missing files from previous commit + clean up of special_element program + billiard picture script
This commit is contained in:
Florian Stecker
20
billiard_picture.sh
Executable file
20
billiard_picture.sh
Executable file
@@ -0,0 +1,20 @@
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#!/bin/bash
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trap 'exit 130' INT
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wordlength=30
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sdenom=100
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sstart=1
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send=100
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qdenom=100
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qstart=1
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qend=100 # 1/sqrt(2) = 0.7071...
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words="$(./billiard_words $wordlength | awk '{print $1}')"
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for s in $(seq $sstart $send); do
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for q in $(seq $qstart $qend); do
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echo -n "$s/$sdenom $q/$qdenom "
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MAXIMUM=only ./special_element $s/$sdenom $q/$qdenom $words
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done
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done
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@@ -9,14 +9,23 @@ main = do
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listWordsUpToLength :: Int -> IO ()
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listWordsUpToLength n = do
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putStrLn $ unlines [printf "%s %d/%d %f" w (x `div` gcd x y) (y `div` gcd x y) (fromIntegral x / fromIntegral y :: Double) | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n, let x = 2*q + p, let y = 2*p + q]
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-- putStrLn $ unlines [printf "%d/%d\t%d/%d\t%.7f\t%d\t%s" p q (x `div` gcd x y) (y `div` gcd x y) (sqrt 3 / (1 + 2*fromIntegral q / fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n, let x = 2*q + p, let y = 2*p + q]
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-- putStrLn $ unlines [printf "%d/%d\t%.5f\t%.5f\t%d\t%s" p q (fromIntegral p / fromIntegral q :: Double) (sqrt 3 / (1 + 2*fromIntegral q / fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n]
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putStrLn $ unlines [printf "%s %d/%d %f"
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w
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(x `div` gcd x y)
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(y `div` gcd x y)
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(fromIntegral x / fromIntegral y :: Double) |
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((p,q),w) <- wordlist (n `div` 2) (n `div` 2),
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length w <= n,
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let x = 2*q + p,
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let y = 2*p + q]
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wordlist :: Int -> Int -> [((Int,Int),String)]
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wordlist pmax qmax = nub $ sortBy (comparing sl) [((p `div` gcd p q, q `div` gcd p q), slopeWord "bca" p q) | p <- [0..pmax], q <- [0..qmax], p /= 0 || q /= 0]
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wordlist pmax qmax = nub $
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sortBy (comparing sl)
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[((p `div` gcd p q, q `div` gcd p q), slopeWord "bca" p q) |
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p <- [0..pmax],
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q <- [0..qmax],
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q /= 0] -- use p /= 0 || q /= 0 for more symmetric output
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where
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sl ((p,q),_) = fromIntegral p / fromIntegral q
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254
enumerate_triangle_group.c
Normal file
254
enumerate_triangle_group.c
Normal file
@@ -0,0 +1,254 @@
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#include "enumerate_triangle_group.h"
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#include "linalg.h"
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int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues)
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{
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mpq_t coeff1, coeff2, zero;
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cplx_t *roots;
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double radii[3];
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double *radii_p[3];
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mps_monomial_poly *poly;
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mps_boolean errors;
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int result = 0;
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mpq_inits(coeff1, coeff2, zero, NULL);
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mpq_set(coeff1, trinv);
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mpq_sub(coeff2, zero, tr);
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poly = mps_monomial_poly_new(solv, 3);
