dense_apply_derivatives
=======================

.. py:function:: t3toolbox.backend.sampling_derivatives.dense_apply_derivatives(ww, pp, T, order)

   .. code-block:: python

      def dense_apply_derivatives(
              ww:     typ.Sequence[NDArray],  # probe vectors X,        len=d, elm_shape=(Ni,)
              pp:     typ.Sequence[NDArray],  # perturbation vectors P, len=d, elm_shape=(Ni,)
              T:      NDArray,                # dense tensor, shape=(N0,...,N(d-1))
              order:  int,                    # highest derivative order
      ) -> NDArray:                           # apply-derivative jets, shape=(order+1,)


   Exact dense symmetric apply derivatives, by the all-modes multilinear subset expansion (oracle).

   ``apply(X+sP)`` is a polynomial in ``s`` of degree ``d``, so the ``t``-th derivative at ``s=0`` is

       ``y^(t) = t! * sum_{|S|=t, S subset of {0..d-1}} T contracted with {p_j: j in S, x_j: else}``,

   here contracting **every** mode (no free mode). Enumerates the size-``t`` subsets ``S`` -- testing
   only, unstacked.