Merge branch 'u/dkrenn/product_cantor_pairing' of trac.sagemath.org:s…

…age into t/19048/asy/an_element

* 'u/dkrenn/product_cantor_pairing' of trac.sagemath.org:sage:
  minor changes to code: spacings, PEP8, remove comment
  Trac #19319: alternative implementation
  remove unneccesary try/except block
  deal with product(empty, infinite)

src/sage/misc/mrange.py

@@ -711,32 +711,32 @@ def product_cantor_pairing(A, B):
         A loads item number 0
         B loads item number 0
         (0, 0)
+        A loads item number 1
         B loads item number 1
         (0, 1)
-        A loads item number 1
         (1, 0)
         (1, 1)
         sage: for p in product_cantor_pairing(it('A', 3), it('B', 2)):
         ....:     print p
         A loads item number 0
         B loads item number 0
         (0, 0)
+        A loads item number 1
         B loads item number 1
         (0, 1)
-        A loads item number 1
         (1, 0)
-        (1, 1)
         A loads item number 2
+        (1, 1)
         (2, 0)
         (2, 1)
         sage: for p in product_cantor_pairing(it('A', 2), it('B', 4)):
         ....:     print p
         A loads item number 0
         B loads item number 0
         (0, 0)
+        A loads item number 1
         B loads item number 1
         (0, 1)
-        A loads item number 1
         (1, 0)
         B loads item number 2
         (0, 2)
@@ -745,39 +745,37 @@ def product_cantor_pairing(A, B):
         (0, 3)
         (1, 2)
         (1, 3)
-    """
-    # when writing this code I thought the solution would be shorter...
-
-    class iter_as_list(list):
-        def __init__(self, iterable):
-            self.it = iter(iterable)
-            self.newdata = True
-        def __getitem__(self, i):
-            self.newdata = False
-            try:
-                while len(self) <= i:
-                    self.append(next(self.it))
-                    self.newdata = True
-            except StopIteration:
-                raise
-            return list.__getitem__(self, i)
 
+    ::
+
+        sage: from itertools import count
+        sage: list(product_cantor_pairing([], count()))
+        []
+        sage: list(product_cantor_pairing(count(), []))
+        []
+    """
     from itertools import count
-    A = iter_as_list(A)
-    B = iter_as_list(B)
+    from sage.rings.infinity import infinity
+
+    A = iter(A)
+    B = iter(B)
+    max_A = infinity
+    max_B = infinity
+    cache_A = []
+    cache_B = []
     for s in count():
-        for i in range(s+1):
-            stopped = False
+        if s <= max_A:
             try:
-                a = A[i]
+                cache_A.append(next(A))
             except StopIteration:
-                stopped = True
+                max_A = s - 1
+        if s <= max_B:
             try:
-                b = B[s-i]
+                cache_B.append(next(B))
             except StopIteration:
-                stopped = True
-            if stopped:
-                continue
-            yield a, b
-        if not A.newdata and not B.newdata and s >= len(A) + len(B):
+                max_B = s - 1
+        if s > max_A + max_B or max_A < 0 or max_B < 0:
             return
+
+        for i in range(max(0, s-max_B), min(s, max_A) + 1):
+            yield cache_A[i], cache_B[s-i]