void isom_options (int format, struct pcp_vars *pcp)
{
register int *y = y_address;
FILE *Status;
FILE *FileName;
FILE *Subgroup;
struct pga_vars pga;
Logical user_supplied = FALSE;
Logical group_present = FALSE;
Logical identity_map;
Logical finished;
Logical valid;
Logical equal;
int output = DEFAULT_STANDARD_PRINT;
int start_class, final_class;
int option;
int t;
int status;
int complete;
int iteration;
int *seq1;
int *seq2;
int len1, len2;
int nmr_items;
int ***auts;
int x_dim, y_dim;
FILE * GAP_library;
char *name;
int nmr_of_exponents;
StandardPresentation = TRUE;
pga.nmr_soluble = 0;
list_isom_menu ();
do {
option = read_option (MAXOPTION);
switch (option) {
case -1:
list_isom_menu ();
break;
case START_INFO:
t = runTime ();
group_present = setup_start_info (FALSE, 0, stdin, format, &pga, pcp);
handle_error (group_present);
user_supplied = TRUE;
t = runTime () - t;
/* it is possible that the p-quotient is trivial */
if (pcp->cc == 0) {
group_present = FALSE;
break;
}
printf ("Class %d %d-quotient and its %d-covering group computed in %.2f seconds\n",
pcp->cc - 1, pcp->p, pcp->p, t * CLK_SCALE);
break;
case CONSTRUCT:
if (!user_supplied) {
name = GetString ("Enter input file name for group information: ");
FileName = OpenFile (name, "r");
if (FileName == NULL) break;
}
name = GetString ("Enter output file name for group information: ");
read_value (TRUE, "Standardise presentation to what class? ",
&final_class, 0);
if (user_supplied && final_class < pcp->cc) {
printf ("Value supplied for end class must be at least %d\n",
pcp->cc);
}
/* read in data from file and set up group to end of start_class
and compute its p-covering group */
if (!user_supplied) {
group_present = setup_start_info (FALSE, 0, FileName,
FILE_INPUT, &pga, pcp);
handle_error (group_present);
if (final_class < pcp->cc) {
CloseFile (FileName);
printf ("Value supplied for end class must be at least %d\n",
pcp->cc);
}
}
if (pcp->cc == 0) {
printf ("%d-quotient is trivial\n", pcp->p);
break;
}
complete = (pcp->newgen == 0) ? TERMINAL : CAPABLE;
iteration = 0;
for (start_class = pcp->cc; start_class <= final_class &&
complete != TERMINAL; ++start_class) {
t = runTime ();
identity_map = FALSE;
Subgroup = OpenFile ("ISOM_Subgroup", "w");
do {
++iteration;
set_defaults (&pga);
/*
pga.space_efficient = TRUE;
*/
/* either prompt for information or read it from file */
if (user_supplied) {
auts = read_auts (STANDARDISE, &pga.m, &nmr_of_exponents, pcp)
;
pga.fixed = 0;
query_solubility (&pga);
user_supplied = FALSE;
#ifdef HAVE_GMP
autgp_order (&pga, pcp);
#endif
}
else {
auts = read_auts_from_file (FileName, &pga.m, pcp);
nmr_items = fscanf (FileName, "%d", &pga.fixed);
verify_read (nmr_items, 1);
nmr_items = fscanf (FileName, "%d", &pga.soluble);
verify_read (nmr_items, 1);
#ifdef HAVE_GMP
fscanf (FileName, "\n");
mpz_init (&pga.aut_order);
mpz_inp_str (&pga.aut_order, FileName, 10);
#endif
CloseFile (FileName);
}
x_dim = pga.m; y_dim = pcp->lastg;
/* construct standard presentation relative to smallest
permissible characteristic subgroup in p-multiplicator */
standard_presentation (&identity_map, output, auts, &pga, pcp);
free_array (auts, x_dim, y_dim, 1);
/* was the characteristic subgroup chosen in this iteration
the whole of the p-multiplicator? */
Status = OpenFile ("ISOM_Status", "r");
fscanf (Status, "%d", &status);
fscanf (Status, "%d", &complete);
CloseFile (Status);
/* have we finished the construction? */
finished = (status == END_OF_CLASS &&
(start_class == final_class || complete == TERMINAL));
/* organise to write modified presentation + automorphisms
to file ISOM_PP */
if (!identity_map || finished)
{
copy_file( "ISOM_present", "ISOM_PP" );
append_file( "ISOM_NextClass", "ISOM_PP" );
}
else
copy_file( "ISOM_NextClass", "ISOM_PP" );
if (finished) break;
/* if necessary, set up new presentation + other information */
FileName = OpenFile ("ISOM_PP", "r");
group_present = setup_start_info (identity_map, status,
FileName, FILE_INPUT, &pga, pcp);
