i] = NEW_FFE(fld, valD);
}
if (lenL < lenR)
for (; i <= len; i++) {
valR = VAL_FFE(ptrR[i]);
valD = NEG_FFV(valR, succ);
ptrD[i] = NEW_FFE(fld, valD);
}
else
for (; i <= len; i++)
ptrD[i] = ptrL[i];
/* return the result */
return vecD;
}
static Obj FIND_BARYCENTER (Obj self, Obj gap_points, Obj gap_init, Obj gap_iter, Obj gap_tol)
{
#ifdef MALLOC_HACK
old_malloc_hook = __malloc_hook;
old_free_hook = __free_hook;
__malloc_hook = my_malloc_hook;
__free_hook = my_free_hook;
#endif
UInt i, j, n = LEN_PLIST(gap_points);
Double __points[n][3];
bparams bparam = { n, __points };
for (i = 0; i < n; i++)
for (j = 0; j < 3; j++)
bparam.points[i][j] = VAL_FLOAT(ELM_PLIST(ELM_PLIST(gap_points,i+1),j+1));
const gsl_multiroot_fsolver_type *T;
gsl_multiroot_fsolver *s;
int status;
size_t iter = 0, max_iter = INT_INTOBJ(gap_iter);
double precision = VAL_FLOAT(gap_tol);
gsl_multiroot_function f = {&barycenter, 3, &bparam};
gsl_vector *x = gsl_vector_alloc (3);
for (i = 0; i < 3; i++) gsl_vector_set (x, i, VAL_FLOAT(ELM_PLIST(gap_init,i+1)));
T = gsl_multiroot_fsolver_hybrids;
s = gsl_multiroot_fsolver_alloc (T, 3);
gsl_multiroot_fsolver_set (s, &f, x);
do {
iter++;
status = gsl_multiroot_fsolver_iterate (s);
if (status) /* check if solver is stuck */
break;
status = gsl_multiroot_test_residual (s->f, precision);
}
while (status == GSL_CONTINUE && iter < max_iter);
Obj result = ALLOC_PLIST(2);
Obj list = ALLOC_PLIST(3); set_elm_plist(result, 1, list);
for (i = 0; i < 3; i++)
set_elm_plist(list, i+1, NEW_FLOAT(gsl_vector_get (s->x, i)));
list = ALLOC_PLIST(3); set_elm_plist(result, 2, list);
for (i = 0; i < 3; i++)
set_elm_plist(list, i+1, NEW_FLOAT(gsl_vector_get (s->f, i)));
gsl_multiroot_fsolver_free (s);
gsl_vector_free (x);
if (status != 0) {
const char *s = gsl_strerror (status);
C_NEW_STRING(result, strlen(s), s);
}
#ifdef MALLOC_HACK
__malloc_hook = old_malloc_hook;
__free_hook = old_free_hook;
#endif
return result;
}
static Obj NFFUNCTION(Obj self, Obj rel, Obj dir, Obj word)
{
/* word is an integer lists. dir is true/false.
rel is a list of lists: square of positive relator+square of negative
relator; positions in 1st of letter i; position in 1st of letter -i
* if dir=true, replace all (>=1/2)-cyclic occurrences of rel in word by the shorter half
* if dir=false, replace all occurrences of the last generator in word by the corresponding bit of rel
*/
Obj posind = ELM_PLIST(rel,2), negind = ELM_PLIST(rel,3);
rel = ELM_PLIST(rel,1);
Int n = LEN_PLIST(posind), allocn = n, i = 0, resulti = 0, match = 0, matchlen = 0, j;
Obj result = ALLOC_PLIST(allocn);
while (i < LEN_PLIST(word)) {
/* we produced result[1..resulti] as the compressed version of word[1..i].
