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idem.c
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idem.c
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#include <typedef.h>
#include <getput.h>
#include <matrix.h>
#include <base.h>
#include <datei.h>
#include <longtools.h>
#include <bravais.h>
#include <idem.h>
int main(int argc,char **argv){
bravais_TYP *G;
matrix_TYP *form,
**idem,
*id;
int i,
anz,
dimc,
dimcc;
char comment[1000];
read_header(argc,argv);
if ((is_option('h') && optionnumber('h')==0) || (FILEANZ < 1)){
printf("Usage: %s file [-d] [-o]\n",argv[0]);
printf("\n");
printf("file: bravais_TYP containing generators of a finite unimodular group.\n");
printf("\n");
printf("Calculates the central primitive idempotents of the rational commuting (or \n");
printf("equivalently envelloping) algebra of the group in file. (This is used\n");
printf("for splitting the natural module Q^n into homogeneous components.)\n");
printf("\n");
printf("CAUTION: The program might give wrong answers for degrees bigger than 6.\n");
printf("\n");
printf("Options:\n");
printf(" -d : Outputs the dimensions of the commuting algebra and its centre.\n");
printf(" -o : Gives a Z-basis of the commuting algebra and its centre.\n");
printf("\n");
if (is_option('h')){
exit(0);
}
else{
exit(31);
}
}
INFO_LEVEL = optionnumber('h');
G = get_bravais(FILENAMES[0]);
/* avoid silly mistakes */
for (i=0;i<G->gen_no;i++){
if (!G->gen[i]->flags.Integral){
fprintf(stderr,"The generators for the bravais group have to be\n");
fprintf(stderr,"integral.\n");
exit(3);
}
}
id = init_mat(G->dim,G->dim,"1");
form = rform(G->gen,G->gen_no,id,101);
idem = idempotente(G->gen,G->gen_no,form,&anz,&dimc,&dimcc);
printf("#%d\n",anz);
for (i=0;i<anz;i++){
sprintf(comment,"%d-th idempotent for group in %s",i+1,FILENAMES[0]);
put_mat(idem[i],NULL,comment,2);
}
if (is_option('o')){
/* tell the user the centralizer */
printf("#%d\n",dimc);
for (i=0;i<dimc;i++){
sprintf(comment,"centralizer of group in %s",FILENAMES[0]);
put_mat(idem[i+anz],NULL,comment,2);
}
/* and it's centre */
printf("#%d\n",dimcc);
for (i=0;i<dimc;i++){
sprintf(comment,"centre of centralizer for group in %s",FILENAMES[0]);
put_mat(idem[i+anz+dimc],NULL,comment,2);
}
}
if (is_option('d')){
printf("dimension of the centralizer: %d\n",dimc);
printf("dimension of it's centre: %d\n",dimcc);
}
for (i=0;i<anz+dimc+dimcc;i++){
free_mat(idem[i]);
}
if (idem != NULL) free(idem);
free_bravais(G);
free_mat(form);
free_mat(id);
exit(0);
} /* main */