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mps_monomial_poly_set_coefficient_int(solv, poly, 0, -1, 0);
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mps_monomial_poly_set_coefficient_q(solv, poly, 1, coeff1, zero);
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mps_monomial_poly_set_coefficient_q(solv, poly, 2, coeff2, zero);
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mps_monomial_poly_set_coefficient_int(solv, poly, 3, 1, 0);
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mps_context_set_input_poly(solv, (mps_polynomial*)poly);
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mps_mpsolve(solv);
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roots = cplx_valloc(3);
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for(int i = 0; i < 3; i++)
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radii_p[i] = &(radii[i]);
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mps_context_get_roots_d(solv, &roots, radii_p);
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errors = mps_context_has_errors(solv);
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if(errors) {
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result = 1;
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} else {
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for(int i = 0; i < 3; i++) {
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eigenvalues[i] = cplx_Re(roots[i]);
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if(fabs(cplx_Im(roots[i])) > radii[i]) // non-real root
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result = 2;
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}
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}
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cplx_vfree(roots);
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mpq_clears(coeff1, coeff2, zero, NULL);
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return result;
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}
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void continued_fraction_approximation(mpq_t out, double in, int level)
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{
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mpq_t tmp;
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if(in < 0) {
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mpq_init(tmp);
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mpq_set_ui(tmp, 0, 1);
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continued_fraction_approximation(out, -in, level);
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mpq_sub(out, tmp, out);
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mpq_clear(tmp);
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return;
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}
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if(level == 0) {
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mpq_set_si(out, (signed long int)round(in), 1); // floor(in)
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} else {
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continued_fraction_approximation(out, 1/(in - floor(in)), level - 1);
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mpq_init(tmp);
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mpq_set_ui(tmp, 1, 1);
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mpq_div(out, tmp, out); // out -> 1/out
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mpq_set_si(tmp, (signed long int)in, 1); // floor(in)
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mpq_add(out, out, tmp);
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mpq_clear(tmp);
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}
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}
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void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
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{
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mpq_t tmp;
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mpq_init(tmp);
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mpq_set_si(out, a, 1);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, b, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, c, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, d, 1);
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mpq_add(out, out, tmp);
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mpq_mul(out, out, in);
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mpq_set_si(tmp, e, 1);
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mpq_add(out, out, tmp);
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mpq_clear(tmp);
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}
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// p1,p2,p3 are only allowed to be 2,3,4,6
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void initialize_triangle_generators(mat_workspace *ws, mat *gen, int p1, int p2, int p3, mpq_t s, mpq_t q)
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{
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mat r1,r2,r3;
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mpq_t rho1, rho2, rho3;
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mpq_t b1,c1,a2,c2,a3,b3;
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mpq_t sinv;
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mpq_inits(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
