delete 'old' folder (still available in old_experiments branch together with other things)
This commit is contained in:
Florian Stecker
parent
4cd76a8d81
commit
e264921831
312
old/coxeter.c
312
old/coxeter.c
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#include "coxeter.h"
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#include "queue.h"
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#include <memory.h>
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#include <gsl/gsl_linalg.h>
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#include <gsl/gsl_blas.h>
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static void applyGenerator(int i, double *x, double *y, int rank, double **schlaefliMatrix)
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{
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memcpy(y, x, rank*sizeof(double));
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for(int j = 0; j < rank; j++)
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y[i] -= schlaefliMatrix[i][j]*x[j];
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}
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static int check_equal_sector(gsl_matrix *x1, gsl_matrix *x2, gsl_matrix *yinv, gsl_matrix *schlaefli, gsl_vector *starting, gsl_vector *i1, gsl_vector *i2)
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{
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double scalarProduct;
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int rank = x1->size1;
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// calculate <y^{-1} * x1 * x2 * s, e_i> for all i, or identically the components of schlaefli*y^{-1}*x*s
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gsl_blas_dgemv(CblasNoTrans, 1.0, x2, starting, 0.0, i1);
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gsl_blas_dgemv(CblasNoTrans, 1.0, x1, i1, 0.0, i2);
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gsl_blas_dgemv(CblasNoTrans, 1.0, yinv, i2, 0.0, i1);
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gsl_blas_dgemv(CblasNoTrans, 1.0, schlaefli, i1, 0.0, i2);
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for(int i = 0; i < rank; i++)
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if(gsl_vector_get(i2, i) < 0)
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return 0;
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return 1;
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}
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static void invert(gsl_matrix *x, gsl_matrix *xinv)
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{
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int rank = x->size1;
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gsl_matrix *xLU = gsl_matrix_alloc(rank, rank);
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gsl_permutation *p = gsl_permutation_alloc(rank);
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int s;
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gsl_matrix_memcpy(xLU, x);
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gsl_linalg_LU_decomp(xLU, p, &s);
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gsl_linalg_LU_invert(xLU, p, xinv);
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gsl_permutation_free(p);
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gsl_matrix_free(xLU);
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}
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static void generate_schlaefli_matrix(semisimple_type_t type, gsl_matrix *mat)
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{
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gsl_matrix_set_zero(mat);
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int offset = 0;
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for(int k = 0; k < type.n; k++) {
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if(type.factors[k].series == 'A') {
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for(int i = 0; i < type.factors[k].rank; i++)
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for(int j = 0; j < type.factors[k].rank; j++)
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if(i == j)
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gsl_matrix_set(mat, offset + i, offset + j, 2.0);
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else if(i - j == 1 || i - j == -1)
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gsl_matrix_set(mat, offset + i, offset + j, -1.0);
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} else if(type.factors[k].series == 'B' || type.factors[k].series == 'C') {
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for(int i = 0; i < type.factors[k].rank; i++)
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for(int j = 0; j < type.factors[k].rank; j++)
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if(i == j)
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gsl_matrix_set(mat, offset + i, offset + j, 2.0);
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else if(i == 0 && j == 1 || i == 1 && j == 0)
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gsl_matrix_set(mat, offset + i, offset + j, -sqrt(2.0));
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else if(i - j == 1 || i - j == -1)
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gsl_matrix_set(mat, offset + i, offset + j, -1.0);
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} else if(type.factors[k].series == 'D') {
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for(int i = 0; i < type.factors[k].rank; i++)
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for(int j = 0; j < type.factors[k].rank; j++)
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if(i == j)
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gsl_matrix_set(mat, offset + i, offset + j, 2.0);
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else if(i > 0 && j > 0 && (i - j == 1 || i - j == -1) || i == 0 && j == 2 || i == 2 && j == 0)
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gsl_matrix_set(mat, offset + i, offset + j, -1.0);
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} else if(type.factors[k].series == 'F') {
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ERROR(type.factors[k].rank != 4, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
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for(int i = 0; i < 4; i++)
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gsl_matrix_set(mat, offset + i, offset + i, 2.0);
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for(int i = 0; i < 3; i++) {
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gsl_matrix_set(mat, offset + i, offset + i + 1, i == 1 ? -sqrt(2.0) : -1.0);
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gsl_matrix_set(mat, offset + i + 1, offset + i, i == 1 ? -sqrt(2.0) : -1.0);
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}
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} else if(type.factors[k].series == 'G') {
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ERROR(type.factors[k].rank != 2, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
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gsl_matrix_set(mat, offset + 0, offset + 0, 2.0);
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gsl_matrix_set(mat, offset + 0, offset + 1, -sqrt(3.0));
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gsl_matrix_set(mat, offset + 1, offset + 0, -sqrt(3.0));
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gsl_matrix_set(mat, offset + 1, offset + 1, 2.0);
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} else {
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ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[k].series, type.factors[k].rank);
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}
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offset += type.factors[k].rank;
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}
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}
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int coxeter_rank(semisimple_type_t type)
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{
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int rank = 0;
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for(int i = 0; i < type.n; i++)
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rank += type.factors[i].rank;
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return rank;
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}
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int coxeter_order(semisimple_type_t type)
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{
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int order = 1;
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for(int i = 0; i < type.n; i++) {
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if(type.factors[i].series == 'A') { // (rank+1)!
