From 0f23a4b4772be7d5159b48502f6451a72fbd5106 Mon Sep 17 00:00:00 2001
From: Florian Stecker <oss@florianstecker.net>
Date: Sat, 8 Mar 2025 11:56:27 -0500
Subject: [PATCH] color principal ideals

---
 graph.c | 125 ++++++++++++++++++++++++++++++++++----------------------
 1 file changed, 76 insertions(+), 49 deletions(-)

diff --git a/graph.c b/graph.c
index 3da69da..5ef8cf2 100644
--- a/graph.c
+++ b/graph.c
@@ -1,16 +1,15 @@
-#include "weyl.h"
 #include "queue.h"
+#include "weyl.h"
 
-#include <strings.h>
-#include <stdio.h>
 #include <memory.h>
+#include <stdio.h>
+#include <strings.h>
 
-static char* alphabetize(weylgroup_element_t *e, char *str)
-{
-  if(e->wordlength == 0)
+static char *alphabetize(weylgroup_element_t *e, char *str) {
+  if (e->wordlength == 0)
     sprintf(str, "1");
   else {
-    for(int j = 0; j < e->wordlength; j++)
+    for (int j = 0; j < e->wordlength; j++)
       str[j] = e->word[j] + 'a';
     str[e->wordlength] = 0;
   }
@@ -18,55 +17,83 @@ static char* alphabetize(weylgroup_element_t *e, char *str)
   return str;
 }
 
-int main(int argc, const char *argv[])
-{
-	semisimple_type_t type;
-	unsigned long right_invariance, left_invariance;
-	doublequotient_t *dq;
-	const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
-	char stringbuffer[100];
-	char stringbuffer2[100];
+int main(int argc, const char *argv[]) {
+  semisimple_type_t type;
+  unsigned long right_invariance, left_invariance;
+  doublequotient_t *dq;
+  const char *alphabet = "abcdefghijklmnopqrstuvwxyz";
+  char stringbuffer[100];
+  char stringbuffer2[100];
 
-	ERROR(argc < 2, "Too few arguments!\n");
+  ERROR(argc < 2, "Too few arguments!\n");
 
-	type.n = 0;
-	for(int i = 0; i < argc - 1; i++) {
-		if(argv[i+1][0] < 'A' || argv[i+1][0] > 'G')
-			break;
-		type.n++;
-	}
+  type.n = 0;
+  for (int i = 0; i < argc - 1; i++) {
+    if (argv[i + 1][0] < 'A' || argv[i + 1][0] > 'G')
+      break;
+    type.n++;
+  }
 
-	type.factors = (simple_type_t*)malloc(type.n*sizeof(simple_type_t));
-	for(int i = 0; i < type.n; i++) {
-		type.factors[i].series = argv[i+1][0];
-		type.factors[i].rank = argv[i+1][1] - '0';
-		ERROR(argv[i+1][0] < 'A' || argv[i+1][0] > 'G' || argv[i+1][1] < '1' || argv[i+1][1] > '9', "Arguments must be Xn with X out of A-G and n out of 1-9\n");
-	}
+  type.factors = (simple_type_t *)malloc(type.n * sizeof(simple_type_t));
+  for (int i = 0; i < type.n; i++) {
+    type.factors[i].series = argv[i + 1][0];
+    type.factors[i].rank = argv[i + 1][1] - '0';
+    ERROR(argv[i + 1][0] < 'A' || argv[i + 1][0] > 'G' ||
+	  argv[i + 1][1] < '1' || argv[i + 1][1] > '9',
+	  "Arguments must be Xn with X out of A-G and n out of 1-9\n");
+  }
 
-	left_invariance = right_invariance = 0;
+  left_invariance = right_invariance = 0;
 
-	if(argc - type.n >= 3) {
-		if(strcmp(argv[type.n + 1], "-") != 0)
-			for(int i = 0; i < strlen(argv[type.n + 1]); i++)
-				left_invariance |= (1 << (argv[type.n + 1][i] - 'a'));
-		if(strcmp(argv[type.n + 2], "-") != 0)
-			for(int i = 0; i < strlen(argv[type.n + 2]); i++)
-				right_invariance |= (1 << (argv[type.n + 2][i] - 'a'));
-	}
+  if (argc - type.n >= 3) {
+    if (strcmp(argv[type.n + 1], "-") != 0)
+      for (int i = 0; i < strlen(argv[type.n + 1]); i++)
+	left_invariance |= (1 << (argv[type.n + 1][i] - 'a'));
+    if (strcmp(argv[type.n + 2], "-") != 0)
+      for (int i = 0; i < strlen(argv[type.n + 2]); i++)
+	right_invariance |= (1 << (argv[type.n + 2][i] - 'a'));
+  }
 
-	// generate graph
+  // generate graph
+  dq = weyl_generate_bruhat(type, left_invariance, right_invariance);
 
-	dq = weyl_generate_bruhat(type, left_invariance, right_invariance);
+  // color ideals
+  int *color = (int*) malloc(dq->count * sizeof(int));
+  memset(color, 0, dq->count * sizeof(int));
+  for(int i = type.n+3; i < argc; i++) {
+    weylgroup_element_t *elem = &dq->group[0]; // identity
+    for(int j = 0; j < strlen(argv[i]); j++) {
+      int gen = argv[i][j] - 'a';
+      elem = elem->right[gen];
+    }
+    color[elem->coset->index] = 1;
+  }
 
-    fprintf(stdout, "digraph test123 {\n");
-    for(int i = 0; i < dq->count; i++)
-      for(doublecoset_list_t *current = dq->cosets[i].bruhat_lower; current; current = current->next)
-        fprintf(stdout, "%s -> %s;\n",
-                alphabetize(dq->cosets[i].min, stringbuffer),
-                alphabetize(current->to->min, stringbuffer2));
-    fprintf(stdout, "}\n\n");
+  for(int i = dq->count - 1; i >= 0; i--) {
+    if(color[i] > 0) {
+      for(doublecoset_list_t *current = dq->cosets[i].bruhat_lower; current; current = current->next) {
+	color[current->to->index] = color[i];
+      }
+    }
+  }
 
-	// clean up
-	weyl_destroy_bruhat(dq);
-	free(type.factors);
+  fprintf(stdout, "digraph bruhat {\n");
+  for (int i = 0; i < dq->count; i++) {
+    fprintf(stdout, "%s [color=\"%s\"];\n",
+	    alphabetize(dq->cosets[i].min, stringbuffer),
+	    color[i] > 0 ? "red" : "black");
+
+    for (doublecoset_list_t *current = dq->cosets[i].bruhat_lower; current; current = current->next) {
+      fprintf(stdout, "%s -> %s [color=\"%s\"];\n",
+	      alphabetize(dq->cosets[i].min, stringbuffer),
+	      alphabetize(current->to->min, stringbuffer2),
+	      color[i] > 0 ? "red" : "black");
+    }
+  }
+  fprintf(stdout, "}\n\n");
+
+  // clean up
+  weyl_destroy_bruhat(dq);
+  free(color);
+  free(type.factors);
 }