handle_error (group_present);
/* if appropriate, factor subgroup from p-multiplicator */
if (status != END_OF_CLASS)
factor_subgroup (pcp);
/* reinitialise pga structure */
initialise_pga (&pga, pcp);
pga.m = 0;
pga.ndgen = y[pcp->clend + 1];
set_values (&pga, pcp);
} while (status != END_OF_CLASS && complete != TERMINAL);
CloseFile (Subgroup);
/* the group may have completed only when relations are enforced;
this is an attempt to determine this case */
if (pga.nuclear_rank != 0 && pcp->complete)
break;
t = runTime () - t;
printf ("Computing standard presentation for class %d took %.2f seconds\n",
start_class, t * CLK_SCALE);
}
/* we currently may have presentation for p-covering group;
or is the starting group terminal? if so, we may want to
use last_class to revert to group presentation */
if (!user_supplied && iteration == 0 && !pcp->complete)
last_class (pcp);
/* is the group terminal? */
if (complete == TERMINAL)
printf ("The largest %d-quotient of the group has class %d\n",
pcp->p, pcp->cc);
if (iteration == 0) break;
/* rename file ISOM_PP containing iteration info to nominated file */
rename( "ISOM_PP", name );
break;
case PRINT_PCP:
if (group_present)
print_presentation (TRUE, pcp);
break;
case SAVE_PRES:
name = GetString ("Enter output file name: ");
FileName = OpenFileOutput (name);
if (group_present && FileName != NULL) {
save_pcp (FileName, pcp);
CloseFile (FileName);
printf ("Presentation written to file\n");
}
break;
case COMPARE:
valid = get_description ("Enter file name storing first presentation: ",
&len1, &seq1, pcp);
if (!valid) break;
valid = get_description ("Enter file name storing second presentation: ",
&len2, &seq2, pcp);
if (!valid) break;
equal = (len1 == len2) ? compare_sequences (seq1, seq2, len1): FALSE;
printf ("Identical presentations? %s\n", equal == TRUE ?
"True" : "False");
free_vector (seq1, 1);
free_vector (seq2, 1);
break;
case STANDARD_PRINT_LEVEL:
read_value (TRUE, "Input print level for construction (0-2): ",
&output, 0);
/* allow user to supply same max print level as for
p-quotient calculations */
if (output == MAX_STANDARD_PRINT + 1)
--output;
if (output > MAX_STANDARD_PRINT) {
printf ("Print level must lie between %d and %d\n",
MIN_STANDARD_PRINT, MAX_STANDARD_PRINT);
output = DEFAULT_STANDARD_PRINT;
}
break;
case PQ_MENU:
options (ISOM_MENU, format, pcp);
break;
case ISOM_OPTION:
FileName = OpenFile (name, "r");
group_present = setup_start_info (FALSE, 0, FileName,
FILE_INPUT, &pga, pcp);
pcp->multiplicator_rank = pcp->lastg - y[pcp->clend + pcp->cc-1];
last_class (pcp);
auts = read_auts_from_file (FileName, &pga.m, pcp);
nmr_items = fscanf (FileName, "%d", &pga.fixed);
verify_read (nmr_items, 1);
nmr_items = fscanf (FileName, "%d", &pga.soluble);
verify_read (nmr_items, 1);
printf ("Images of user-supplied generators are listed last below\n");
print_map (pcp);
#ifdef HAVE_GMP
fscanf (FileName, "\n");
mpz_init (&pga.aut_order);
mpz_inp_str (&pga.aut_order, FileName, 10);
#endif
CloseFile (FileName);
GAP_library = OpenFile ("GAP_library", "a+");
write_GAP_library (GAP_library, pcp);
pga.nmr_centrals = pga.m;
pga.nmr_stabilisers = 0;
GAP_auts (GAP_library, auts, auts, &pga, pcp);
CloseFile (GAP_library);
printf ("Presentation listing images of user-supplied generators written to GAP_library\n");
break;
case EXIT: case MAXOPTION:
unlink( "ISOM_present" );
unlink( "ISOM_Subgroup" );
unlink( "ISOM_cover_file" );
unlink( "ISOM_group_file" );
unlink( "ISOM_XX" );
unlink( "ISOM_NextClass" );
unlink( "ISOM_Status" );
printf ("Exiting from ANU p-Quotient Program\n");
break;
} /* switch */
} while (option != 0 && option != MAXOPTION);
}
int echelon(struct pcp_vars *pcp)
{
register int *y = y_address;
register int i;
register int j;
register int k;
register int p1;
register int exp;
register int redgen = 0;
register int count = 0;
register int factor;
register int bound;
register int offset;
register int temp;
register int value;
register int free;
register Logical trivial;