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for(int j = 1; j <= type.factors[i].rank + 1; j++)
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order *= j;
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} else if(type.factors[i].series == 'B' || type.factors[i].series == 'C') { // 2^rank * rank!
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for(int j = 1; j <= type.factors[i].rank; j++)
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order *= 2*j;
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} else if(type.factors[i].series == 'D') { // 2^(rank-1) * rank!
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for(int j = 2; j <= type.factors[i].rank; j++)
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order *= 2*j;
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} else if(type.factors[i].series == 'E') {
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if(type.factors[i].rank == 6)
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order *= 51840;
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else if(type.factors[i].rank == 7)
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order *= 2903040;
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else if(type.factors[i].rank == 8)
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order *= 696729600;
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else
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ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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} else if(type.factors[i].series == 'F') {
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ERROR(type.factors[i].rank != 4, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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order *= 1152;
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} else if(type.factors[i].series == 'G') {
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ERROR(type.factors[i].rank != 2, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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order *= 12;
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} else if(type.factors[i].series == 'H') {
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if(type.factors[i].rank == 2)
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order *= 10;
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else if(type.factors[i].rank == 3)
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order *= 120;
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else if(type.factors[i].rank == 4)
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order *= 14400;
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else
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ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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} else {
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ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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}
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}
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return order;
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}
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int coxeter_hyperplanes(semisimple_type_t type)
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{
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int hyperplanes = 0;
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for(int i = 0; i < type.n; i++) {
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if(type.factors[i].series == 'A') // rank*(rank+1)/2
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hyperplanes += (type.factors[i].rank * (type.factors[i].rank + 1)) / 2;
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else if(type.factors[i].series == 'B' || type.factors[i].series == 'C') // rank * rank
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hyperplanes += type.factors[i].rank * type.factors[i].rank;
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else if(type.factors[i].series == 'D') // rank * (rank - 1)
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hyperplanes += type.factors[i].rank * (type.factors[i].rank - 1);
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else if(type.factors[i].series == 'E') {
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if(type.factors[i].rank == 6)
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hyperplanes += 36;
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else if(type.factors[i].rank == 7)
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hyperplanes += 63;
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else if(type.factors[i].rank == 8)
