/**************************************************************************** ** *A GAP_present.c ANUPQ source Eamonn O'Brien *A & Frank Celler *A & Benedikt Rothe ** *Y Copyright 1995-1997, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany *Y Copyright 1995-1997, School of Mathematical Sciences, ANU, Australia **
*/ #include"pq_defs.h" #include"pcp_vars.h" #include"pga_vars.h" #include"constants.h" #include"pq_functions.h" #include"menus.h"
/**************************************************************************** ** *F print_GAP_word ** print out a word of a pcp presentation
*/ staticvoid print_GAP_word(FILE *file, int ptr)
{ registerint *y = y_address;
int gen, exp; int i; int count; #include"access.h"
if (ptr == 0)
fprintf(file, " One(F)"); elseif (ptr > 0)
fprintf(file, " F.%d", ptr); else {
ptr = -ptr + 1;
count = y[ptr];
fprintf(file, " %s", (1 < count) ? "(" : ""); for (i = 1; i <= count; i++) {
exp = FIELD1(y[ptr + i]);
gen = FIELD2(y[ptr + i]);
fprintf(file, "F.%d", gen); if (exp != 1)
fprintf(file, "^%d", exp); if (i != count)
fprintf(file, "*");
} if (1 < count)
fprintf(file, ")");
}
}
/**************************************************************************** ** *F GAP_presentation ** write pq presentation to file in GAP format
*/ void GAP_presentation(FILE *file, struct pcp_vars *pcp, int aspcgroup)
{ registerint *y = y_address;
int i; int j; int k; int l; int p1; int p2; int weight; int comma; int ndgen = pcp->ndgen; int dgen = pcp->dgen;
#include"access.h"
/* construct a free group with enough generators */
fprintf(file, "F := FreeGroup( %d );\n", pcp->lastg);
if (aspcgroup) {
fprintf(file, "F := PcGroupFpGroupNC( F / [\n");
} else
fprintf(file, "F := F / [\n");
/* write power-relators with possible non-trivial rhs */
comma = 0;
k = y[pcp->clend + pcp->cc - 1]; for (i = 1; i <= k; i++) { if (comma)
fprintf(file, ",\n"); else
comma = 1;
p2 = y[pcp->ppower + i]; if (p2 == 0)
fprintf(file, " F.%d^%d", i, pcp->p); else {
fprintf(file, " F.%d^%d /", i, pcp->p);
print_GAP_word(file, p2);
}
}
/* write power-relators with trivial rhs */ for (i = k + 1; i <= pcp->lastg; ++i) { if (comma)
fprintf(file, ",\n"); else
comma = 1;
fprintf(file, " F.%d^%d", i, pcp->p);
}
/* write commutator-relators */ for (i = 2; i <= k; i++) {
weight = WT(y[pcp->structure + i]);
p1 = y[pcp->ppcomm + i];
l = MIN(i - 1, y[pcp->clend + pcp->cc - weight]); for (j = 1; j <= l; j++) {
p2 = y[p1 + j]; if (p2 != 0) {
fprintf(file, ",\n");
fprintf(file, " Comm( F.%d, F.%d ) /", i, j);
print_GAP_word(file, p2);
}
}
}
if (aspcgroup)
fprintf(file, "] );\n"); else
fprintf(file, "];\n");
/* store the relation between pc gens and fp gens */
fprintf(file, "MapImages := [];\n"); for (i = 1; i <= ndgen; i++) {
p2 = y[dgen + i];
fprintf(file, "MapImages[%d] := ", i);
print_GAP_word(file, p2);
fprintf(file, ";\n");
}
}
/**************************************************************************** ** *F MakeNameList ** create p-group generation identifier for group
*/ char *nextnumber(char *ident)
{ while (*ident != '\0' && *ident != '#')
ident++; if (*ident == '#')
ident++; return ident;
}
void MakeNameList(FILE *file, char *ident)
{ int first = 1;
fprintf(file, "SetANUPQIdentity( F, [ "); while (*(ident = nextnumber(ident)) != '\0') { if (!first)
fprintf(file, ",");
first = 0;
fprintf(file, "["); do
fprintf(file, "%c", *ident); while (*++ident != ';');
ident++;
fprintf(file, ","); do {
fprintf(file, "%c", *ident);
ident++;
} while ('0' <= *ident && *ident <= '9');
fprintf(file, "]");
}
fprintf(file, " ] );\n");
}
/**************************************************************************** ** *F write_GAP_library ** write GAP library file in form suitable for reading into GAP
*/ int countcall = 0;
void write_GAP_library(FILE *file, struct pcp_vars *pcp)
{ /* if this is the first call initialise 'ANUgroups' */ if (countcall == 0) {
