64 lines
1.8 KiB
Python
64 lines
1.8 KiB
Python
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from sympy.core import S
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from sympy.core.sympify import sympify
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from sympy.core.relational import Eq, Ne
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from sympy.core.parameters import global_parameters
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from sympy.logic.boolalg import Boolean
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from sympy.utilities.misc import func_name
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from .sets import Set
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class Contains(Boolean):
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"""
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Asserts that x is an element of the set S.
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Examples
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========
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>>> from sympy import Symbol, Integer, S, Contains
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>>> Contains(Integer(2), S.Integers)
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True
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>>> Contains(Integer(-2), S.Naturals)
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False
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>>> i = Symbol('i', integer=True)
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>>> Contains(i, S.Naturals)
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Contains(i, Naturals)
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References
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==========
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.. [1] https://en.wikipedia.org/wiki/Element_%28mathematics%29
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"""
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def __new__(cls, x, s, evaluate=None):
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x = sympify(x)
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s = sympify(s)
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if evaluate is None:
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evaluate = global_parameters.evaluate
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if not isinstance(s, Set):
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raise TypeError('expecting Set, not %s' % func_name(s))
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if evaluate:
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# _contains can return symbolic booleans that would be returned by
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# s.contains(x) but here for Contains(x, s) we only evaluate to
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# true, false or return the unevaluated Contains.
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result = s._contains(x)
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if isinstance(result, Boolean):
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if result in (S.true, S.false):
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return result
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elif result is not None:
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raise TypeError("_contains() should return Boolean or None")
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return super().__new__(cls, x, s)
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@property
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def binary_symbols(self):
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return set().union(*[i.binary_symbols
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for i in self.args[1].args
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if i.is_Boolean or i.is_Symbol or
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isinstance(i, (Eq, Ne))])
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def as_set(self):
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return self.args[1]
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