Merge branch 'public/combinat/words/longest_common_extension-23131' o…

…f git://trac.sagemath.org/sage into t/23131/public/combinat/words/longest_common_extension-23131

src/sage/combinat/words/finite_word.py

@@ -2205,6 +2205,70 @@ def is_cadence(self, seq):
             return False
         return True
 
+    def longest_forward_extension(self, x, y):
+        r"""
+        Compute the length of the longest factor of ``self`` that
+        starts at ``x`` and that matches a factor that starts at ``y``.
+
+        INPUT:
+
+        - ``x``, ``y`` -- positions in ``self``
+
+        EXAMPLES::
+
+            sage: w = Word('0011001')
+            sage: w.longest_forward_extension(0, 4)
+            3
+            sage: w.longest_forward_extension(0, 2)
+            0
+            sage: w.longest_forward_extension(-3, 2)
+            Traceback (most recent call last):
+            ...
+            ValueError: x and y must be valid positions in self
+        """
+        length = self.length()
+        if not (0 <= x and 0 <= y and x < length and y < length):
+            raise ValueError("x and y must be valid positions in self")
+        l = 0
+        while x < length and y < length and self[x] == self[y]:
+            l += 1
+            x += 1
+            y += 1
+        return l
+
+    def longest_backward_extension(self, x, y):
+        r"""
+        Compute the length of the longest factor of ``self`` that
+        ends at ``x`` and that matches a factor that ends at ``y``.
+
+        INPUT:
+
+        - ``x``, ``y`` -- positions in ``self``
+
+        EXAMPLES::
+            
+            sage: w = Word('0011001')
+            sage: w.longest_backward_extension(6, 2)
+            3
+            sage: w.longest_backward_extension(1, 4)
+            1
+            sage: w.longest_backward_extension(1, 3)
+            0
+            sage: w.longest_backward_extension(4, 23)
+            Traceback (most recent call last):
+            ...
+            ValueError: x and y must be valid positions in self
+        """
+        length = self.length()
+        if not (0 <= x and 0 <= y and x < length and y < length):
+            raise ValueError("x and y must be valid positions in self")
+        l = 0
+        while x >= 0 and y >= 0 and self[x] == self[y]:
+            l += 1
+            x -= 1
+            y -= 1
+        return l
+
     def longest_common_suffix(self, other):
         r"""
         Return the longest common suffix of ``self`` and ``other``.