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