303 lines
7.0 KiB
Python
303 lines
7.0 KiB
Python
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"""
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Module for mathematical equality [1] and inequalities [2].
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The purpose of this module is to provide the instances which represent the
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binary predicates in order to combine the relationals into logical inference
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system. Objects such as ``Q.eq``, ``Q.lt`` should remain internal to
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assumptions module, and user must use the classes such as :obj:`~.Eq()`,
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:obj:`~.Lt()` instead to construct the relational expressions.
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References
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==========
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.. [1] https://en.wikipedia.org/wiki/Equality_(mathematics)
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.. [2] https://en.wikipedia.org/wiki/Inequality_(mathematics)
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"""
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from sympy.assumptions import Q
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from sympy.core.relational import is_eq, is_neq, is_gt, is_ge, is_lt, is_le
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from .binrel import BinaryRelation
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__all__ = ['EqualityPredicate', 'UnequalityPredicate', 'StrictGreaterThanPredicate',
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'GreaterThanPredicate', 'StrictLessThanPredicate', 'LessThanPredicate']
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class EqualityPredicate(BinaryRelation):
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"""
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Binary predicate for $=$.
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The purpose of this class is to provide the instance which represent
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the equality predicate in order to allow the logical inference.
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This class must remain internal to assumptions module and user must
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use :obj:`~.Eq()` instead to construct the equality expression.
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Evaluating this predicate to ``True`` or ``False`` is done by
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:func:`~.core.relational.is_eq()`
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Examples
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========
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>>> from sympy import ask, Q
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>>> Q.eq(0, 0)
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Q.eq(0, 0)
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>>> ask(_)
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True
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See Also
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========
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sympy.core.relational.Eq
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"""
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is_reflexive = True
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is_symmetric = True
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name = 'eq'
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handler = None # Do not allow dispatching by this predicate
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@property
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def negated(self):
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return Q.ne
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def eval(self, args, assumptions=True):
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if assumptions == True:
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# default assumptions for is_eq is None
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assumptions = None
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return is_eq(*args, assumptions)
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class UnequalityPredicate(BinaryRelation):
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r"""
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Binary predicate for $\neq$.
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The purpose of this class is to provide the instance which represent
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the inequation predicate in order to allow the logical inference.
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This class must remain internal to assumptions module and user must
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use :obj:`~.Ne()` instead to construct the inequation expression.
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Evaluating this predicate to ``True`` or ``False`` is done by
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:func:`~.core.relational.is_neq()`
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Examples
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========
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>>> from sympy import ask, Q
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>>> Q.ne(0, 0)
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Q.ne(0, 0)
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>>> ask(_)
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False
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See Also
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========
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sympy.core.relational.Ne
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"""
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is_reflexive = False
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is_symmetric = True
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name = 'ne'
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handler = None
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@property
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def negated(self):
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return Q.eq
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def eval(self, args, assumptions=True):
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if assumptions == True:
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# default assumptions for is_neq is None
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assumptions = None
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return is_neq(*args, assumptions)
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class StrictGreaterThanPredicate(BinaryRelation):
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"""
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Binary predicate for $>$.
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The purpose of this class is to provide the instance which represent
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the ">" predicate in order to allow the logical inference.
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This class must remain internal to assumptions module and user must
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use :obj:`~.Gt()` instead to construct the equality expression.
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Evaluating this predicate to ``True`` or ``False`` is done by
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:func:`~.core.relational.is_gt()`
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Examples
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========
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>>> from sympy import ask, Q
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>>> Q.gt(0, 0)
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Q.gt(0, 0)
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>>> ask(_)
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False
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See Also
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========
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sympy.core.relational.Gt
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"""
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is_reflexive = False
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is_symmetric = False
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name = 'gt'
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handler = None
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@property
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def reversed(self):
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return Q.lt
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@property
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def negated(self):
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return Q.le
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def eval(self, args, assumptions=True):
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if assumptions == True:
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# default assumptions for is_gt is None
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assumptions = None
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return is_gt(*args, assumptions)
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class GreaterThanPredicate(BinaryRelation):
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"""
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Binary predicate for $>=$.
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The purpose of this class is to provide the instance which represent
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the ">=" predicate in order to allow the logical inference.
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This class must remain internal to assumptions module and user must
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use :obj:`~.Ge()` instead to construct the equality expression.
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Evaluating this predicate to ``True`` or ``False`` is done by
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:func:`~.core.relational.is_ge()`
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Examples
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========
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>>> from sympy import ask, Q
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>>> Q.ge(0, 0)
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Q.ge(0, 0)
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>>> ask(_)
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True
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See Also
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========
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sympy.core.relational.Ge
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"""
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is_reflexive = True
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is_symmetric = False
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name = 'ge'
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handler = None
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@property
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def reversed(self):
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return Q.le
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@property
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def negated(self):
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return Q.lt
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def eval(self, args, assumptions=True):
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if assumptions == True:
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# default assumptions for is_ge is None
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assumptions = None
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return is_ge(*args, assumptions)
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class StrictLessThanPredicate(BinaryRelation):
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"""
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Binary predicate for $<$.
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The purpose of this class is to provide the instance which represent
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the "<" predicate in order to allow the logical inference.
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This class must remain internal to assumptions module and user must
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use :obj:`~.Lt()` instead to construct the equality expression.
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Evaluating this predicate to ``True`` or ``False`` is done by
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:func:`~.core.relational.is_lt()`
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Examples
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========
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>>> from sympy import ask, Q
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>>> Q.lt(0, 0)
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Q.lt(0, 0)
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>>> ask(_)
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False
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See Also
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========
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sympy.core.relational.Lt
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"""
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is_reflexive = False
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is_symmetric = False
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name = 'lt'
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handler = None
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@property
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def reversed(self):
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return Q.gt
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@property
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def negated(self):
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return Q.ge
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def eval(self, args, assumptions=True):
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if assumptions == True:
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# default assumptions for is_lt is None
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assumptions = None
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return is_lt(*args, assumptions)
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class LessThanPredicate(BinaryRelation):
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"""
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Binary predicate for $<=$.
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The purpose of this class is to provide the instance which represent
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the "<=" predicate in order to allow the logical inference.
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This class must remain internal to assumptions module and user must
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use :obj:`~.Le()` instead to construct the equality expression.
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Evaluating this predicate to ``True`` or ``False`` is done by
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:func:`~.core.relational.is_le()`
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Examples
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========
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>>> from sympy import ask, Q
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>>> Q.le(0, 0)
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Q.le(0, 0)
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>>> ask(_)
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True
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See Also
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========
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sympy.core.relational.Le
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"""
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is_reflexive = True
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is_symmetric = False
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name = 'le'
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handler = None
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@property
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def reversed(self):
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return Q.ge
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@property
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def negated(self):
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return Q.gt
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def eval(self, args, assumptions=True):
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if assumptions == True:
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# default assumptions for is_le is None
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assumptions = None
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return is_le(*args, assumptions)
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