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mat_init(r1, 3);
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mat_init(r2, 3);
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mat_init(r3, 3);
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mpq_set_ui(sinv, 1, 1);
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mpq_div(sinv, sinv, s);
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// coefficient 2 is the value for p=infinity, not sure if that would even work
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quartic(rho1, s, 0, 0, 1, p1 == 2 ? -2 : p1 == 3 ? -1 : p1 == 4 ? 0 : p1 == 6 ? 1 : 2, 1);
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quartic(rho2, s, 0, 0, 1, p2 == 2 ? -2 : p2 == 3 ? -1 : p2 == 4 ? 0 : p2 == 6 ? 1 : 2, 1);
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quartic(rho3, s, 0, 0, 1, p3 == 2 ? -2 : p3 == 3 ? -1 : p3 == 4 ? 0 : p3 == 6 ? 1 : 2, 1);
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mpq_mul(c1, rho2, q);
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mpq_mul(a2, rho3, q);
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mpq_mul(b3, rho1, q);
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mpq_set_ui(b1, 1, 1);
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mpq_set_ui(c2, 1, 1);
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mpq_set_ui(a3, 1, 1);
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mpq_div(b1, b1, q);
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mpq_div(c2, c2, q);
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mpq_div(a3, a3, q);
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// actually, we want minus everything
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mat_zero(r1);
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mat_zero(r2);
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mat_zero(r3);
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mpq_set_si(*mat_ref(r1, 0, 0), -1, 1);
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mpq_set_si(*mat_ref(r1, 1, 1), 1, 1);
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mpq_set_si(*mat_ref(r1, 2, 2), 1, 1);
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mpq_set_si(*mat_ref(r2, 0, 0), 1, 1);
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mpq_set_si(*mat_ref(r2, 1, 1), -1, 1);
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mpq_set_si(*mat_ref(r2, 2, 2), 1, 1);
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mpq_set_si(*mat_ref(r3, 0, 0), 1, 1);
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mpq_set_si(*mat_ref(r3, 1, 1), 1, 1);
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mpq_set_si(*mat_ref(r3, 2, 2), -1, 1);
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mpq_set(*mat_ref(r1, 1, 0), b1);
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mpq_set(*mat_ref(r1, 2, 0), c1);
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mpq_set(*mat_ref(r2, 0, 1), a2);
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mpq_set(*mat_ref(r2, 2, 1), c2);
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mpq_set(*mat_ref(r3, 0, 2), a3);
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mpq_set(*mat_ref(r3, 1, 2), b3);
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mat_zero(gen[0]);
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mat_zero(gen[1]);
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mat_zero(gen[2]);
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mpq_set_ui(*mat_ref(gen[0], 0, 0), 1, 1);
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mat_set(gen[0], 1, 1, sinv);
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mat_set(gen[0], 2, 2, s);
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mat_set(gen[1], 0, 0, s);
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mpq_set_ui(*mat_ref(gen[1], 1, 1), 1, 1);
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mat_set(gen[1], 2, 2, sinv);
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mat_set(gen[2], 0, 0, sinv);
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mat_set(gen[2], 1, 1, s);
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mpq_set_ui(*mat_ref(gen[2], 2, 2), 1, 1);
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mat_multiply(ws, gen[0], r2, gen[0]);
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mat_multiply(ws, gen[0], gen[0], r3);
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mat_multiply(ws, gen[1], r3, gen[1]);
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mat_multiply(ws, gen[1], gen[1], r1);
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mat_multiply(ws, gen[2], r1, gen[2]);
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mat_multiply(ws, gen[2], gen[2], r2);
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mat_pseudoinverse(ws, gen[3], gen[0]);
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mat_pseudoinverse(ws, gen[4], gen[1]);
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mat_pseudoinverse(ws, gen[5], gen[2]);
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/*
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mat_print(r1);
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mat_print(r2);
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mat_print(r3);
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mat_print(gen[0]);
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mat_print(gen[1]);