fprintf(file, "ANUPQgroups := [];\n");
fprintf(file, "ANUPQautos := [];\n\n");
}
countcall++;
/* write function call to <countcall>.th position of <ANUPQgroups> */
fprintf(file, "## group number: %d\n", countcall);
fprintf(file, "ANUPQgroups[%d] := function( L )\n", countcall);
fprintf(file, "local MapImages, F;\n\n");
/* write the GAP presentation to file */
GAP_presentation(file, pcp, 0);
/* convert <F> to a pc group in descendants case
... has to be done here; otherwise, we lose the property/attributes */
fprintf(file, "if IsList(L) then\n F := PcGroupFpGroupNC(F);\nfi;\n");
/* add info. whether group is capable, and its nuclear and mult'r ranks*/
fprintf(file, "SetIsCapable(F, %s);\n", (pcp->newgen) ? "true" : "false");
fprintf(file, "SetNuclearRank(F, %d);\n", pcp->newgen);
fprintf(file, "SetMultiplicatorRank (F, %d);\n", pcp->multiplicator_rank);
/* add the pq identitfier */
MakeNameList(file, pcp->ident);
/* add the group <F> to <L> */
fprintf(file, "if IsList(L) then\n Add( L, F );\n");
fprintf(file, "else\n L.group := F;\n L.map := MapImages;\nfi;");
fprintf(file, "\nend;\n\n\n");
}
/**************************************************************************** ** *F GAP_auts ** write a description of the automorphism group of the current ** group to a file in a format suitable for input to GAP
*/ void GAP_auts(FILE *file, int ***central, int ***stabiliser, struct pga_vars *pga, struct pcp_vars *pcp)
{ registerint *y = y_address;
int i, j, k, ngens, first;
/* if this is the first call something is wrong ' */ if (countcall == 0) {
fprintf(stderr, "internal error in 'GAP_auts'"); exit(FAILURE);
}
/* write function call to <countcall>.th position of <ANUPQgroups> */
fprintf(file, "## automorphisms number: %d\n", countcall);
fprintf(file, "ANUPQautos[%d] := function( G )\n", countcall);
fprintf(file, "local frattGens,\n");
fprintf(file, " relOrders,\n");
fprintf(file, " centralAutos,\n");
fprintf(file, " otherAutos;\n");
/* write information about automorphisms to file */
ngens = y[pcp->clend + 1];
fprintf(file, "SetIsPcgsAutomorphisms(G,%s);\n",
pga->soluble ? "true" : "false");
fprintf(file, "SetIsCapable(G,%s);\n", pga->capable ? "true" : "false");
/* first write the Frattini generators */
fprintf(file, "frattGens := ["); for (k = 1; k <= ngens; k++) { if (k != 1)
fprintf(file, ",");
fprintf(file, "G.%d", k);
}
fprintf(file, "];\n");
fprintf(file, "centralAutos := []; # nr of central autos: %d\n",
pga->nmr_centrals);
/* write out all central automorphisms */ for (i = 1; i <= pga->nmr_centrals; ++i) {
fprintf(file, "Add( centralAutos, ["); for (j = 1; j <= pga->ndgen; ++j) { if (j != 1)
fprintf(file, ",");
first = 1; for (k = 1; k <= pcp->lastg; ++k) { if (0 != central[i][j][k]) { if (!first)
fprintf(file, "*");
first = 0; if (1 != central[i][j][k])
fprintf(file, "G.%d^%d", k, central[i][j][k]); else
fprintf(file, "G.%d", k);
}
} if (first) {
fprintf(stderr, "internal error in 'GAP_auts'\n"); exit(FAILURE);
}
}
fprintf(file, "] );\n");
}
fprintf(file, "otherAutos := []; # nr of other autos: %d\n",
pga->nmr_stabilisers);
/* write out all other automorphisms */ for (i = 1; i <= pga->nmr_stabilisers; ++i) {
fprintf(file, "Add( otherAutos, ["); for (j = 1; j <= pga->ndgen; ++j) { if (j != 1)
fprintf(file, ",");
first = 1; for (k = 1; k <= pcp->lastg; ++k) { if (0 != stabiliser[i][j][k]) { if (!first)
fprintf(file, "*");
first = 0; if (1 != stabiliser[i][j][k])
fprintf(file, "G.%d^%d", k, stabiliser[i][j][k]); else
fprintf(file, "G.%d", k);
}
} if (first) {
fprintf(stderr, "internal error in 'GAP_auts'\n"); exit(FAILURE);
}
}
fprintf(file, "] );\n");
}
fprintf(file, "relOrders := ["); if (pga->nmr_soluble > 0) { for (i = 1; i <= pga->nmr_soluble; ++i)
fprintf(file, "%d, ", pga->relative[i]);
fprintf(file, "%d", pga->relative[pga->nmr_soluble]);
}
fprintf(file, "];\n");
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