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long-reid-thistlethwaite groups with rationals

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This commit is contained in:
Florian Stecker 2020-07-06 10:23:14 -05:00
parent c566a8741e
commit b7c7d7245c
2 changed files with 174 additions and 91 deletions
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177
singular_values.c
View File

@ -9,7 +9,33 @@
#define MAX_ELEMENTS 14000 #define MAX_ELEMENTS 14000
//#define DRAW_PICTURE 1 //#define DRAW_PICTURE 1
void mpq_quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e) void continued_fraction_approximation(mpq_t out, double in, int level)
{
mpq_t tmp;
if(in < 0) {
mpq_init(tmp);
mpq_set_ui(tmp, 0, 1);
continued_fraction_approximation(out, -in, level);
mpq_sub(out, tmp, out);
mpq_clear(tmp);
return;
}
if(level == 0) {
mpq_set_si(out, (signed long int)round(in), 1); // floor(in)
} else {
continued_fraction_approximation(out, 1/(in - floor(in)), level - 1);
mpq_init(tmp);
mpq_set_ui(tmp, 1, 1);
mpq_div(out, tmp, out); // out -> 1/out
mpq_set_si(tmp, (signed long int)in, 1); // floor(in)
mpq_add(out, out, tmp);
mpq_clear(tmp);
}
}
void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
{ {
mpq_t tmp; mpq_t tmp;
mpq_init(tmp); mpq_init(tmp);
@ -46,12 +72,12 @@ void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t s, mpq_t
mpq_set_ui(*mat_ref(gen[1], 0, 0), 1, 1); mpq_set_ui(*mat_ref(gen[1], 0, 0), 1, 1);
mpq_set_ui(*mat_ref(gen[1], 1, 0), 0, 1); mpq_set_ui(*mat_ref(gen[1], 1, 0), 0, 1);
mpq_set_ui(*mat_ref(gen[1], 2, 0), 0, 1); mpq_set_ui(*mat_ref(gen[1], 2, 0), 0, 1);
mpq_quartic(*mat_ref(gen[1], 0, 1), t, 0, 0, 1, -1, 2); quartic(*mat_ref(gen[1], 0, 1), t, 0, 0, 1, -1, 2);
mpq_quartic(*mat_ref(gen[1], 1, 1), t, 0, 0, -1, 2, -2); quartic(*mat_ref(gen[1], 1, 1), t, 0, 0, -1, 2, -2);
mpq_quartic(*mat_ref(gen[1], 2, 1), t, 0, 0, 1, -3, 3); quartic(*mat_ref(gen[1], 2, 1), t, 0, 0, 1, -3, 3);
mpq_quartic(*mat_ref(gen[1], 0, 2), t, 0, 0, 1, 0, 3); quartic(*mat_ref(gen[1], 0, 2), t, 0, 0, 1, 0, 3);
mpq_quartic(*mat_ref(gen[1], 1, 2), t, 0, 0, -1, 1, -1); quartic(*mat_ref(gen[1], 1, 2), t, 0, 0, -1, 1, -1);
mpq_quartic(*mat_ref(gen[1], 2, 2), t, 0, 0, 1, -2, 1); quartic(*mat_ref(gen[1], 2, 2), t, 0, 0, 1, -2, 1);
mat_pseudoinverse(ws, gen[3], gen[0]); // p^{-1} mat_pseudoinverse(ws, gen[3], gen[0]); // p^{-1}
mat_pseudoinverse(ws, gen[4], gen[1]); // q^{-1} mat_pseudoinverse(ws, gen[4], gen[1]); // q^{-1}
@ -79,37 +105,19 @@ char *print_word(groupelement_t *g, char *str)
return str; return str;
} }
int main(int argc, char *argv[]) void enumerate(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t)
{ {
groupelement_t *group;
mat_workspace *ws; mat_workspace *ws;
mat *matrices;
mat tmp; mat tmp;
mat gen[6]; mat gen[6];
char buf[100], buf2[100], buf3[100]; char buf[100], buf2[100], buf3[100];
mpq_t s,t;
mpq_t det, tr, trinv;
// allocate stuff // allocate stuff
group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
ws = mat_workspace_init(3); ws = mat_workspace_init(3);
matrices = malloc(MAX_ELEMENTS*sizeof(mat));
for(int i = 0; i < MAX_ELEMENTS; i++)
mat_init(matrices[i], 3);
for(int i = 0; i < 6; i++) for(int i = 0; i < 6; i++)
mat_init(gen[i], 3); mat_init(gen[i], 3);
mat_init(tmp, 3); mat_init(tmp, 3);
mpq_inits(s, t, det, tr, trinv, NULL);
mpq_set_ui(s,1,1);
double t_ = atof(argv[1]);
mpq_set_ui(t,(int)(t_*100),100);
mpq_canonicalize(s);
mpq_canonicalize(t);
// the real action
generate_triangle_group(group, MAX_ELEMENTS, 3, 3, 4);
initialize_triangle_generators(ws, gen, s, t); initialize_triangle_generators(ws, gen, s, t);
mat_identity(matrices[0]); mat_identity(matrices[0]);
@ -139,35 +147,110 @@ int main(int argc, char *argv[])
mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]); mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
} }
// free stuff
for(int i = 0; i < 6; i++)
mat_clear(gen[i]);
mat_clear(tmp);
mat_workspace_clear(ws);
}
void output_invariants(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t)
{
mpq_t tr, trinv;
char buf[100];
mpq_inits(tr, trinv, NULL);
for(int i = 0; i < MAX_ELEMENTS; i++) { for(int i = 0; i < MAX_ELEMENTS; i++) {
if(group[i].length % 2 != 0) if(group[i].length % 2 != 0 || !group[i].inverse)
continue;
if(!group[i].inverse)
continue; continue;
mat_trace(tr, matrices[i]); mat_trace(tr, matrices[i]);
mat_trace(trinv, matrices[group[i].inverse->id]); mat_trace(trinv, matrices[group[i].inverse->id]);
double lambda1, lambda2, lambda3; gmp_printf("%d %d %s %Qd %Qd %f %f\n", i, group[i].length, print_word(&group[i], buf), tr, trinv, log(mpq_get_d(tr)), log(mpq_get_d(trinv)));
// int realevs = gsl_poly_solve_cubic(-mpq_get_d(tr), mpq_get_d(trinv), -1, &lambda3, &lambda2, &lambda1);
// if(realevs != 3)
// continue;
// if(lambda1 < 0 || lambda2 < 0 || lambda3 < 0)
// continue;
// gmp_printf("%d %d %s %Qd %Qd\n", i, group[i].length, print_word(&group[i], buf), tr, trinv);
printf("%d %d %s %f %f %f\n", i, group[i].length, print_word(&group[i], buf), log(mpq_get_d(tr)), log(mpq_get_d(trinv)));
} }
// free stuff mpq_clears(tr, trinv, NULL);
for(int i = 0; i < MAX_ELEMENTS; i++) }
mat_clear(matrices[i]);
for(int i = 0; i < 6; i++)
mat_clear(gen[i]);
mat_clear(tmp);
mpq_clears(s, t, det, tr, trinv, NULL);
mat_workspace_clear(ws);
double max_slope(groupelement_t *group, mat *matrices, mpq_t s, mpq_t t, int *index)
{
double max = 0;
double slope;
mpq_t tr, trinv;
char buf[100];
mpq_inits(tr, trinv, NULL);
for(int i = 0; i < MAX_ELEMENTS; i++) {
if(group[i].length % 2 != 0 || !group[i].inverse)
continue;
mat_trace(tr, matrices[i]);
mat_trace(trinv, matrices[group[i].inverse->id]);
slope = log(mpq_get_d(trinv))/log(mpq_get_d(tr));
if(slope > max)
{
*index = i;
max = slope;
}
}
mpq_clears(tr, trinv, NULL);
return max;
}
int main(int argc, char *argv[])
{
mpq_t s, t, tmp;
mpz_t accuracy;
double t_;
mat *matrices;
groupelement_t *group;
int index;
mpq_inits(s, t, tmp, NULL);
mpz_init(accuracy);
group = malloc(MAX_ELEMENTS*sizeof(groupelement_t));
matrices = malloc(MAX_ELEMENTS*sizeof(mat));
for(int i = 0; i < MAX_ELEMENTS; i++)
mat_init(matrices[i], 3);
// mpq_set_str(t, argv[1], 10);
mpz_set_ui(accuracy, 100);
for(int i = 0; ; i++) {
mpq_set(t, tmp);
continued_fraction_approximation(tmp, atof(argv[1]), i);
if(mpz_cmp(mpq_numref(tmp),accuracy) > 0 && mpz_cmp(mpq_denref(tmp),accuracy) > 0)
break;
}
mpq_canonicalize(t);
gmp_fprintf(stdout, "\"t = %Qd = %.3f\"\n", mpq_get_d(t), t);
if(argc > 2 && strcmp(argv[2],"p") == 0) {
gmp_fprintf(stdout, "%Qd\n", t);
return 0; return 0;
} }
generate_triangle_group(group, MAX_ELEMENTS, 3, 3, 4);
// for(int i = 0; i < 10; i++) {
// mpq_set_ui(t,100+i,100);
// mpq_canonicalize(t);
enumerate(group, matrices, s, t);
//printf("%f %f\n", mpq_get_d(t), max_slope(group, matrices, s, t, &index));
output_invariants(group, matrices, s, t);
// }
for(int i = 0; i < MAX_ELEMENTS; i++)
mat_clear(matrices[i]);
free(matrices);
free(group);
mpq_clears(s, t, tmp, NULL);
mpz_clear(accuracy);
}

4
singular_values.plt
View File

@ -3,7 +3,7 @@ if(!exists("logs")) logs = log(1.0)
file = sprintf("< ./singular_values %f", exp(logt)) file = sprintf("< ./singular_values %f", exp(logt))
#title = sprintf("s = %f, t = %f", exp(logs), exp(logt)) #title = sprintf("s = %f, t = %f", exp(logs), exp(logt))
title = sprintf("t = %.3f", floor(exp(logt)*100)/100.0) title = sprintf("t = %.3f", exp(logt))
# print title # print title
set zeroaxis set zeroaxis
@ -23,7 +23,7 @@ set parametric
tr(a,b) = exp(a) + exp(b-a) + exp(-b) tr(a,b) = exp(a) + exp(b-a) + exp(-b)
trinv(a,b) = exp(-a) + exp(a-b) + exp(b) trinv(a,b) = exp(-a) + exp(a-b) + exp(b)
plot file using 4:5 w p pt 7 ps 0.5 lc 1 t title, \ plot file using 6:7 w p pt 7 ps 0.5 lc 1 t columnheader, \
log(tr(t,t*2)),log(trinv(t,2*t)) w l lw 2 t "", \ log(tr(t,t*2)),log(trinv(t,2*t)) w l lw 2 t "", \
log(tr(t,t/2)),log(trinv(t,t/2)) w l lw 2 t "" log(tr(t,t/2)),log(trinv(t,t/2)) w l lw 2 t ""