compute whether a representation in the barbot component of the (5,5,5) group is (almost) all loxodromic

2022-04-13 19:23:38 -05:00
parent 7f6ad68f53
commit 721b139307
7 changed files with 843 additions and 104 deletions
--- a/mat.h
+++ b/mat.h
@@ -8,27 +8,139 @@

 // library for matrix computations in variable rings (based on GMP types)

-/*
-  needed features:
-  x multiply matrices
-  - inverse
-  x pseudoinverse
-  x set
-  - eigenvalues
- */
+#ifdef QEXT_SQRT5
+
+typedef mpq_t NUMBER [2];
+#define INIT(x)         do { mpq_init((x)[0]);         mpq_init((x)[1]);       } while(0)
+#define CLEAR(x)        do { mpq_clear((x)[0]);        mpq_clear((x)[1]);      } while(0)
+#define SET(x,y)        do { mpq_set((x)[0],(y)[0]);   mpq_set((x)[1],(y)[1]); } while(0)
+#define SET_INT(x,y)    do { mpq_set_si((x)[0],(y),1); mpq_set_si((x)[1],0,1); } while(0)
+#define SET_ZERO(x) SET_INT(x,0)
+#define SET_ONE(x)  SET_INT(x,1)
+#define ADD(x,y,z)      do { mpq_add((x)[0],(y)[0],(z)[0]); mpq_add((x)[1],(y)[1],(z)[1]); } while(0)
+#define SUB(x,y,z)      do { mpq_sub((x)[0],(y)[0],(z)[0]); mpq_sub((x)[1],(y)[1],(z)[1]); } while(0)
+#define MUL multiply_sqrt5
+#define DIV divide_sqrt5
+#define CMP compare_sqrt5
+#define PRINT(x) gmp_printf("%Qd + %Qd*sqrt(5)", (x)[0], (x)[1])
+#define SPRINT(buf, x) gmp_sprintf(buf, "%Qd+%Qd*sqrt(5)", (x)[0], (x)[1])
+
+static void multiply_sqrt5(NUMBER out, NUMBER a, NUMBER b)
+{
+	// could be in place!!!
+
+	mpq_t tmp, result[2];
+	mpq_inits(tmp, result[0], result[1], 0);
+
+	mpq_mul(result[0], a[1], b[1]);
+	mpq_set_si(tmp, 5, 1);
+	mpq_mul(result[0], result[0], tmp);
+	mpq_mul(tmp, a[0], b[0]);
+	mpq_add(result[0], result[0], tmp);
+
+	mpq_mul(result[1], a[1], b[0]);
+	mpq_mul(tmp, a[0], b[1]);
+	mpq_add(result[1], result[1], tmp);
+
+	mpq_set(out[0], result[0]);
+	mpq_set(out[1], result[1]);
+
+	mpq_clears(tmp, result[0], result[1], 0);
+}
+
+static void divide_sqrt5(NUMBER out, NUMBER a, NUMBER b)
+{
+	mpq_t denom, num, tmp, neg5, result[2];
+	mpq_inits(denom, num, tmp, neg5, result[0], result[1], 0);
+	mpq_set_si(neg5, -5, 1);
+
+	mpq_mul(denom, b[1], b[1]);
+	mpq_mul(denom, denom, neg5);
+	mpq_mul(tmp, b[0], b[0]);
+	mpq_add(denom, denom, tmp);
+
+	mpq_mul(num, a[1], b[1]);
+	mpq_mul(num, num, neg5);
+	mpq_mul(tmp, a[0], b[0]);
+	mpq_add(num, num, tmp);
+
+	mpq_div(result[0], num, denom);
+
+	mpq_mul(num, a[1], b[0]);
+	mpq_mul(tmp, a[0], b[1]);
+	mpq_sub(num, num, tmp);
+
+	mpq_div(result[1], num, denom);
+
+	mpq_set(out[0], result[0]);
+	mpq_set(out[1], result[1]);
+
+	mpq_clears(denom, num, tmp, neg5, result[0], result[1], 0);
+}
+
+static int compare_sqrt5(NUMBER x, NUMBER y)
+{
+	int result;
+	mpq_t p, q, p2, q2, c5;
+	mpq_inits(p, q, p2, q2, c5, 0);
+
+	mpq_sub(p, x[0], y[0]);
+	mpq_sub(q, x[1], y[1]);
+
+	/*
+	  want to know if p + sqrt(5) q > 0
+	  if p>0 and q>0: always true
+	  if p>0 and q<0: equivalent to |p|^2 > 5 |q|^2
+	  if p<0 and q>0: equivalent to |p|^2 < 5 |q|^2
+	  if p<0 and q<0: always false
+	*/
+
+	if(mpq_sgn(p) > 0 && mpq_sgn(q) > 0) {
+		result = 1;
+		goto done;
+	}
+
+	if(mpq_sgn(p) < 0 && mpq_sgn(q) < 0) {
+		result = -1;
+		goto done;
+	}
+
+	mpq_mul(p2, p, p);
+	mpq_mul(q2, q, q);
+	mpq_set_si(c5, 5, 1);
+	mpq_mul(q2, q2, c5);
+
+	if(mpq_sgn(p) > 0)
+		result = mpq_cmp(p2, q2);  // this can't be zero, or else |p/q| = sqrt(5), but it's irrational
+	else if(mpq_sgn(p) < 0)
+		result = -mpq_cmp(p2, q2); // this can be zero if p = 0 and q = 0
+	else // p = 0
+		return mpq_sgn(q);
+
+done:
+	mpq_clears(p, q, p2, q2, c5, 0);
+	return result;
+}
+
+#endif
+
+#ifdef QEXT_TRIVIAL

 #define NUMBER mpq_t
 #define INIT mpq_init
 #define CLEAR mpq_clear
 #define SET mpq_set
-#define SET_ZERO(x) mpq_set_ui(x,0,1)
-#define SET_ONE(x) mpq_set_ui(x,1,1)
+#define SET_INT(x,y) mpq_set_si(x,y,1)
+#define SET_ZERO(x) SET_INT(x,0)
+#define SET_ONE(x)  SET_INT(x,1)
 #define ADD mpq_add
 #define SUB mpq_sub
-#define MULTIPLY mpq_mul
+#define MUL mpq_mul
 #define DIV mpq_div
 #define PRINT(x) gmp_printf("%Qd", x)

+#endif
+
 #define M(m,i,j) ((m)->x[(i)+(m)->n*(j)])

 struct _mat{