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mat_print(gen[2]);
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mat_print(gen[3]);
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mat_print(gen[4]);
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mat_print(gen[5]);
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*/
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mpq_clears(sinv,rho1,rho2,rho3,b1,c1,a2,c2,a3,b3,NULL);
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mat_clear(r1);
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mat_clear(r2);
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mat_clear(r3);
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}
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char *print_word(groupelement_t *g, char *str)
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{
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int i = g->length - 1;
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str[g->length] = 0;
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while(g->parent) {
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str[i--] = 'a' + g->letter;
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g = g->parent;
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}
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return str;
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}
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void enumerate(group_t *group, mat *matrices, int p1, int p2, int p3, mpq_t s, mpq_t t)
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{
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mat_workspace *ws;
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mat tmp;
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mat gen[6];
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char buf[100], buf2[100], buf3[100];
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// allocate stuff
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ws = mat_workspace_init(3);
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for(int i = 0; i < 6; i++)
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mat_init(gen[i], 3);
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mat_init(tmp, 3);
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initialize_triangle_generators(ws, gen, p1, p2, p3, s, t);
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mat_identity(matrices[0]);
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for(int i = 1; i < group->size; i++) {
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if(group->elements[i].length % 2 != 0)
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continue;
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if(!group->elements[i].inverse)
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continue;
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int parent = group->elements[i].parent->id;
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int grandparent = group->elements[i].parent->parent->id;
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int letter;
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if(group->elements[parent].letter == 1 && group->elements[i].letter == 2)
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letter = 0; // p = bc
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else if(group->elements[parent].letter == 2 && group->elements[i].letter == 0)
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letter = 1; // q = ca
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else if(group->elements[parent].letter == 0 && group->elements[i].letter == 1)
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letter = 2; // r = ab
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if(group->elements[parent].letter == 2 && group->elements[i].letter == 1)
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letter = 3; // p^{-1} = cb
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else if(group->elements[parent].letter == 0 && group->elements[i].letter == 2)
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letter = 4; // q^{-1} = ac
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else if(group->elements[parent].letter == 1 && group->elements[i].letter == 0)
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letter = 5; // r^{-1} = ba
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mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
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}
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// free stuff
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for(int i = 0; i < 6; i++)
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mat_clear(gen[i]);
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mat_clear(tmp);
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mat_workspace_clear(ws);
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}
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17
enumerate_triangle_group.h
Normal file
17
enumerate_triangle_group.h
Normal file
@@ -0,0 +1,17 @@
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#ifndef ENUMERATE_TRIANGLE_GROUP_H
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#define ENUMERATE_TRIANGLE_GROUP_H
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#include "mat.h"
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#include "coxeter.h"
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#include <mps/mps.h>
