You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
303 lines
7.0 KiB
303 lines
7.0 KiB
"""
|
|
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)
|