From 69d975bac9c15720ef914000d72690613e280a5c Mon Sep 17 00:00:00 2001
From: Florian Stecker <mail@florianstecker.de>
Date: Thu, 3 Jan 2019 20:15:36 +0100
Subject: [PATCH] dominant weights

---
 Makefile           | 10 +++++--
 dominant_weights.c | 69 ++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 77 insertions(+), 2 deletions(-)
 create mode 100644 dominant_weights.c

diff --git a/Makefile b/Makefile
index f31c3c8..53912fa 100644
--- a/Makefile
+++ b/Makefile
@@ -7,7 +7,7 @@ SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
 OPTIONS=-m64 -march=native -mtune=native -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
 NAME=enumerate-balanced-ideals
 
-all: enumerate graph D2n
+all: enumerate graph D2n dominant_weights
 
 $(NAME).tar.bz2: $(NAME) $(HEADERS) enumerate.c weyl.c thickenings.c
 	tar cjhf $(NAME).tar.bz2 $(NAME)/enumerate.c $(NAME)/weyl.c $(NAME)/thickenings.c $(NAME)/weyl.h $(NAME)/thickenings.h $(NAME)/queue.h $(NAME)/bitvec.h $(NAME)/Makefile $(NAME)/graph.c
@@ -24,6 +24,9 @@ graph: graph.o weyl.o
 D2n: D2n.o weyl.o thickenings.o
 	gcc $(OPTIONS) -o D2n D2n.o weyl.o thickenings.o
 
+dominant_weights: dominant_weights.o weyl.o
+	gcc $(OPTIONS) -o dominant_weights dominant_weights.o weyl.o
+
 enumerate.o: enumerate.c $(HEADERS)
 	gcc $(OPTIONS) -c enumerate.c
 
@@ -39,5 +42,8 @@ weyl.o: weyl.c $(HEADERS)
 graph.o: graph.c $(HEADERS)
 	gcc $(OPTIONS) -c graph.c
 
+dominant_weights.o: dominant_weights.c $(HEADERS)
+	gcc $(OPTIONS) -c dominant_weights.c
+
 clean:
-	rm -f enumerate graph D2n thickenings.o weyl.o enumerate.o graph.o D2n.o $(NAME) $(NAME).tar.bz2
+	rm -f enumerate graph D2n dominant_weights thickenings.o weyl.o enumerate.o graph.o D2n.o dominant_weights.o $(NAME) $(NAME).tar.bz2
diff --git a/dominant_weights.c b/dominant_weights.c
new file mode 100644
index 0000000..f94ee46
--- /dev/null
+++ b/dominant_weights.c
@@ -0,0 +1,69 @@
+#include <stdio.h>
+#include <string.h>
+#include <malloc.h>
+
+#include "weyl.h"
+
+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++)
+      str[j] = e->word[j] + 'a';
+    str[e->wordlength] = 0;
+  }
+
+  return str;
+}
+
+static int apply_reflection(double *in, double *out, int rank, int reflection)
+{
+	memcpy(out, in, rank*sizeof(double));
+	out[reflection] *= -1;
+	if(reflection != 0)
+		out[reflection-1] += in[reflection];
+	if(reflection != rank-1)
+		out[reflection+1] += in[reflection];
+}
+
+int main(int argc, char *argv[])
+{
+	semisimple_type_t type;
+	simple_type_t simple;
+	doublequotient_t *dq;
+	double *vector;
+	char buf[1000];
+
+	type.n = 1;
+	type.factors = &simple;
+	simple.series = 'A';
+	simple.rank = 3;
+
+	dq = weyl_generate_bruhat(type, 0, 0);
+
+	int order = weyl_order(type);
+	int rank = weyl_rank(type);
+	weylgroup_element_t *group = dq->group;
+	vector = malloc(weyl_order(type)*weyl_rank(type)*sizeof(double));
+
+	for(int i = 0; i < rank; i++) {
+		vector[i] = 1.0;
+	}
+
+	for(int i = 0; i < order; i++) {
+		printf("%s %.2f %.2f %.2f\n", alphabetize(&group[i], buf),
+		       1.0/4.0*(3*vector[3*i] + 2*vector[3*i+1] + 1*vector[3*i+2]),
+		       1.0/4.0*(2*vector[3*i] + 4*vector[3*i+1] + 2*vector[3*i+2]),
+		       1.0/4.0*(1*vector[3*i] + 2*vector[3*i+1] + 3*vector[3*i+2]));
+
+		for(int j = 0; j < rank; j++)
+			if(group[i].left[j]->wordlength > group[i].wordlength)
+				apply_reflection(&vector[3*i], &vector[3*group[i].left[j]->index], rank, j);
+	}
+
+	weyl_destroy_bruhat(dq);
+	free(vector);
+
+	return 0;
+}