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hyperplanes += 120;
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else
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ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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} else if(type.factors[i].series == 'F') {
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ERROR(type.factors[i].rank != 4, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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hyperplanes += 24;
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} else if(type.factors[i].series == 'G') {
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ERROR(type.factors[i].rank != 2, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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hyperplanes += 6;
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} else {
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ERROR(1, "A Coxeter group of type %c%d does not exist or is not implemented!\n", type.factors[i].series, type.factors[i].rank);
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}
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}
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return hyperplanes;
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}
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unsigned long opposition_involution(semisimple_type_t type, unsigned long theta)
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{
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int offset = 0;
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unsigned long result = 0;
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for(int i = 0; i < type.n; i++) {
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unsigned long current = (theta >> offset) & ((1 << type.factors[i].rank) - 1);
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unsigned long iota_current;
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if(type.factors[i].series == 'B' || type.factors[i].series == 'C' || type.factors[i].series == 'F' || type.factors[i].series == 'G') {
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iota_current = current;
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} else if(type.factors[i].series == 'A') {
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iota_current = 0;
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for(int j = 0; j < type.factors[i].rank; j++)
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iota_current += ((current >> j) & 1) << (type.factors[i].rank - 1 - j);
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} else if(type.factors[i].series == 'D') {
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if(type.factors[i].rank % 2 == 0) {
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iota_current = current;
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} else {
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ERROR(1, "The opposition involution for type %c%d is not yet implemented!\n", type.factors[i].series, type.factors[i].rank);
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}
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} else if(type.factors[i].series == 'E') {
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ERROR(1, "The opposition involution for En is not yet implemented!\n");
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}
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result += iota_current << offset;
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offset += type.factors[i].rank;
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}
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return result;
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}
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static void generate_starting_vector(int rank, gsl_matrix *schlaefli, gsl_vector *result)
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{
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gsl_matrix *schlaefliLU = gsl_matrix_alloc(rank, rank);
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gsl_vector *diagonal = gsl_vector_alloc(rank);
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gsl_permutation *p = gsl_permutation_alloc(rank);
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int s;
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for(int i = 0; i < rank; i++)
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gsl_vector_set(diagonal, i, 1.0);
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gsl_matrix_memcpy(schlaefliLU, schlaefli);
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gsl_linalg_LU_decomp(schlaefliLU, p, &s);