register Logical first;
register int p = pcp->p;
register int pm1 = pcp->pm1;
#include "access.h"
pcp->redgen = 0;
pcp->eliminate_flag = FALSE;
/* check that the relation is homogeneous of class pcp->cc */
if (pcp->cc != 1) {
offset = pcp->lused - 1;
temp = pcp->lastg;
for (i = 2, bound = pcp->ccbeg; i <= bound; i++) {
if (y[offset + i] != y[offset + temp + i]) {
text(6, pcp->cc, 0, 0, 0);
pcp->eliminate_flag = TRUE;
return -1;
}
}
}
/* compute quotient of the relations and store quotient as an exponent
vector in y[pcp->lused + pcp->ccbeg] to y[pcp->lused + pcp->lastg] */
k = 0;
offset = pcp->lused;
for (i = pcp->ccbeg, bound = pcp->lastg; i <= bound; i++) {
y[offset + i] -= y[offset + bound + i];
if ((j = y[offset + i])) {
if (j < 0)
y[offset + i] += p;
k = i;
}
}
if (k <= 0)
return -1;
/* print out the quotient of the relations */
if (pcp->diagn) {
/* a call to compact is not permitted at this point */
if (pcp->lused + 4 * pcp->lastg + 2 < pcp->structure) {
/* first copy relevant entries to new position in y */
free = pcp->lused + 2 * pcp->lastg + 1;
for (i = 1; i < pcp->ccbeg; ++i)
y[free + i] = 0;
for (i = pcp->ccbeg; i <= pcp->lastg; ++i)
y[free + i] = y[pcp->lused + i];
setup_word_to_print(
"quotient relation", free, free + pcp->lastg + 1, pcp);
}
}
first = TRUE;
while (first || --k >= pcp->ccbeg) {
/* does generator k occur in the unechelonised relation? */
if (!first && y[pcp->lused + k] <= 0)
continue;
/* yes */
first = FALSE;
exp = y[pcp->lused + k];
if ((i = y[pcp->structure + k]) <= 0) {
if (i < 0) {
/* generator k was previously redundant, so eliminate it */
p1 = -y[pcp->structure + k];
count = y[p1 + 1];
offset = pcp->lused;
for (i = 1; i <= count; i++) {
value = y[p1 + i + 1];
j = FIELD2(value);
/* integer overflow can occur here; see comments in collect */
y[offset + j] = (y[offset + j] + exp * FIELD1(value)) % p;
}
}
y[pcp->lused + k] = 0;
} else {
/* generator k was previously irredundant; have we already
found a generator to eliminate using this relation? */
if (redgen > 0) {
/* yes, so multiply this term by the appropriate factor
and note that the value of redgen is not trivial */
trivial = FALSE;
/* integer overflow can occur here; see comments in collect */
y[pcp->lused + k] = (y[pcp->lused + k] * factor) % p;
} else {
/* no, we will eliminate k using this relation */
redgen = k;
trivial = TRUE;
/* we want to compute the value of k so we will multiply the
rest of the relation by the appropriate factor;
integer overflow can occur here; see comments in collect */
factor = pm1 * invert_modp(exp, p);
/* we carry out this mod computation to reduce possibility
of integer overflow */
#if defined(CAREFUL)
factor = factor % p;
#endif
y[pcp->lused + k] = 0;
}
}
}
if (redgen <= 0)
return -1;
else
pcp->redgen = redgen;
/* the relation is nontrivial; redgen is either trivial or redundant */
if (trivial) {
/* mark redgen as trivial */
y[pcp->structure + redgen] = 0;
if (pcp->fullop)
text(3, redgen, 0, 0, 0);
complete_echelon(1, redgen, pcp);
} else {
/* redgen has value in exponent form in y[pcp->lused + pcp->ccbeg]
to y[pcp->lused + redgen(-1)] */
count = 0;
offset = pcp->lused;
for (i = pcp->ccbeg; i <= redgen; i++)
if (y[offset + i] > 0) {
count++;
y[offset + count] = PACK2(y[offset + i], i);
}
offset = pcp->lused + count + 1;
for (i = 1; i <= count; i++)
y[offset + 2 - i] = y[offset - i];
/* set up the relation for redgen */
y[pcp->lused + 1] = pcp->structure + redgen;
y[pcp->lused + 2] = count;
y[pcp->structure + redgen] = -(pcp->lused + 1);
pcp->lused += count + 2;
if (pcp->fullop)
text(4, redgen, 0, 0, 0);
complete_echelon(0, redgen, pcp);
}
pcp->eliminate_flag = TRUE;
if (redgen < pcp->first_pseudo)
pcp->newgen--;
if (pcp->newgen != 0 || pcp->multiplicator)
return count;
/* group is completed because all actual generators are redundant,
so it is not necessary to continue calculation of this class */
pcp->complete = 1;
last_class(pcp);
if (pcp->fullop || pcp->diagn)
text(5, pcp->cc, p, pcp->lastg, 0);
return -1;
}