additionally, matchlen is maximal such that
rel[match..match+matchlen-1] = result[resulti-matchlen+1..resulti]
*/
i++;
Obj wi = ELM_PLIST(word,i);
Int vi = INT_INTOBJ(wi);
if (dir == False) {
if (vi == n) {
match = INT_INTOBJ(ELM_PLIST(negind,n));
for (j = 1; j < n; j++)
PUSH_LETTER(INT_INTOBJ(ELM_PLIST(rel,j+match)));
} else if (vi == -n) {
match = INT_INTOBJ(ELM_PLIST(posind,n));
for (j = 1; j < n; j++)
PUSH_LETTER(INT_INTOBJ(ELM_PLIST(rel,j+match)));
} else
PUSH_LETTER(vi);
} else {
if (resulti && vi == -INT_INTOBJ(ELM_PLIST(result,resulti))) {
/* pop letter, and update match */
resulti--;
matchlen--;
if (matchlen == 0 && resulti) {
MATCH_POS(match,INT_INTOBJ(ELM_PLIST(result,resulti)));
matchlen = 1;
while (resulti > matchlen && ELM_PLIST(result,resulti-matchlen) == ELM_PLIST(rel,match+n-1)) {
matchlen++;
if (!--match)
match = n;
}
} else
match = 0;
} else {
PUSH_LETTER(vi);
if (match && wi == ELM_PLIST(rel,match+matchlen)) {
matchlen++;
if (matchlen >= (n+1+(match < 2*n))/2) { /* more than half, or exactly half and negatives */
resulti -= matchlen;
for (j = n-1; j >= matchlen; j--)
PUSH_LETTER(-INT_INTOBJ(ELM_PLIST(rel,j+match)));
matchlen = n-matchlen;
match = 4*n+1 - (match+n-1);
}
} else {
matchlen = 1;
MATCH_POS(match,vi);
}
}
}
}
SET_LEN_PLIST(result,resulti);
return result;
}
Obj CollectPolycyc (
Obj pcp,
Obj list,
Obj word )
{
Int ngens = INT_INTOBJ( ADDR_OBJ(pcp)[ PC_NUMBER_OF_GENERATORS ] );
Obj commute = ADDR_OBJ(pcp)[ PC_COMMUTE ];
Obj gens = ADDR_OBJ(pcp)[ PC_GENERATORS ];
Obj igens = ADDR_OBJ(pcp)[ PC_INVERSES ];
Obj pow = ADDR_OBJ(pcp)[ PC_POWERS ];
Obj ipow = ADDR_OBJ(pcp)[ PC_INVERSEPOWERS ];
Obj exp = ADDR_OBJ(pcp)[ PC_EXPONENTS ];
Obj wst = ADDR_OBJ(pcp)[ PC_WORD_STACK ];
Obj west = ADDR_OBJ(pcp)[ PC_WORD_EXPONENT_STACK ];
Obj sst = ADDR_OBJ(pcp)[ PC_SYLLABLE_STACK ];
Obj est = ADDR_OBJ(pcp)[ PC_EXPONENT_STACK ];
Obj conj=0, iconj=0; /*QQ initialize to please compiler */
Int st, bottom = INT_INTOBJ( ADDR_OBJ(pcp)[ PC_STACK_POINTER ] );
Int g, syl, h, hh;
Obj e, ee, ge, mge, we, s, t;
Obj w, x = (Obj)0, y = (Obj)0;
if( LEN_PLIST(word) == 0 ) return (Obj)0;
if( LEN_PLIST(list) < ngens ) {
ErrorQuit( "vector too short", 0L, 0L );
return (Obj)0;
}
if( LEN_PLIST(word) % 2 != 0 ) {
ErrorQuit( "Length of word odd", 0L, 0L );
return (Obj)0;
}
st = bottom;
PUSH_STACK( word, INTOBJ_INT(1) );
while( st > bottom ) {
w = ELM_PLIST( wst, st );
syl = INT_INTOBJ( ELM_PLIST( sst, st ) );
g = INT_INTOBJ( ELM_PLIST( w, syl ) );
if( st > bottom+1 && syl==1 && g == GET_COMMUTE(g) ) {
/* Collect word^exponent in one go. */
e = ELM_PLIST( west, st );
/* Add in. */
AddIn( list, w, e );
/* Reduce. */
for( h = g; h <= ngens; h++ ) {
s = ELM_PLIST( list, h );
if( IS_INT_ZERO( s ) ) continue;
y = (Obj)0;
if( (e = GET_EXPONENT( h )) != (Obj)0 ) {
if( !LtInt( s, e ) ) {
t = ModInt( s, e );
SET_ELM_PLIST( list, h, t ); CHANGED_BAG( list );
if( (y = GET_POWER( h )) ) e = QuoInt( s, e );
}
else if( LtInt( s, INTOBJ_INT(0) ) ) {
t = ModInt( s, e );
SET_ELM_PLIST( list, h, t ); CHANGED_BAG( list );
if( (y = GET_IPOWER( h )) ) {
e = QuoInt( s, e );
if( !IS_INT_ZERO( t ) ) e = DiffInt( e, INTOBJ_INT(1) );
