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Domains

.. module:: diofant.domains

Here we document the various implemented ground domains. There are three types: abstract domains, concrete domains, and "implementation domains". Abstract domains cannot be (usefully) instantiated at all, and just collect together functionality shared by many other domains. Concrete domains are those meant to be instantiated and used. In some cases, there are various possible ways to implement the data type the domain provides. For example, depending on what libraries are available on the system, the integers are implemented either using the python built-in integers, or using gmpy. Note that various aliases are created automatically depending on the libraries available. As such e.g. ZZ always refers to the most efficient implementation of the integer ring available.

Abstract Domains

.. autoclass:: diofant.domains.domain.Domain
   :members:

.. autoclass:: diofant.domains.field.Field
   :members:

.. autoclass:: diofant.domains.ring.Ring
   :members:

.. autoclass:: diofant.domains.simpledomain.SimpleDomain
   :members:

.. autoclass:: diofant.domains.compositedomain.CompositeDomain
   :members:

.. autoclass:: diofant.domains.characteristiczero.CharacteristicZero
   :members:

Concrete Domains

.. autoclass:: FiniteField
   :members:

.. autoclass:: IntegerRing
   :members:

.. autoclass:: RationalField
   :members:

.. autoclass:: AlgebraicField
   :members:

.. autoclass:: RealAlgebraicField
   :members:

.. autoclass:: ComplexAlgebraicField
   :members:

.. autoclass:: diofant.polys.rings.PolynomialRing
   :members:

.. autoclass:: diofant.polys.fields.FractionField
   :members:

.. autoclass:: RealField
   :members:

.. autoclass:: ComplexField
   :members:

.. autoclass:: ExpressionDomain
   :members:

Implementation Domains

.. autoclass:: diofant.domains.finitefield.PythonFiniteField
.. autoclass:: diofant.domains.finitefield.GMPYFiniteField

.. autoclass:: diofant.domains.integerring.PythonIntegerRing
.. autoclass:: diofant.domains.integerring.GMPYIntegerRing

.. autoclass:: diofant.domains.rationalfield.PythonRationalField
.. autoclass:: diofant.domains.rationalfield.GMPYRationalField