Add support for expanding dimensions using None

spec/API_specification/indexing.rst

@@ -137,7 +137,7 @@ Multi-dimensional arrays must extend the concept of single-axis indexing to mult
 
 - Providing a single negative integer ``i`` as a single-axis index must index the same elements as the slice ``n+i:n+i+1``, where ``n`` is the axis (dimension) size.
 
-- Providing a single integer as a single-axis index must reduce the number of array dimensions by ``1`` (i.e., the array rank should decrease by one; if ``A`` has rank ``2``, ``rank(A)-1 == rank(A[0, :])``). In particular, a selection tuple with the ``m``\th element an integer (and all other entries ``:``) indexes a sub-array with rank ``N-1``.
+- Providing a single integer as a single-axis index must reduce the number of array dimensions by ``1`` (i.e., the array rank must decrease by one; if ``A`` has rank ``2``, ``rank(A)-1 == rank(A[0, :])``). In particular, a selection tuple with the ``m``\th element an integer (and all other entries ``:``) indexes a sub-array with rank ``N-1``.
 
   .. note::
     When providing a single integer as a single-axis index to an array of rank ``1``, the result should be an array of rank ``0``, not a NumPy scalar. Note that this behavior differs from NumPy.
@@ -151,14 +151,19 @@ Multi-dimensional arrays must extend the concept of single-axis indexing to mult
   .. note::
     This behavior differs from NumPy where providing an empty tuple to an array of rank ``0`` returns a NumPy scalar.
 
-- Except in the case of providing a single ellipsis (e.g., ``A[2:10, ...]`` or ``A[1:, ..., 2:5]``), the number of provided single-axis indexing expressions should equal ``N``. For example, if ``A`` has rank ``2``, a single-axis indexing expression should be explicitly provided for both axes (e.g., ``A[2:10, :]``). An ``IndexError`` exception should be raised if the number of provided single-axis indexing expressions is less than ``N``.
+- Each ``None`` in the selection tuple must expand the dimensions of the resulting selection by one dimension of size ``1``. The position of the added dimension must be the same as the position of ``None`` in the selection tuple.
+
+  .. note::
+    Expanding dimensions can be equivalently achieved via repeated invocation of :func:`~signatures.manipulation_functions.expand_dims`.
+
+- Except in the case of providing a single ellipsis (e.g., ``A[2:10, ...]`` or ``A[1:, ..., 2:5]``), the number of provided single-axis indexing expressions (excluding ``None``) should equal ``N``. For example, if ``A`` has rank ``2``, a single-axis indexing expression should be explicitly provided for both axes (e.g., ``A[2:10, :]``). An ``IndexError`` exception should be raised if the number of provided single-axis indexing expressions (excluding ``None``) is less than ``N``.
 
   .. note::
     Some libraries, such as SymPy, support flat indexing (i.e., providing a single-axis indexing expression to a higher-dimensional array). That practice is not supported here.
 
     To perform flat indexing, use ``reshape(x, (-1,))[integer]``.
 
-- An ``IndexError`` exception must be raised if the number of provided single-axis indexing expressions is greater than ``N``.
+- An ``IndexError`` exception must be raised if the number of provided single-axis indexing expressions (excluding ``None``) is greater than ``N``.
 
   .. note::
     This specification leaves unspecified the behavior of providing a slice which attempts to select elements along a particular axis, but whose starting index is out-of-bounds.
@@ -175,6 +180,9 @@ Boolean Array Indexing
 
 An array must support indexing where the **sole index** is an ``M``-dimensional boolean array ``B`` with shape ``S1 = (s1, ..., sM)`` according to the following rules. Let ``A`` be an ``N``-dimensional array with shape ``S2 = (s1, ..., sM, ..., sN)``.
 
+  .. note::
+     The prohibition against combining boolean array indices with other single-axis indexing expressions includes the use of ``None``. To expand dimensions of the returned array, use repeated invocation of :func:`~signatures.manipulation_functions.expand_dims`.
+
 - If ``N >= M``, then ``A[B]`` must replace the first ``M`` dimensions of ``A`` with a single dimension having a size equal to the number of ``True`` elements in ``B``. The values in the resulting array must be in row-major (C-style order); this is equivalent to ``A[nonzero(B)]``.
 
   .. note::