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gsl_linalg_LU_solve(schlaefliLU, p, diagonal, result);
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gsl_permutation_free(p);
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gsl_vector_free(diagonal);
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gsl_matrix_free(schlaefliLU);
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}
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void generate_coxeter_graph(semisimple_type_t type, int *result)
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{
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int rank = coxeter_rank(type);
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int order = coxeter_order(type);
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int element_count;
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gsl_matrix *schlaefliMatrix = gsl_matrix_alloc(rank, rank);
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gsl_vector *startingVector = gsl_vector_alloc(rank);
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gsl_matrix *generators = (gsl_matrix*)malloc(rank*sizeof(gsl_matrix));
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double *generators_data = (double*)malloc(rank*rank*rank*sizeof(double));
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gsl_matrix *elements = (gsl_matrix*)malloc(order*sizeof(gsl_matrix));
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double *elements_data = (double*)malloc(rank*rank*order*sizeof(double));
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gsl_matrix *inverses = (gsl_matrix*)malloc(order*sizeof(gsl_matrix));
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double *inverses_data = (double*)malloc(rank*rank*order*sizeof(double));
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gsl_vector *i1 = gsl_vector_alloc(rank);
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gsl_vector *i2 = gsl_vector_alloc(rank);
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gsl_matrix *current_element = gsl_matrix_alloc(rank, rank);
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queue_t queue;
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int current;
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for(int i = 0; i < rank; i++)
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generators[i] = gsl_matrix_view_array(generators_data + i*rank*rank, rank, rank).matrix;
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for(int i = 0; i < order; i++)
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elements[i] = gsl_matrix_view_array(elements_data + i*rank*rank, rank, rank).matrix;
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for(int i = 0; i < order; i++)
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inverses[i] = gsl_matrix_view_array(inverses_data + i*rank*rank, rank, rank).matrix;
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generate_schlaefli_matrix(type, schlaefliMatrix);
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generate_starting_vector(rank, schlaefliMatrix, startingVector);
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for(int i = 0; i < rank; i++) {
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gsl_matrix_set_identity(&generators[i]);
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for(int j = 0; j < rank; j++)
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if(i == j)
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gsl_matrix_set(&generators[i], i, j, -1.0);
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else
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gsl_matrix_set(&generators[i], i, j, -gsl_matrix_get(schlaefliMatrix, i, j));
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// gsl_matrix_fprintf(stdout, &generators[i], "%f");
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// printf("\n");
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}
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queue_init(&queue);
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queue_put(&queue, 0);
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element_count = 1;
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gsl_matrix_set_identity(&elements[0]);
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gsl_matrix_set_identity(&inverses[0]);
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while((current = queue_get(&queue)) != -1) {
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for(int i = 0; i < rank; i++) {
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int j;
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for(j = 0; j < element_count; j++) {
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if(check_equal_sector(&generators[i], &elements[current], &inverses[j], schlaefliMatrix, startingVector, i1, i2)) { // generators[i] * elements[current] = elements[j]
