[gatest] Add a commutesWith method to blades

It came about from a discussion in the bivector discord about
programmatic testing for blade commutativity and why no texts talked
about it. I came up with an idea that turned out not to work (I guess
I'd overthought how count_flips works). In the end, I decided to keep
it, and simplified metric's sign check.

ruamoko/gatest/basisblade.h

@@ -21,6 +21,8 @@
 -(unsigned) mask;
 -(double) scale;
 -(string) name;
+-(int) commutesWith:(BasisBlade *) b;
+-(int) commutesWith:(BasisBlade *) b metric:(Metric *)m;
 @end
 
 #endif//__basisblade_h

ruamoko/gatest/basisblade.r

@@ -103,4 +103,17 @@
 {
 	return sprintf ("%g%s", scale, [self name]);
 }
+
+-(int) commutesWith:(BasisBlade *) b metric:(Metric *)m
+{
+	int         sign1 = count_flips (mask, b.mask) & 1;
+	int         sign2 = count_flips (b.mask, mask) & 1;
+	return sign1 == sign2 || (m && ![m apply:mask, b.mask]);
+}
+
+-(int) commutesWith:(BasisBlade *) b
+{
+	return [self commutesWith: b metric:nil];
+}
+
 @end

ruamoko/gatest/main.r

@@ -43,6 +43,44 @@ basic_test (void)
 //	printf ("d: %@\n", d);
 
 	arp_end ();
+
+	arp_start ();
+	{
+		auto ab = [a outerProduct:b];
+		auto ac = [a outerProduct:c];
+		auto ad = [a outerProduct:d];
+		auto bc = [b outerProduct:c];
+		auto bd = [b outerProduct:d];
+		auto cd = [c outerProduct:d];
+		auto abc = [ab outerProduct:c];
+		auto bcd = [bc outerProduct:d];
+		auto cda = [cd outerProduct:a];
+		auto dab = [d outerProduct:ab];
+		auto abcd = [abc outerProduct:d];
+		printf ("a, bcd: %d\n", [a commutesWith:bcd]);
+		printf ("b, bcd: %d\n", [b commutesWith:bcd]);
+		printf ("c, bcd: %d\n", [c commutesWith:bcd]);
+		printf ("d, bcd: %d\n", [d commutesWith:bcd]);
+		printf ("bcd, a: %d\n", [bcd commutesWith:a]);
+		printf ("bcd, b: %d\n", [bcd commutesWith:b]);
+		printf ("bcd, c: %d\n", [bcd commutesWith:c]);
+		printf ("bcd, d: %d\n", [bcd commutesWith:d]);
+
+		printf ("ab, bcd: %d\n", [ab commutesWith:bcd]);
+		printf ("ac, bcd: %d\n", [ac commutesWith:bcd]);
+		printf ("ad, bcd: %d\n", [ad commutesWith:bcd]);
+		printf ("bc, bcd: %d\n", [bc commutesWith:bcd]);
+		printf ("bd, bcd: %d\n", [bd commutesWith:bcd]);
+		printf ("cd, bcd: %d\n", [cd commutesWith:bcd]);
+
+		printf ("ab, bc: %d\n", [ab commutesWith:bc]);
+		printf ("ac, bc: %d\n", [ac commutesWith:bc]);
+		printf ("ad, bc: %d\n", [ad commutesWith:bc]);
+		printf ("bc, bc: %d\n", [bc commutesWith:bc]);
+		printf ("bd, bc: %d\n", [bd commutesWith:bc]);
+		printf ("cd, bc: %d\n", [cd commutesWith:bc]);
+	}
+	arp_end ();
 #if 0
 	arp_start ();
 	for (int i = 0; i < 4; i++) {

ruamoko/gatest/metric.r

@@ -1,4 +1,5 @@
 #include "metric.h"
+#include "util.h"
 
 @implementation Metric
 +(Metric *)R:(int)p, int m, int z
@@ -13,14 +14,7 @@
 static double
 count_minus (unsigned minus)
 {
-	double      s = 1;
+	return count_bits (minus) & 1 ? -1 : 1;
-	while (minus) {
-		if (minus & 1) {
-			s = -s;
-		}
-		minus >>= 1;
-	}
-	return s;
 }
 
 -(double)apply:(unsigned) a, unsigned b