Mathematics
===========

Implements a rudimentary symbolic mathematical model. The entities of the model are termed operations. A system of operations is termed a program.

.. cpp:namespace:: hysj

.. cpp:namespace-push:: mathematics

In namespace :cpp:any:`mathematics`:

Operations
----------

:cpp:include:`#include<hysj/mathematics/operations.hpp>`

Datum
^^^^^

.. cpp:enum-class:: datum

   .. rest-script::

      from hysj import mathematics
      Enum = mathematics.Datum

      for e in Enum.__members__.values():
        print(f'.. cpp:enumerator:: {e.name}')

   | Enum for representing symbolic constants.
   |


Operation
^^^^^^^^^

The operation is the building blocks of our mathematical model.

.. cpp:enum-class:: operation_tag

   .. rest-script::

      from hysj import mathematics
      Enum = mathematics.OperationTag

      for e in Enum.__members__.values():
        print(f'.. cpp:enumerator:: {e.name}')

   | Names the different types of operations.
   | 

.. cpp:struct:: template<operation_tag t> operation_id

   .. cpp:member:: static constexpr operation_tag tag = t
   .. cpp:member:: natural number

   |  Each operation has a unique id consiting of a tag which denotes the type of operation, and an number which is unique to all operation ids of that type.
		   
*Shorthands*

.. rest-script::

   from hysj import mathematics
   Enum = mathematics.OperationTag
   for e in Enum.__members__.values():
     print(f'.. cpp:type:: {e.name}_id = operation_id<operation_tag::{e.name}>')

|
   
.. cpp:type:: template<operation_tag i> operation_ids = std::vector<operation_id<i>>

   | Alias template for list of operation ids.
   
*Shorthands*

.. rest-script::

   from hysj import mathematics
   Enum = mathematics.OperationTag
   for e in Enum.__members__.values():
     print(f'.. cpp:type:: {e.name}_ids = operation_ids<operation_tag::{e.name}>')


Groups
^^^^^^

.. cpp:enum-class:: operation_group_tag

   .. rest-script::

     from hysj import mathematics
     Enum = mathematics.OperationGroupTag

     for e in Enum.__members__.values():
       print(f'.. cpp:enumerator:: {e.name}')

   | Names the different types of operation-groups.
   |

.. cpp:var:: template<operation_group_tag G> unspecified operation_group_members

   .. rest-script::

      from hysj import mathematics
      Enum = mathematics.OperationGroupTag

      print('| An operation group is defined in terms of a tuple of :cpp:type:`operation_tag`-constants, with:')
      for e in Enum.__members__.values():
        members = mathematics.operation_group_members[e.value]
	print(f'|   {e.name} :math:`\\rightarrow` {", ".join([m.name for m in members])}')

   |

   
.. cpp:struct:: template<operation_group_tag> operation_group_id

   .. cpp:member:: unspecified operation

   | A group-id holds a variant over the operation-ids of its member-operations.

*Shorthands*

.. rest-script::

   from hysj import mathematics
   Enum = mathematics.OperationGroupTag

   for e in Enum.__members__.values():
     print(f'.. cpp:type:: {e.name}_id = operation_group_id<operation_group_tag::{e.name}>')

|

.. cpp:type:: template<operation_group_tag g> operation_group_ids = std::vector<operation_group_id<g>>

   | List of operation group ids.

*Shorthands*

.. rest-script::

   from hysj import mathematics
   Enum = mathematics.OperationGroupTag
   for e in Enum.__members__.values():
     print(f'.. cpp:type:: {e.name}_ids = operation_group_ids<operation_group_tag::{e.name}>')


Operands
^^^^^^^^

.. cpp:struct:: template<operation_tag> operation_operands

   | Models the operands of an operation. The primary template is an empty struct, and signifies a nullary operator. Its members are operation-ids, operation-group-ids or list of these.

*Specializations*

.. rest-script::

   import inspect
   from hysj import mathematics
   Enum = mathematics.OperationTag

   for e in Enum.__members__.values():
     print(f'.. cpp:struct:: template<> operation_operands<operation_tag::{e.name}>')
     print('')
     OperandsType = mathematics.operation_operand_types[e.value]
     for m in inspect.getmembers(OperandsType,lambda m:isinstance(m,property)):
       print(f'  .. cpp:member:: unspecified {m[0]}')

Infos
^^^^^

Some operations have semantics beyond operand-relations. This information is taken care of by a operation-type specific operation info-type.

.. cpp:var:: unspecified operation_info_type

   | Function mapping from operation-tag to the operation-info-type.
   | The only operations with a non :cpp:type:`nothing` info-type are:
   |   Constants :math:`\rightarrow` :cpp:expr:`std::variant<datum,integer,real>`
   |   Booleans :math:`\rightarrow` :cpp:expr:`bool`
   |   Symbols :math:`\rightarrow` :cpp:expr:`natural`
   |

Programs
--------

:cpp:include:`#include<hysj/mathematics/programs.hpp>`

.. cpp:struct:: program

   | A program represents a system of operations. This system consists of a set of operations for each type, the operation infos and operands.

   .. cpp:member:: unspecified counts

		   Maintains the arity of the operation-sets.

   .. cpp:member:: unspecified graph

		   Models operand-relations between operations.
		   
   .. cpp:member:: unspecified vertex_map

		   Mapping between :cpp:type:`operation_id` and :cpp:member:`graph` vertex.
      
   .. cpp:member:: unspecified infos

		   Mapping between :cpp:type:`operation_id` and :cpp:member:`operation_info` vertex.
		   
.. cpp:namespace-pop::