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result[rank*current + i] = j;
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break;
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}
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}
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// if no existing element equals generators[i] * elements[current], create one
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if(j == element_count) {
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ERROR(element_count >= order, "Got more elements than the order of the group should be!\n");
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &generators[i], &elements[current], 0.0, &elements[element_count]);
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invert(&elements[element_count], &inverses[element_count]);
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result[rank*current + i] = element_count;
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queue_put(&queue, element_count);
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element_count++;
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}
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}
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}
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ERROR(element_count != order, "Something went wrong building the Coxeter group. Found %d elements, %d expected\n", element_count, order);
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/*
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for(int i = 0; i < order; i++) {
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printf("%d: ", i);
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for(int j = 0; j < rank; j++)
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printf("%d ", result[rank*i + j]);
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printf("\n");
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}
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*/
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gsl_vector_free(startingVector);
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gsl_vector_free(i1);
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gsl_vector_free(i2);
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|
||||||
gsl_matrix_free(schlaefliMatrix);
|
|
||||||
gsl_matrix_free(current_element);
|
|
||||||
free(generators);
|
|
||||||
free(elements);
|
|
||||||
free(generators_data);
|
|
||||||
free(elements_data);
|
|
||||||
}
|
|
||||||
@ -1,20 +0,0 @@
|
|||||||
#ifndef COXETER_H
|
|
||||||
#define COXETER_H
|
|
||||||
|
|
||||||
typedef struct {
|
|
||||||
char series;
|
|
||||||
int rank;
|
|
||||||
} simple_type_t;
|
|
||||||
|
|
||||||
typedef struct {
|
|
||||||
int n;
|
|
||||||
simple_type_t *factors;
|
|
||||||
} semisimple_type_t;
|
|
||||||
|
|
||||||
void generate_coxeter_graph(semisimple_type_t type, int *result);
|
|
||||||
int coxeter_order(semisimple_type_t type);
|
|
||||||
int coxeter_hyperplanes(semisimple_type_t type);
|
|
||||||
int coxeter_rank(semisimple_type_t type);
|
|
||||||
unsigned long opposition_involution(semisimple_type_t type, unsigned long theta);
|
|
||||||
|
|
||||||
#endif
|
|
||||||
@ -1,193 +0,0 @@
|
|||||||
#include <stdio.h>
|
|
||||||
#include <string.h>
|
|
||||||
#include <sys/stat.h>
|
|
||||||
|
|
||||||
#include "thickenings.h"
|
|
||||||
#include "coxeter.h"
|
|
||||||
#include "queue.h"
|
|
||||||
|
|
||||||
#define SWAP(t, a, b) do {t tmp = a; a = b; b = tmp;} while(0)
|
|
||||||
|
|
||||||
char *stringify_SLn1_permutation(int *word, int wordlength, int rank, char *str)
|
|
||||||
{
|
|
||||||
for(int i = 0; i <= rank; i++)
|
|
||||||
str[i] = '1' + i;
|
|
||||||
str[rank+1] = 0;
|
|
||||||
|
|
||||||
for(int i = 0; i < wordlength; i++) {
|
|
||||||
char tmp = str[word[i]];
|
|
||||||
str[word[i]] = str[word[i]+1];
|
|
||||||
str[word[i]+1] = tmp;
|
|
||||||
}
|
|
||||||
return str;
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
char *stringify_Onn1_permutation(int *word, int wordlength, int rank, char *str)
|
|
||||||
{
|
|
||||||
for(int i = 0; i <= rank*2; i++)
|
|
||||||
str[i] = '1' + i;
|
|
||||||
str[2*rank+1] = 0;
|
|
||||||
|
|
||||||
for(int i = 0; i < wordlength; i++) {
|
|
||||||
if(word[i] == 0)
|
|
||||||
SWAP(char, str[rank-1], str[rank+1]);
|
|
||||||
else {
|
|
||||||
SWAP(char, str[rank-word[i]], str[rank-word[i]-1]);
|
|
||||||
SWAP(char, str[rank+word[i]], str[rank+word[i]+1]);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
return str;
|
|
||||||
}
|
|
||||||
|
|
||||||
int main(int argc, const char *argv[])
|
|
||||||
{
|
|
||||||
FILE *infile;
|
|
||||||
struct stat st;
|
|
||||||
int rank, order, hyperplanes;
|
|
||||||
semisimple_type_t type;
|
|
||||||
int n;
|
|
||||||
signed char *level;
|
|
||||||
node_t *graph;
|
|
||||||
int *left, *right;
|
|
||||||
int left_invariant, right_invariant;
|
|
||||||
int left_invariant_wanted = 0, right_invariant_wanted = 0;
|
|
||||||
|
|
||||||
unsigned long left_invariance, right_invariance;
|
|
||||||
edgelist_t *edgelists;
|
|
||||||
int *words;
|
|
||||||
|
|
||||||
queue_t queue;
|
|
||||||
int current;
|
|
||||||
int *seen;
|
|
||||||
int *generators;
|
|
||||||
int ngens;
|
|
||||||
|
|
||||||
char string_buffer1[1000];
|
|
||||||
const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
|
|
||||||
|
|
||||||
// parse arguments
|
|
||||||
|
|
||||||
if(argc < 2)
|
|
||||||
infile = stdin;
|
|
||||||
else {
|
|
||||||
if(strcmp(argv[1], "-") == 0)
|
|
||||||
infile = stdin;
|
|
||||||
else
|
|
||||||
infile = fopen(argv[1], "rb");
|
|
||||||
|
|
||||||
if(argc >= 4) {
|
|
||||||
if(strcmp(argv[2], "-") != 0)
|
|
||||||
for(int i = 0; i < strlen(argv[2]); i++)
|
|
||||||
left_invariant_wanted |= (1 << (argv[2][i] - 'a'));
|
|
||||||
if(strcmp(argv[3], "-") != 0)
|
|
||||||
for(int i = 0; i < strlen(argv[3]); i++)
|
|
||||||
right_invariant_wanted |= (1 << (argv[3][i] - 'a'));
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
fread(&type.n, sizeof(int), 1, infile); // we completely trust the input data
|
|
||||||
type.factors = malloc(type.n * sizeof(simple_type_t));
|
|
||||||
fread(type.factors, sizeof(simple_type_t), type.n, infile);
|
|
||||||
fread(&left_invariance, sizeof(simple_type_t), type.n, infile);
|
|
||||||
fread(&right_invariance, sizeof(simple_type_t), type.n, infile);
|
|
||||||
|
|
||||||
// get graph
|
|
||||||
|
|
||||||
rank = coxeter_rank(type);
|
|
||||||
order = coxeter_order(type);
|
|
||||||
hyperplanes = coxeter_hyperplanes(type);
|
|
||||||
ERROR(strlen(alphabet) < rank, "The alphabet has too few letters\n");
|
|
||||||
seen = (int*)malloc(order*sizeof(int));
|
|
||||||
generators = (int*)malloc(order*sizeof(int));
|
|
||||||
level = (signed char*)malloc(order*sizeof(int));
|
|
||||||
|
|
||||||
graph = graph_alloc(type);
|
|
||||||
prepare_graph(type, graph);
|
|
||||||
|
|
||||||
// finally do stuff
|
|
||||||
|
|
||||||
int counter = 0;
|
|
||||||
|
|
||||||
while(fread(level, sizeof(signed char), order, infile) == order) {
|
|
||||||
|
|
||||||
/*
|
|
||||||
if((counter++) % 100000 == 0)
|
|
||||||
print_thickening(rank, order, level, 0, 0, 0, alphabet, stdout);
|
|
||||||
continue;
|
|
||||||
*/
|
|
||||||
|
|
||||||
left_invariant = right_invariant = -1; // all 1s
|
|
||||||
for(int j = 0; j < order; j++) {
|
|
||||||
for(int k = 0; k < rank; k++) {
|
|
||||||
if(level[j] > 0 && level[graph[j].left[k]] < 0 || level[j] < 0 && level[graph[j].left[k]] > 0) {
|
|
||||||
left_invariant &= ~(1 << k);
|
|
||||||
}
|
|
||||||
if(level[j] > 0 && level[graph[j].right[k]] < 0 || level[j] < 0 && level[graph[j].right[k]] > 0) {
|
|
||||||
right_invariant &= ~(1 << k);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
if((~left_invariant & left_invariant_wanted) == 0 && (~right_invariant & right_invariant_wanted) == 0) {
|
|
||||||
ngens = 0;
|
|
||||||
memset(generators, 0, order*sizeof(int));
|
|
||||||
for(int j = 0; j < order; j++) {
|
|
||||||
if(level[j] == HEAD_MARKER && generators[j] == 0) { // ignore the generator, if it is equivalent to one already seen
|
|
||||||
ngens++;
|
|
||||||
queue_init(&queue);
|
|
||||||
queue_put(&queue, j);
|
|
||||||
while((current = queue_get(&queue)) != -1) {
|
|
||||||
if(generators[current] == 0) { // visit everyone only once
|
|
||||||
generators[current] = ngens;
|
|
||||||
for(int k = 0; k < rank; k++) {
|
|
||||||
if(left_invariant & (1 << k))
|
|
||||||
queue_put(&queue, graph[current].left[k]);
|
|
||||||
if(right_invariant & (1 << k))
|
|
||||||
queue_put(&queue, graph[current].right[k]);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
printf("left: ");
|
|
||||||
for(int j = 0; j < rank; j++)
|
|
||||||
printf("%c", left_invariant & (1 << j) ? alphabet[j] : ' ');
|
|
||||||
printf(" right: ");
|
|
||||||
for(int j = 0; j < rank; j++)
|
|
||||||
printf("%c", right_invariant & (1 << j) ? alphabet[j] : ' ');
|
|
||||||
printf(" generators: ");
|
|
||||||
|
|
||||||
memset(seen, 0, order*sizeof(int));
|
|
||||||
for(int i = 0; i < order; i++) {
|
|
||||||
if(generators[i] != 0 && seen[generators[i]-1] == 0) {
|
|
||||||
seen[generators[i]-1] = 1;
|
|
||||||
// if(type.n == 1 && type.factors[0].series == 'A')
|
|
||||||
// printf("%s ", stringify_SLn1_permutation(graph[i].word, graph[i].wordlength, rank, string_buffer1));
|
|
||||||
// else if(type.n == 1 && (type.factors[0].series == 'B' || type.factors[0].series == 'C'))