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int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues);
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void continued_fraction_approximation(mpq_t out, double in, int level);
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void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e);
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// p1,p2,p3 are only allowed to be 2,3,4,6
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void initialize_triangle_generators(mat_workspace *ws, mat *gen, int p1, int p2, int p3, mpq_t s, mpq_t q);
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char *print_word(groupelement_t *g, char *str);
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void enumerate(group_t *group, mat *matrices, int p1, int p2, int p3, mpq_t s, mpq_t t);
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#endif
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@@ -5,11 +5,6 @@
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#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
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#define DEBUG(msg, ...)
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#define DENOMINATOR 300
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#define WIDTH 135
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#define STARTX 121
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#define HEIGHT 300
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#define IDX(i,j) (((i)-1)*HEIGHT + ((j)-1))
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double mpq_log(mpq_t m_op)
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{
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@@ -45,10 +40,25 @@ int main(int argc, char *argv[])
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int retval;
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double evs[3];
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char buf[100];
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double *max_slope;
|
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int *max_slope_index;
|
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double max_slope = 0;
|
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int max_slope_index = 0;
|
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double min_slope = INFINITY;
|
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int min_slope_index = 0;
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char *env;
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int mode;
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|
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DEBUG("Allocate\n");
|
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if(argc < 2) {
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fprintf(stderr,
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"Usage: %s <s> <q> <word1> <word2> ...\n"
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"Computes jordan slopes of a list of group elements for a fixed representation.\n"
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"s,q: representation in the Hitchin component, given as rational numbers, e.g. 2/7\n"
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"word1, word2, ...: elements in the triangle rotation group, given as reflection group words\n"
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"output: word - jordan slope pairs\n"
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"+max slope index, max slope value, max slope word, min slope index, min slope value, min slope word\n"
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"controlled by environment variable MAXIMUM=no/yes/only, default yes\n",
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argv[0]);
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exit(0);
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}
|
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|
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mpq_inits(m, t, s, q, tmp, tmp2, tr, trinv, NULL);
|
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ws = mat_workspace_init(3);
|
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@@ -56,10 +66,6 @@ int main(int argc, char *argv[])
|
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mat_init(gen[i], 3);
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mat_init(element, 3);
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mat_init(inverse, 3);
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max_slope = malloc(sizeof(double)*WIDTH*HEIGHT);
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max_slope_index = malloc(sizeof(int)*WIDTH*HEIGHT);
|
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memset(max_slope_index, 0, sizeof(int)*WIDTH*HEIGHT);
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memset(max_slope, 0, sizeof(int)*WIDTH*HEIGHT);
|
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|
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solver = mps_context_new();
|
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mps_context_set_output_prec(solver, 20); // relative precision
|
||||
@@ -68,92 +74,91 @@ int main(int argc, char *argv[])
|
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mpq_set_str(s, argv[1], 10);
|
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mpq_set_str(q, argv[2], 10);
|
||||
|
||||