e = AInvInt(e);
}
}
}
if( y != (Obj)0 ) AddIn( list, y, e );
}
st--;
}
else {
if( g == GET_COMMUTE( g ) ) {
s = ELM_PLIST( list, g );
t = ELM_PLIST( est, st );
C_SUM_FIA( ge, s, t );
SET_ELM_PLIST( est, st, INTOBJ_INT(0) );
}
else {
/* Assume that the top of the exponent stack is non-zero. */
e = ELM_PLIST( est, st );
if( LtInt( INTOBJ_INT(0), e ) ) {
C_DIFF_FIA( ee, e, INTOBJ_INT(1) ); e = ee;
SET_ELM_PLIST( est, st, e );
conj = ADDR_OBJ(pcp)[PC_CONJUGATES];
iconj = ADDR_OBJ(pcp)[PC_INVERSECONJUGATES];
C_SUM_FIA( ge, ELM_PLIST( list, g ), INTOBJ_INT(1) );
}
else {
C_SUM_FIA( ee, e, INTOBJ_INT(1) ); e = ee;
SET_ELM_PLIST( est, st, e );
conj = ADDR_OBJ(pcp)[PC_CONJUGATESINVERSE];
iconj = ADDR_OBJ(pcp)[PC_INVERSECONJUGATESINVERSE];
C_DIFF_FIA( ge, ELM_PLIST( list, g ), INTOBJ_INT(1) );
}
}
SET_ELM_PLIST( list, g, ge ); CHANGED_BAG( list );
/* Reduce the exponent. We delay putting the power onto the
stack until all the conjugates are on the stack. The power is
stored in y, its exponent in ge. */
y = (Obj)0;
if( (e = GET_EXPONENT( g )) ) {
if( !LtInt( ge, e ) ) {
mge = ModInt( ge, e );
SET_ELM_PLIST( list, g, mge ); CHANGED_BAG( list );
if( (y = GET_POWER( g )) ) ge = QuoInt( ge, e );
}
else if( LtInt( ge, INTOBJ_INT(0) ) ) {
mge = ModInt( ge, e );
SET_ELM_PLIST( list, g, mge ); CHANGED_BAG( list );
if( (y = GET_IPOWER( g )) ) {
ge = QuoInt( ge, e );
if( !IS_INT_ZERO( mge ) )
ge = DiffInt( ge, INTOBJ_INT(1) );
ge = AInvInt(ge);
}
}
}
hh = h = GET_COMMUTE( g );
/* Find the place where we start to collect. */
for( ; h > g; h-- ) {
e = ELM_PLIST( list, h );
if( !IS_INT_ZERO(e) ) {
if( LtInt( INTOBJ_INT(0), e ) ) {
if( GET_CONJ( h, g ) ) break;
}
else {
if( GET_ICONJ( h, g ) ) break;
}
}
}
/* Put those onto the stack, if necessary. */
if( h > g || y != (Obj)0 )
for( ; hh > h; hh-- ) {
e = ELM_PLIST( list, hh );
if( !IS_INT_ZERO(e) ) {
SET_ELM_PLIST( list, hh, INTOBJ_INT(0) );
if( LtInt( INTOBJ_INT(0), e ) ) {
x = ELM_PLIST( gens, hh );
}
else {
x = ELM_PLIST( igens, hh );
C_PROD_FIA( ee, e, INTOBJ_INT(-1) ); e = ee;
}
PUSH_STACK( x, e );
}
}
for( ; h > g; h-- ) {
e = ELM_PLIST( list, h );
if( !IS_INT_ZERO(e) ) {
SET_ELM_PLIST( list, h, INTOBJ_INT(0) );
x = (Obj)0;
if( LtInt( INTOBJ_INT(0), e ) ) x = GET_CONJ( h, g );
else x = GET_ICONJ( h, g );
if( x == (Obj)0 ) {
if( LtInt( INTOBJ_INT(0), e ) ) x = ELM_PLIST( gens, h );
else x = ELM_PLIST( igens, h );
}
if( LtInt( e, INTOBJ_INT(0) ) ) {
C_PROD_FIA( ee, e, INTOBJ_INT(-1) ); e = ee;
}
PUSH_STACK( x, e );
}
}
if( y != (Obj)0 ) PUSH_STACK( y, ge );
}
while( st > bottom && IS_INT_ZERO( ELM_PLIST( est, st ) ) ) {
w = ELM_PLIST( wst, st );
syl = INT_INTOBJ( ELM_PLIST( sst, st ) ) + 2;
if( syl > LEN_PLIST( w ) ) {
we = DiffInt( ELM_PLIST( west, st ), INTOBJ_INT(1) );
if( EqInt( we, INTOBJ_INT(0) ) ) { st--; }
else {
SET_ELM_PLIST( west, st, we );
SET_ELM_PLIST( sst, st, INTOBJ_INT(1) );
SET_ELM_PLIST( est, st, ELM_PLIST( w, 2 ) );
CHANGED_BAG( west ); CHANGED_BAG( est );
}
}
else {
SET_ELM_PLIST( sst, st, INTOBJ_INT(syl) );
SET_ELM_PLIST( est, st, ELM_PLIST( w, syl+1 ));
CHANGED_BAG( est );
}
}
}
ADDR_OBJ(pcp)[ PC_STACK_POINTER ] = INTOBJ_INT( bottom );
return (Obj)0;
}
/****************************************************************************
**
*F FuncADD_SET( <self>, <set>, <obj> ) . . . . . . . add an element to a set
**
** 'FuncADD_SET' implements the internal function 'AddSet'.
**
** 'AddSet( <set>, <obj> )'
**
** 'AddSet' adds <obj>, which may be an object of an arbitrary type, to the
** set <set>, which must be a proper set. If <obj> is already an element of
** the set <set>, then <set> is not changed. Otherwise <obj> is inserted at
** the correct position such that <set> is again a set afterwards.
**
** 'AddSet' does not return anything, it is only called for the side effect
** of changing <set>.
*/
Obj FuncADD_SET (
Obj self,
Obj set,
Obj obj )
{
UInt len; /* logical length of the list */
UInt pos; /* position */
UInt isCyc; /* True if the set being added to consists
of kernel cyclotomics */
UInt notpos; /* position of an original element
(not the new one) */
UInt wasHom;
UInt wasNHom;
UInt wasTab;
/* check the arguments */
while ( ! IsSet(set) || ! IS_MUTABLE_OBJ(set) ) {
set = ErrorReturnObj(
"AddSet: <set> must be a mutable proper set (not a %s)",
(Int)TNAM_OBJ(set), 0L,
"you can replace <set> via 'return <set>;'" );
}
len = LEN_LIST(set);
/* perform the binary search to find the position */
pos = PositionSortedDensePlist( set, obj );
/* add the element to the set if it is not already there */
if ( len < pos || ! EQ( ELM_PLIST(set,pos), obj ) ) {
GROW_PLIST( set, len+1 );
SET_LEN_PLIST( set, len+1 );
{
Obj *ptr;
ptr = PTR_BAG(set);
memmove((void *)(ptr + pos+1),(void*)(ptr+pos),(size_t)(sizeof(Obj)*(len+1-pos)));
#if 0
for ( i = len+1; pos < i; i-- ) {
*ptr = *(ptr-1);
ptr--; */
/* SET_ELM_PLIST( set, i, ELM_PLIST(set,i-1) ); */
}
#endif
}
SET_ELM_PLIST( set, pos, obj );
CHANGED_BAG( set );
/* fix up the type of the result */
if ( HAS_FILT_LIST( set, FN_IS_SSORT ) ) {
isCyc = (TNUM_OBJ(set) == T_PLIST_CYC_SSORT);
wasHom = HAS_FILT_LIST(set, FN_IS_HOMOG);
wasTab = HAS_FILT_LIST(set, FN_IS_TABLE);
wasNHom = HAS_FILT_LIST(set, FN_IS_NHOMOG);
CLEAR_FILTS_LIST(set);
/* the result of addset is always dense */
SET_FILT_LIST( set, FN_IS_DENSE );
/* if the object we added was not
mutable then we might be able to
conclude more */
if ( ! IS_MUTABLE_OBJ(obj) ) {
/* a one element list is automatically
homogenous and ssorted */
if (len == 0 )
{
if (TNUM_OBJ(obj) <= T_CYC)
RetypeBagIfWritable( set, T_PLIST_CYC_SSORT);
else
{
SET_FILT_LIST( set, FN_IS_HOMOG );
SET_FILT_LIST( set, FN_IS_SSORT );
if (IS_HOMOG_LIST(obj)) /* it might be a table */
SET_FILT_LIST( set, FN_IS_TABLE );
}
}
else
{
/* Now determine homogeneity */
if (isCyc)
if (TNUM_OBJ(obj) <= T_CYC)
RetypeBagIfWritable( set, T_PLIST_CYC_SSORT);
else
{
RESET_FILT_LIST(set, FN_IS_HOMOG);
SET_FILT_LIST(set, FN_IS_NHOMOG);
}
else if (wasHom)
{
if (!SyInitializing) {
notpos = (pos == 1) ? 2 : 1;
if (FAMILY_OBJ(ELM_PLIST(set,notpos)) == FAMILY_OBJ(obj))