|
|
||||||
// printf("%s ", stringify_Onn1_permutation(graph[i].word, graph[i].wordlength, rank, string_buffer1));
|
|
||||||
// else
|
|
||||||
if(i == 0)
|
|
||||||
printf("1 ");
|
|
||||||
else
|
|
||||||
printf("%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
printf("\n");
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
if(infile != stdin)
|
|
||||||
fclose(infile);
|
|
||||||
|
|
||||||
// cleanup
|
|
||||||
|
|
||||||
graph_free(type, graph);
|
|
||||||
free(seen);
|
|
||||||
free(generators);
|
|
||||||
free(type.factors);
|
|
||||||
|
|
||||||
return 0;
|
|
||||||
}
|
|
||||||
189
old/process.c
189
old/process.c
@ -1,189 +0,0 @@
|
|||||||
#include <stdio.h>
|
|
||||||
#include <string.h>
|
|
||||||
#include <sys/stat.h>
|
|
||||||
|
|
||||||
#include "thickenings.h"
|
|
||||||
#include "weyl.h"
|
|
||||||
#include "queue.h"
|
|
||||||
|
|
||||||
int main(int argc, const char *argv[])
|
|
||||||
{
|
|
||||||
FILE *infile;
|
|
||||||
semisimple_type_t type;
|
|
||||||
unsigned long left_invariance, right_invariance; // these are the invariances we have already modded out
|
|
||||||
unsigned long left_invariant, right_invariant; // these are the invariances of the thickening under consideration
|
|
||||||
int rank, cosets;
|
|
||||||
node_t *graph;
|
|
||||||
signed char *thickening;
|
|
||||||
int *seen, *generators;
|
|
||||||
queue_t queue;
|
|
||||||
int ngenerators;
|
|
||||||
int current;
|
|
||||||
|
|
||||||
char string_buffer1[1000];
|
|
||||||
const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
|
|
||||||
|
|
||||||
if(argc < 2)
|
|
||||||
infile = stdin;
|
|
||||||
else
|
|
||||||
infile = fopen(argv[1], "rb");
|
|
||||||
|
|
||||||
// we completely trust the input data
|
|
||||||
ERROR(fread(&type.n, sizeof(int), 1, infile) == 0, "The input file seems to be empty!\n");
|
|
||||||
type.factors = malloc(type.n * sizeof(simple_type_t));
|
|
||||||
fread(type.factors, sizeof(simple_type_t), type.n, infile);
|
|
||||||
fread(&left_invariance, sizeof(simple_type_t), type.n, infile);
|
|
||||||
fread(&right_invariance, sizeof(simple_type_t), type.n, infile);
|
|
||||||
|
|
||||||
rank = weyl_rank(type);
|
|
||||||
graph = graph_alloc(type);
|
|
||||||
cosets = prepare_simplified_graph(type, left_invariance, right_invariance, graph);
|
|
||||||
|
|
||||||
thickening = (signed char*)malloc(cosets*sizeof(signed char));
|
|
||||||
generators = (int*)malloc(cosets*sizeof(int));
|
|
||||||
seen = (int*)malloc(cosets*sizeof(int));
|
|
||||||
|
|
||||||
while(fread(thickening, sizeof(signed char), cosets, infile) == cosets) {
|
|
||||||
|
|
||||||
// determine invariances of this thickening
|
|
||||||
left_invariant = right_invariant = -1; // set all bits to 1
|
|
||||||
for(int j = 0; j < cosets; j++) {
|
|
||||||
for(int k = 0; k < rank; k++) {
|
|
||||||
if(thickening[j] > 0 && thickening[graph[j].left[k]] < 0 ||
|
|
||||||
thickening[j] < 0 && thickening[graph[j].left[k]] > 0)
|
|
||||||
left_invariant &= ~(1 << k);
|
|
||||||
if(thickening[j] > 0 && thickening[graph[j].right[k]] < 0 ||
|
|
||||||
thickening[j] < 0 && thickening[graph[j].right[k]] > 0)
|
|
||||||
right_invariant &= ~(1 << k);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
// print this stuff
|
|
||||||
printf("left: ");
|
|
||||||
for(int j = 0; j < rank; j++)
|
|
||||||
printf("%c", left_invariant & (1 << j) ? alphabet[j] : ' ');
|
|
||||||
printf(" right: ");
|
|
||||||
for(int j = 0; j < rank; j++)
|
|
||||||
printf("%c", right_invariant & (1 << j) ? alphabet[j] : ' ');
|
|
||||||
printf(" generators: ");
|
|
||||||
|
|
||||||
// find a minimal set of weyl group elements such that the union of the ideals generated by their cosets wrt the invariances determined above gives the thickening
|
|
||||||
// in the first step, mark everything which is equivalent to a "head" by a generator id
|
|
||||||
ngenerators = 0;
|
|
||||||
memset(generators, 0, cosets*sizeof(int));
|
|
||||||
for(int j = 0; j < cosets; j++) {
|
|
||||||
if(thickening[j] == HEAD_MARKER && generators[j] == 0) { // ignore the generator, if it is equivalent to one already seen
|
|
||||||
ngenerators++;
|
|
||||||
queue_init(&queue);
|
|
||||||
queue_put(&queue, j);
|
|
||||||
while((current = queue_get(&queue)) != -1) {
|
|
||||||
if(generators[current] == 0) { // visit everyone only once
|
|
||||||
generators[current] = ngenerators;
|
|
||||||
for(int k = 0; k < rank; k++) {
|
|
||||||
if(left_invariant & (1 << k))
|
|
||||||
queue_put(&queue, graph[current].left[k]);
|
|
||||||
if(right_invariant & (1 << k))
|
|
||||||
queue_put(&queue, graph[current].right[k]);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
// in the second step, go through the list in ascending word length order and print the first appearance of each generator id
