[gatest] Implement undual and antiwedge

ruamoko/gatest/algebra.h

@@ -25,6 +25,7 @@
 -(Metric *) metric;
 -(int)count;
 -(int)dimension;
+-(int)dim;
 
 -(MultiVector *) group:(int)group;
 -(MultiVector *) group:(int)group values:(double *)values;

ruamoko/gatest/algebra.r

@@ -130,6 +130,11 @@
 	return dimension;
 }
 
+-(int)dim
+{
+	return dimension - zero;
+}
+
 -(MultiVector *) group:(int)group
 {
 	return [MultiVector new:self group:[layout group:group]];

ruamoko/gatest/main.r

@@ -117,7 +117,7 @@ typedef enum {
 	OPENS, CLOSES,
 	MUL, DIV, PLUS, MINUS,
 	WEDGE, ANTIWEDGE, DOT,
-	REVERSE, DUAL,
+	REVERSE, DUAL, UNDUAL,
 } token_e;
 
 script_t script;
@@ -158,6 +158,7 @@ get_token ()
 		case ".":   return {DOT, nil};
 		case "~":   return {REVERSE, nil};
 		case "!":   return {DUAL, nil};
+		case "?":   return {UNDUAL, nil};
 	}
 	return {ID, .name = token_str };
 }
@@ -212,6 +213,9 @@ factor ()
 	} else if (match (DUAL)) {
 		advance ();
 		vec = [factor () dual];
+	} else if (match (UNDUAL)) {
+		advance ();
+		vec = [factor () undual];
 	} else if (match (MINUS)) {
 		advance ();
 		vec = [minus_one product:factor ()];
@@ -274,6 +278,9 @@ high_term ()
 		if (match (WEDGE)) {
 			op = @selector(wedge:);
 			advance ();
+		} else if (match (ANTIWEDGE)) {
+			op = @selector(antiwedge:);
+			advance ();
 		} else if (match (DOT)) {
 			op = @selector(dot:);
 			advance ();

ruamoko/gatest/multivector.h

@@ -28,10 +28,12 @@
 -(MultiVector *) product:(MultiVector *) rhs;
 -(MultiVector *) divide:(MultiVector *) rhs;
 -(MultiVector *) wedge:(MultiVector *) rhs;
+-(MultiVector *) antiwedge:(MultiVector *) rhs;
 -(MultiVector *) dot:(MultiVector *) rhs;
 -(MultiVector *) plus:(MultiVector *) rhs;
 -(MultiVector *) minus:(MultiVector *) rhs;
 -(MultiVector *) dual;
+-(MultiVector *) undual;
 -(MultiVector *) reverse;
 @end
 

ruamoko/gatest/multivector.r

@@ -169,6 +169,11 @@ static MultiVector *new_mv (Algebra *algebra, BasisLayout *layout)
 	return prod;
 }
 
+-(MultiVector *) antiwedge:(MultiVector *) rhs
+{
+	return [[[self dual] wedge:[rhs dual]] undual];
+}
+
 -(MultiVector *) dot:(MultiVector *) rhs
 {
 	MultiVector *prod = [MultiVector new:algebra];
@@ -253,10 +258,11 @@ static MultiVector *new_mv (Algebra *algebra, BasisLayout *layout)
 	return minus;
 }
 
--(MultiVector *) dual
+-(MultiVector *) dual:(int) undual
 {
 	MultiVector *dual = [MultiVector new:algebra];
 	unsigned dual_mask = (1 << [algebra dimension]) - 1;
+	int dim = [algebra dim];
 	for (int i = 0; i < num_components; i++) {
 		if (!components[i]) {
 			continue;
@@ -267,12 +273,23 @@ static MultiVector *new_mv (Algebra *algebra, BasisLayout *layout)
 		unsigned mask = lb_mask ^ dual_mask;
 		double ls = [lb scale];
 		double s = count_flips (lb_mask, mask) & 1 ? -1 : 1;
+		s *= (dim * [lb grade]) & 1 ? -1 : 1;
 		int ind = [dual.layout bladeIndex:mask];
 		dual.components[ind] += s * lc;
 	}
 	return dual;
 }
 
+-(MultiVector *) dual
+{
+	return [self dual:0];
+}
+
+-(MultiVector *) undual
+{
+	return [self dual:1];
+}
+
 -(MultiVector *) reverse
 {
 	MultiVector *reverse = [MultiVector new:algebra];