{
SET_FILT_LIST(set, FN_IS_HOMOG);
if (wasTab) {
if (IS_HOMOG_LIST( obj ))
SET_FILT_LIST(set, FN_IS_TABLE);
}
}
else
SET_FILT_LIST(set, FN_IS_NHOMOG);
}
}
else if (wasNHom)
SET_FILT_LIST(set, FN_IS_NHOMOG);
}
}
SET_FILT_LIST( set, FN_IS_SSORT );
}
else {
CLEAR_FILTS_LIST(set);
SET_FILT_LIST( set, FN_IS_DENSE );
}
}
/****************************************************************************
**
*F FuncIS_SUBSET_SET(<self>,<s1>,<s2>) test if a set is a subset of another
**
** 'FuncIS_SUBSET_SET' implements the internal function 'IsSubsetSet'.
**
** 'IsSubsetSet( <set1>, <set2> )'
**
** 'IsSubsetSet' returns 'true' if the set <set2> is a subset of the set
** <set1>, that is if every element of <set2> is also an element of <set1>.
** Either argument may also be a list that is not a proper set, in which
** case 'IsSubsetSet' silently applies 'Set' (see "Set") to it first.
*/
Obj FuncIS_SUBSET_SET (
Obj self,
Obj set1,
Obj set2 )
{
UInt len1; /* length of the left set */
UInt len2; /* length of the right set */
UInt i1; /* index into the left set */
UInt i2; /* index into the right set */
Obj e1; /* element of left set */
Obj e2; /* element of right set */
UInt pos; /* position */
/* check the arguments, convert to sets if necessary */
while ( ! IS_SMALL_LIST(set1) ) {
set1 = ErrorReturnObj(
"IsSubsetSet: <set1> must be a small list (not a %s)",
(Int)TNAM_OBJ(set1), 0L,
"you can replace <set1> via 'return <set1>;'" );
}
while ( ! IS_SMALL_LIST(set2) ) {
set2 = ErrorReturnObj(
"IsSubsetSet: <set2> must be a small list (not a %s)",
(Int)TNAM_OBJ(set2), 0L,
"you can replace <set2> via 'return <set2>;'" );
}
if ( ! IsSet( set1 ) ) set1 = SetList( set1 );
if ( ! IsSet( set2 ) ) set2 = SetList( set2 );
/* special case if the second argument is a set */
if ( IsSet( set2 ) ) {
/* get the logical lengths and get the pointer */
len1 = LEN_PLIST( set1 );
len2 = LEN_PLIST( set2 );
i1 = 1;
i2 = 1;
/* now compare the two sets */
while ( i1 <= len1 && i2 <= len2 && len2 - i2 <= len1 - i1 ) {
e1 = ELM_PLIST( set1, i1 );
e2 = ELM_PLIST( set2, i2 );
if ( EQ( e1, e2 ) ) {
i1++; i2++;
}
else if ( LT( e1, e2 ) ) {
i1++;
}
else {
break;
}
}
}
/* general case */
else {
/* first convert the other argument into a proper list */
PLAIN_LIST( set2 );
/* get the logical lengths */
len1 = LEN_PLIST( set1 );
len2 = LEN_PLIST( set2 );
/* loop over the second list and look for every element */
for ( i2 = 1; i2 <= len2; i2++ ) {
/* ignore holes */
if ( ELM_PLIST(set2,i2) == 0 )
continue;
/* perform the binary search to find the position */
pos = PositionSortedDensePlist( set1, ELM_PLIST(set2,i2) );
/* test if the element was found at position k */
if ( len1<pos || ! EQ(ELM_PLIST(set1,pos),ELM_PLIST(set2,i2)) ) {
break;
}
}
}
/* return 'true' if every element of <set2> appeared in <set1> */
return ((i2 == len2 + 1) ? True : False);
}