|
|
||||||
memset(seen, 0, cosets*sizeof(int));
|
|
||||||
for(int i = 0; i < cosets; i++) {
|
|
||||||
if(generators[i] != 0 && seen[generators[i]-1] == 0) {
|
|
||||||
seen[generators[i]-1] = 1;
|
|
||||||
printf("%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
printf("\n");
|
|
||||||
}
|
|
||||||
|
|
||||||
if(infile != stdin)
|
|
||||||
fclose(infile);
|
|
||||||
|
|
||||||
graph_free(type, graph);
|
|
||||||
free(type.factors);
|
|
||||||
free(thickening);
|
|
||||||
}
|
|
||||||
/*******************************************************************************************
|
|
||||||
|
|
||||||
seen = (int*)malloc(order*sizeof(int));
|
|
||||||
generators = (int*)malloc(order*sizeof(int));
|
|
||||||
level = (signed char*)malloc(order*sizeof(int));
|
|
||||||
|
|
||||||
graph = graph_alloc(type);
|
|
||||||
prepare_graph(type, graph);
|
|
||||||
|
|
||||||
// finally do stuff
|
|
||||||
|
|
||||||
int counter = 0;
|
|
||||||
|
|
||||||
while(fread(level, sizeof(signed char), order, infile) == order) {
|
|
||||||
|
|
||||||
if((~left_invariant & left_invariant_wanted) == 0 && (~right_invariant & right_invariant_wanted) == 0) {
|
|
||||||
ngens = 0;
|
|
||||||
memset(generators, 0, order*sizeof(int));
|
|
||||||
for(int j = 0; j < order; j++) {
|
|
||||||
if(level[j] == HEAD_MARKER && generators[j] == 0) { // ignore the generator, if it is equivalent to one already seen
|
|
||||||
ngens++;
|
|
||||||
queue_init(&queue);
|
|
||||||
queue_put(&queue, j);
|
|
||||||
while((current = queue_get(&queue)) != -1) {
|
|
||||||
if(generators[current] == 0) { // visit everyone only once
|
|
||||||
generators[current] = ngens;
|
|
||||||
for(int k = 0; k < rank; k++) {
|
|
||||||
if(left_invariant & (1 << k))
|
|
||||||
queue_put(&queue, graph[current].left[k]);
|
|
||||||
if(right_invariant & (1 << k))
|
|
||||||
queue_put(&queue, graph[current].right[k]);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
printf("left: ");
|
|
||||||
for(int j = 0; j < rank; j++)
|
|
||||||
printf("%c", left_invariant & (1 << j) ? alphabet[j] : ' ');
|
|
||||||
printf(" right: ");
|
|
||||||
for(int j = 0; j < rank; j++)
|
|
||||||
printf("%c", right_invariant & (1 << j) ? alphabet[j] : ' ');
|
|
||||||
printf(" generators: ");
|
|
||||||
|
|
||||||
memset(seen, 0, order*sizeof(int));
|
|
||||||
for(int i = 0; i < order; i++) {
|
|
||||||
if(generators[i] != 0 && seen[generators[i]-1] == 0) {
|
|
||||||
seen[generators[i]-1] = 1;
|
|
||||||
// if(type.n == 1 && type.factors[0].series == 'A')
|
|
||||||
// printf("%s ", stringify_SLn1_permutation(graph[i].word, graph[i].wordlength, rank, string_buffer1));
|
|
||||||
// else if(type.n == 1 && (type.factors[0].series == 'B' || type.factors[0].series == 'C'))
|
|
||||||
// printf("%s ", stringify_Onn1_permutation(graph[i].word, graph[i].wordlength, rank, string_buffer1));
|
|
||||||
// else
|
|
||||||
if(i == 0)
|
|
||||||
printf("1 ");
|
|
||||||
else
|
|
||||||
printf("%s ", alphabetize(graph[i].word, graph[i].wordlength, alphabet, string_buffer1));
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
printf("\n");
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
if(infile != stdin)
|
|
||||||
fclose(infile);
|
|
||||||
|
|
||||||
// cleanup
|
|
||||||
|
|
||||||
graph_free(type, graph);
|
|
||||||
free(seen);
|
|
||||||
free(generators);
|
|
||||||
free(type.factors);
|
|
||||||
|
|
||||||
return 0;
|
|
||||||
}
|
|
||||||
*/
|
|
||||||
41
old/test.c
41
old/test.c
@ -1,41 +0,0 @@
|
|||||||
#include <stdio.h>
|
|
||||||
|
|
||||||
#include "weyl.h"
|
|
||||||
|
|
||||||
static void print_element(weylgroup_element_t *e)
|
|
||||||
{
|
|
||||||
if(e->wordlength == 0)
|
|
||||||
printf("1");
|
|
||||||
else
|
|
||||||
for(int j = 0; j < e->wordlength; j++)
|
|
||||||
printf("%c", e->word[j] + 'a');
|
|
||||||
}
|
|
||||||
|
|
||||||
int main()
|
|
||||||
{
|
|
||||||
semisimple_type_t type;
|
|
||||||
simple_type_t t;
|
|
||||||
type.n = 1;
|
|
||||||
type.factors = &t;
|
|
||||||
t.series = 'A';
|
|
||||||
t.rank = 3;
|
|
||||||
|
|
||||||
int order = weyl_order(type);
|
|
||||||
doublequotient_t *dq = weyl_generate_bruhat(type, 0x02, 0x03);
|
|
||||||
|
|
||||||
for(int i = 0; i < dq->count; i++) {
|
|
||||||
print_element(dq->cosets[i].min);
|
|
||||||
printf(" -> ");
|
|
||||||
for(doublecoset_list_t *current = dq->cosets[i].bruhat_lower; current; current = current->next) {
|
|
||||||
print_element(current->to->min);
|
|
||||||
printf(" ");
|
|
||||||
}
|
|
||||||
printf("| ");
|
|
||||||
print_element(dq->cosets[i].opposite->min);
|
|
||||||
printf("\n");
|
|
||||||
}
|
|
||||||
|
|
||||||
weyl_destroy_bruhat(dq);
|
|
||||||
|
|
||||||
return 0;
|
|
||||||
}
|
|
||||||
Loading…
Reference in New Issue
Block a user