use new product_cantor_pairing and delete old product_diagonal

src/sage/rings/asymptotic/asymptotic_ring.py

@@ -1112,12 +1112,12 @@ def some_elements(self):
              O(z^(-1/2)),
              -8*z^(3/2) + O(z^(1/2)))
         """
-        from sage.rings.asymptotic.term_monoid import product_diagonal
+        from sage.misc.mrange import product_cantor_pairing
         from sage.rings.asymptotic.term_monoid import TermMonoid
         E = TermMonoid('exact', self.growth_group, self.coefficient_ring)
         O = TermMonoid('O', self.growth_group, self.coefficient_ring)
         return iter(-self(e)**3 + self(o)
-                    for e, o in product_diagonal(
+                    for e, o in product_cantor_pairing(
                             E.some_elements(), O.some_elements()))
 
 

src/sage/rings/asymptotic/term_monoid.py

@@ -205,123 +205,6 @@
 
 import sage
 
-
-def product_diagonal(A, B):
-    r"""
-    Return an iterator over the product of `A` and `B` which iterates
-    along the diagonal.
-
-    INPUT:
-
-    - ``A`` and ``B`` -- iterables (over a finite number of elements)
-
-    OUTPUT:
-
-    An iterator over `(a,b)` for `a \in A` and `b \in B`.
-
-    EXAMPLES::
-
-        sage: from sage.rings.asymptotic.term_monoid import product_diagonal
-        sage: tuple(product_diagonal(srange(2), srange(2)))
-        ((0, 0), (0, 1), (1, 0), (1, 1))
-        sage: tuple(product_diagonal(srange(4), srange(2)))
-        ((0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1))
-        sage: tuple(product_diagonal(srange(2), srange(3)))
-        ((0, 0), (0, 1), (1, 0), (0, 2), (1, 1), (1, 2))
-        sage: tuple(''.join(p) for p in product_diagonal('abc', 'xyz'))
-        ('ax', 'ay', 'bx', 'az', 'by', 'cx', 'bz', 'cy', 'cz')
-
-    TESTS:
-
-    Check that all pairs are returned::
-
-        sage: all(len(tuple(product_diagonal(srange(m), srange(n)))) == m*n
-        ....:     for m in srange(5) for n in srange(5))
-        True
-
-    Check that everthing is loaded in the correct order::
-
-        sage: def it(s, n):
-        ....:     for i in srange(n):
-        ....:         print '%s loads item number %s' % (s, i)
-        ....:         yield i
-        sage: for p in product_diagonal(it('A', 2), it('B', 2)):
-        ....:     print p
-        A loads item number 0
-        B loads item number 0
-        (0, 0)
-        B loads item number 1
-        (0, 1)
-        A loads item number 1
-        (1, 0)
-        (1, 1)
-        sage: for p in product_diagonal(it('A', 3), it('B', 2)):
-        ....:     print p
-        A loads item number 0
-        B loads item number 0
-        (0, 0)
-        B loads item number 1
-        (0, 1)
-        A loads item number 1
-        (1, 0)
-        (1, 1)
-        A loads item number 2
-        (2, 0)
-        (2, 1)
-        sage: for p in product_diagonal(it('A', 2), it('B', 4)):
-        ....:     print p
-        A loads item number 0
-        B loads item number 0
-        (0, 0)
-        B loads item number 1
-        (0, 1)
-        A loads item number 1
-        (1, 0)
-        B loads item number 2
-        (0, 2)
-        (1, 1)
-        B loads item number 3
-        (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)
-
-    from itertools import count
-    A = iter_as_list(A)
-    B = iter_as_list(B)
-    for s in count():
-        for i in range(s+1):
-            stopped = False
-            try:
-                a = A[i]
-            except StopIteration:
-                stopped = True
-            try:
-                b = B[s-i]
-            except StopIteration:
-                stopped = True
-            if stopped:
-                continue
-            yield a, b
-        if not A.newdata and not B.newdata and s >= len(A) + len(B):
-            return
-
-
 def absorption(left, right):
     r"""
     Let one of the two passed terms absorb the other.
@@ -2073,7 +1956,8 @@ def some_elements(self):
              z^2, -2*z^(1/2), 2*z^(-1/2), -z^2, z^(-2))
 
         """
-        return iter(self(g, c) for g, c in product_diagonal(
+        from sage.misc.mrange import product_cantor_pairing
+        return iter(self(g, c) for g, c in product_cantor_pairing(
             self.growth_group.some_elements(),
             iter(c for c in self.base_ring().some_elements() if c != 0)))