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from sympy.assumptions import Predicate
from sympy.multipledispatch import Dispatcher
class FinitePredicate(Predicate):
"""
Finite number predicate.
Explanation
===========
``Q.finite(x)`` is true if ``x`` is a number but neither an infinity
nor a ``NaN``. In other words, ``ask(Q.finite(x))`` is true for all
numerical ``x`` having a bounded absolute value.
Examples
========
>>> from sympy import Q, ask, S, oo, I, zoo
>>> from sympy.abc import x
>>> ask(Q.finite(oo))
False
>>> ask(Q.finite(-oo))
False
>>> ask(Q.finite(zoo))
False
>>> ask(Q.finite(1))
True
>>> ask(Q.finite(2 + 3*I))
True
>>> ask(Q.finite(x), Q.positive(x))
True
>>> print(ask(Q.finite(S.NaN)))
None
References
==========
.. [1] https://en.wikipedia.org/wiki/Finite
"""
name = 'finite'
handler = Dispatcher(
"FiniteHandler",
doc=("Handler for Q.finite. Test that an expression is bounded respect"
" to all its variables.")
)
class InfinitePredicate(Predicate):
"""
Infinite number predicate.
``Q.infinite(x)`` is true iff the absolute value of ``x`` is
infinity.
"""
# TODO: Add examples
name = 'infinite'
handler = Dispatcher(
"InfiniteHandler",
doc="""Handler for Q.infinite key."""
)
class PositiveInfinitePredicate(Predicate):
"""
Positive infinity predicate.
``Q.positive_infinite(x)`` is true iff ``x`` is positive infinity ``oo``.
"""
name = 'positive_infinite'
handler = Dispatcher("PositiveInfiniteHandler")
class NegativeInfinitePredicate(Predicate):
"""
Negative infinity predicate.
``Q.negative_infinite(x)`` is true iff ``x`` is negative infinity ``-oo``.
"""
name = 'negative_infinite'
handler = Dispatcher("NegativeInfiniteHandler")
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