Derivatives and Integrals API Reference
=======================================

All fractional derivative and integral classes and functions exposed through ``core``
and ``algorithms``.

Layout
------

**Derivatives (RL / Caputo / Grünwald–Letnikov)**

* **Canonical engines** — :mod:`hpfracc.algorithms.derivatives` (``RiemannLiouville``,
  ``Caputo``, ``GrunwaldLetnikov``). These are the only numerical kernels for those
  operators.
* **Legacy names** — :mod:`hpfracc.algorithms.optimized_methods` exposes ``Optimized*``
  and ``ParallelOptimized*`` as aliases of the same engine classes.
* **High-level adapters** — :mod:`hpfracc.core.fractional_implementations` (``*Derivative``)
  implement :mod:`hpfracc.core.derivatives.BaseFractionalDerivative` and delegate to the
  engines. The factory in :mod:`hpfracc.core.derivatives` is populated when
  ``fractional_implementations`` is imported (registration uses ``logging``, not prints).

**Integrals**

* **Canonical** — :mod:`hpfracc.core.integrals` (``FractionalIntegral`` subclasses, quad-based).
* **Algorithms helpers** — :mod:`hpfracc.algorithms.integral_methods` (FFT-oriented RL/Caputo
  API; direct RL and Weyl paths delegate to ``core.integrals`` for normal orders).

Canonical derivative engines
----------------------------

.. automodule:: hpfracc.algorithms.derivatives
   :no-index:
   :members: RiemannLiouville, Caputo, GrunwaldLetnikov
   :undoc-members:
   :show-inheritance:

Core Derivatives (factory and base classes)
-------------------------------------------

.. automodule:: hpfracc.core.derivatives
   :no-index:
   :members:
   :undoc-members:
   :show-inheritance:

Optimized Methods (aliases)
---------------------------

.. automodule:: hpfracc.algorithms.optimized_methods
   :no-index:
   :members:
   :undoc-members:
   :show-inheritance:

Integral methods (algorithms)
-------------------------------

.. automodule:: hpfracc.algorithms.integral_methods
   :no-index:
   :members:
   :undoc-members:
   :show-inheritance:

Advanced Methods
----------------

.. automodule:: hpfracc.algorithms.advanced_methods
   :no-index:
   :members:
   :undoc-members:
   :show-inheritance:

Special Methods
---------------

.. automodule:: hpfracc.algorithms.fractional_operator_methods
   :no-index:
   :members:
   :undoc-members:
   :show-inheritance:

Fractional Implementations
---------------------------

.. automodule:: hpfracc.core.fractional_implementations
   :no-index:
   :members:
   :undoc-members:
   :show-inheritance:

Core Integrals
--------------

.. automodule:: hpfracc.core.integrals
   :no-index:
   :members:
   :undoc-members:
   :show-inheritance: