diff --git a/MathPad/MPRangePath.m b/MathPad/MPRangePath.m
index 801c6b7..9e4dcd0 100644
--- a/MathPad/MPRangePath.m
+++ b/MathPad/MPRangePath.m
@@ -116,6 +116,20 @@
     return [self.location isEqual:aRangePath.location] && self.length == aRangePath.length;
 }
 
+- (NSString *)description
+{
+    NSMutableString *description = [[NSMutableString alloc] initWithString:@"MPRangePath<location="];
+    if (self.location.length > 0) {
+        [description appendFormat:@"%ld", [self.location indexAtPosition:0]];
+    }
+    for (NSUInteger position = 1; position < self.location.length; position ++) {
+        [description appendFormat:@",%ld", [self.location indexAtPosition:position]];
+    }
+    [description appendFormat:@" length=%ld", self.length];
+    [description appendString:@">"];
+    return description.copy;
+}
+
 #pragma mark - NSCopying
 
 - (id)copyWithZone:(NSZone *)zone
diff --git a/MathPad/NSIndexPath+MPAdditions.m b/MathPad/NSIndexPath+MPAdditions.m
index ee58bce..43a975f 100644
--- a/MathPad/NSIndexPath+MPAdditions.m
+++ b/MathPad/NSIndexPath+MPAdditions.m
@@ -58,4 +58,29 @@
     return [[self indexPathByRemovingLastIndex] indexPathByAddingIndex:lastIndex];
 }
 
+- (NSIndexPath *)indexPathWithLength:(NSUInteger)length
+{
+    NSIndexPath *indexPath = [[NSIndexPath alloc] init];
+    for (NSUInteger position = 0; position < length; position++) {
+        indexPath = [indexPath indexPathByAddingIndex:[self indexAtPosition:position]];
+    }
+    return indexPath;
+}
+
+- (NSIndexPath *)commonIndexPathWith:(NSIndexPath *)indexPath
+{
+    NSIndexPath *commonPath = [[NSIndexPath alloc] init];
+    NSUInteger length = MIN(self.length, indexPath.length);
+    for (NSUInteger position = 0; position < length; position++) {
+        NSUInteger selfIndex = [self indexAtPosition:position];
+        NSUInteger otherIndex = [indexPath indexAtPosition:position];
+        if (selfIndex == otherIndex) {
+            commonPath = [commonPath indexPathByAddingIndex:selfIndex];
+        } else {
+            break;
+        }
+    }
+    return commonPath;
+}
+
 @end