// for(int i = STARTX; i <= WIDTH; i++) {
|
||||
// for(int j = 1; j <= HEIGHT; j++) {
|
||||
for(int w = 3; w < argc; w++) {
|
||||
// mpq_set_ui(t, j, DENOMINATOR);
|
||||
// mpq_set_ui(m, i, DENOMINATOR); // 414/1000 ~ sqrt(2)-1 <-> s=1
|
||||
// s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
|
||||
env = getenv("MAXIMUM");
|
||||
if(!env || strcmp(env, "yes") == 0) {
|
||||
mode = 1; // yes
|
||||
} else if(strcmp(env, "no") == 0) {
|
||||
mode = 0; // no
|
||||
} else if(strcmp(env, "only") == 0) {
|
||||
mode = 2; // only
|
||||
}
|
||||
|
||||
DEBUG("Compute matrix\n");
|
||||
initialize_triangle_generators(ws, gen, 6, 4, 3, s, q);
|
||||
for(int w = 0; w < argc - 3; w++) {
|
||||
initialize_triangle_generators(ws, gen, 4, 4, 4, s, q);
|
||||
|
||||
mat_identity(element);
|
||||
mat_identity(inverse);
|
||||
for(int k = 0; k < strlen(argv[w]); k+=2) {
|
||||
letter1 = argv[w][k] - 'a';
|
||||
letter2 = argv[w][k+1] - 'a';
|
||||
mat_identity(element);
|
||||
mat_identity(inverse);
|
||||
for(int k = 0; k < strlen(argv[w+3]); k+=2) {
|
||||
letter1 = argv[w+3][k] - 'a';
|
||||
letter2 = argv[w+3][k+1] - 'a';
|
||||
|
||||
if(letter1 == 1 && letter2 == 2)
|
||||
letter = 0; // p = bc
|
||||
else if(letter1 == 2 && letter2 == 0)
|
||||
letter = 1; // q = ca
|
||||
else if(letter1 == 0 && letter2 == 1)
|
||||
letter = 2; // r = ab
|
||||
else if(letter1 == 2 && letter2 == 1)
|
||||
letter = 3; // p^{-1} = cb
|
||||
else if(letter1 == 0 && letter2 == 2)
|
||||
letter = 4; // q^{-1} = ac
|
||||
else if(letter1 == 1 && letter2 == 0)
|
||||
letter = 5; // r^{-1} = ba
|
||||
if(letter1 == 1 && letter2 == 2)
|
||||
letter = 0; // p = bc
|
||||
else if(letter1 == 2 && letter2 == 0)
|
||||
letter = 1; // q = ca
|
||||
else if(letter1 == 0 && letter2 == 1)
|
||||
letter = 2; // r = ab
|
||||
else if(letter1 == 2 && letter2 == 1)
|
||||
letter = 3; // p^{-1} = cb
|
||||
else if(letter1 == 0 && letter2 == 2)
|
||||
letter = 4; // q^{-1} = ac
|
||||
else if(letter1 == 1 && letter2 == 0)
|
||||
letter = 5; // r^{-1} = ba
|
||||
|
||||
mat_multiply(ws, element, element, gen[letter]);
|
||||
mat_multiply(ws, inverse, gen[(letter+3)%6], inverse);
|
||||
}
|
||||
mat_multiply(ws, element, element, gen[letter]);
|
||||
mat_multiply(ws, inverse, gen[(letter+3)%6], inverse);
|
||||
}
|
||||
|
||||
DEBUG("Compute traces\n");
|
||||
mat_trace(tr, element);
|
||||
mat_trace(trinv, inverse);
|
||||
|
||||
mat_trace(tr, element);
|
||||
mat_trace(trinv, inverse);
|
||||
retval = solve_characteristic_polynomial(solver, tr, trinv, evs);
|
||||
if(retval == 1) {
|
||||
fprintf(stderr, "Error! Could not solve polynomial.\n");
|
||||
return 1;
|
||||
}
|
||||
|
||||
DEBUG("Solve characteristic polynomials\n");
|
||||
retval = solve_characteristic_polynomial(solver, tr, trinv, evs);
|
||||
if(retval == 1) {
|
||||
fprintf(stderr, "Error! Could not solve polynomial.\n");
|
||||
return 1;
|
||||
}
|
||||
if(fabs(evs[0]) < fabs(evs[1]))
|
||||
SWAP(double, evs[0], evs[1]);
|
||||
if(fabs(evs[1]) < fabs(evs[2]))
|
||||
SWAP(double, evs[1], evs[2]);
|
||||
if(fabs(evs[0]) < fabs(evs[1]))
|
||||
SWAP(double, evs[0], evs[1]);
|
||||
|
||||
if(fabs(evs[0]) < fabs(evs[1]))
|
||||
SWAP(double, evs[0], evs[1]);
|
||||
if(fabs(evs[1]) < fabs(evs[2]))
|
||||
SWAP(double, evs[1], evs[2]);
|
||||
if(fabs(evs[0]) < fabs(evs[1]))
|
||||
SWAP(double, evs[0], evs[1]);
|
||||
x = log(fabs(evs[0]));
|
||||
y = -log(fabs(evs[2]));
|
||||
|
||||
x = log(fabs(evs[0]));
|
||||
y = -log(fabs(evs[2]));
|
||||
if(x > DBL_MAX || y > DBL_MAX) {
|
||||
mpq_abs(tmp, tr);
|
||||
mpq_abs(tmp2, trinv);
|
||||
slope = mpq_log(tmp)/mpq_log(tmp2);
|
||||
} else {
|
||||
slope = y/x;
|
||||
}
|
||||
|
||||
if(x > DBL_MAX || y > DBL_MAX) {
|
||||
mpq_abs(tmp, tr);
|
||||
mpq_abs(tmp2, trinv);
|
||||
slope = mpq_log(tmp)/mpq_log(tmp2);
|
||||
} else {
|
||||
slope = y/x;
|
||||
}
|
||||
if(slope < 1)
|
||||
slope = 1/slope;
|
||||
|
||||
if(slope < 1)
|
||||
slope = 1/slope;
|
||||
if(slope > max_slope) {
|
||||
max_slope = slope;
|
||||
max_slope_index = w;
|
||||
}
|
||||
|
||||
if(slope < min_slope) {
|
||||
min_slope = slope;
|
||||
min_slope_index = w;
|
||||
}
|
||||
|
||||
// if(slope > max_slope[IDX(i,j)]) {
|
||||
// max_slope[IDX(i,j)] = slope;
|
||||
// max_slope_index[IDX(i,j)] = w;
|
||||
// }
|
||||
if(mode != 2)
|
||||
gmp_printf("%s %.9f\n", argv[w+3], slope);
|
||||
}
|
||||
|
||||
// gmp_printf("%Qd %Qd %f %f %f\n", tr, trinv, x, y, y/x);
|
||||
// gmp_printf("%s %.5f %.5f %Qd %Qd %.9f %.9f %.9f\n", argv[w], mpq_get_d(s), mpq_get_d(q),
|
||||
// tr, trinv,
|
||||
// x, y, slope);
|
||||
gmp_printf("%s %.9f\n", argv[w], slope);
|
||||
if(mode != 0)
|
||||
printf("%d %.9f %s %d %.9f %s\n",
|
||||
max_slope_index, max_slope, argv[max_slope_index+3],
|
||||
min_slope_index, min_slope, argv[min_slope_index+3]);
|
||||
fflush(stdout);
|
||||
|
||||
}
|
||||
|
||||
// printf("%.5f %.5f %d %.9f\n", (double)i/DENOMINATOR, (double)j/DENOMINATOR, max_slope_index[IDX(i,j)], max_slope[IDX(i,j)]);
|
||||
fflush(stdout);
|
||||
// }
|
||||
// }
|
||||
|
||||
DEBUG("Clean up\n");
|
||||
mpq_clears(m, t, s, q, tmp, tmp2, tr, trinv, NULL);
|
||||
mat_workspace_clear(ws);
|
||||
for(int i = 0; i < 6; i++)
|
||||
@@ -161,6 +166,4 @@ int main(int argc, char *argv[])
|
||||
mat_clear(element);
|
||||
mat_clear(inverse);
|
||||
mps_context_free(solver);
|
||||
free(max_slope);
|
||||
free(max_slope_index);
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user