391 lines
9.3 KiB
Python
391 lines
9.3 KiB
Python
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from sympy.assumptions import Predicate
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from sympy.multipledispatch import Dispatcher
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class NegativePredicate(Predicate):
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r"""
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Negative number predicate.
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Explanation
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===========
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``Q.negative(x)`` is true iff ``x`` is a real number and :math:`x < 0`, that is,
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it is in the interval :math:`(-\infty, 0)`. Note in particular that negative
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infinity is not negative.
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A few important facts about negative numbers:
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- Note that ``Q.nonnegative`` and ``~Q.negative`` are *not* the same
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thing. ``~Q.negative(x)`` simply means that ``x`` is not negative,
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whereas ``Q.nonnegative(x)`` means that ``x`` is real and not
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negative, i.e., ``Q.nonnegative(x)`` is logically equivalent to
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``Q.zero(x) | Q.positive(x)``. So for example, ``~Q.negative(I)`` is
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true, whereas ``Q.nonnegative(I)`` is false.
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- See the documentation of ``Q.real`` for more information about
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related facts.
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Examples
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========
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>>> from sympy import Q, ask, symbols, I
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>>> x = symbols('x')
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>>> ask(Q.negative(x), Q.real(x) & ~Q.positive(x) & ~Q.zero(x))
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True
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>>> ask(Q.negative(-1))
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True
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>>> ask(Q.nonnegative(I))
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False
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>>> ask(~Q.negative(I))
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True
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"""
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name = 'negative'
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handler = Dispatcher(
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"NegativeHandler",
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doc=("Handler for Q.negative. Test that an expression is strictly less"
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" than zero.")
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)
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class NonNegativePredicate(Predicate):
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"""
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Nonnegative real number predicate.
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Explanation
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===========
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``ask(Q.nonnegative(x))`` is true iff ``x`` belongs to the set of
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positive numbers including zero.
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- Note that ``Q.nonnegative`` and ``~Q.negative`` are *not* the same
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thing. ``~Q.negative(x)`` simply means that ``x`` is not negative,
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whereas ``Q.nonnegative(x)`` means that ``x`` is real and not
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negative, i.e., ``Q.nonnegative(x)`` is logically equivalent to
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``Q.zero(x) | Q.positive(x)``. So for example, ``~Q.negative(I)`` is
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true, whereas ``Q.nonnegative(I)`` is false.
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Examples
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========
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>>> from sympy import Q, ask, I
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>>> ask(Q.nonnegative(1))
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True
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>>> ask(Q.nonnegative(0))
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True
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>>> ask(Q.nonnegative(-1))
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False
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>>> ask(Q.nonnegative(I))
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False
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>>> ask(Q.nonnegative(-I))
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False
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"""
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name = 'nonnegative'
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handler = Dispatcher(
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"NonNegativeHandler",
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doc=("Handler for Q.nonnegative.")
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)
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class NonZeroPredicate(Predicate):
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"""
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Nonzero real number predicate.
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Explanation
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===========
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``ask(Q.nonzero(x))`` is true iff ``x`` is real and ``x`` is not zero. Note in
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particular that ``Q.nonzero(x)`` is false if ``x`` is not real. Use
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``~Q.zero(x)`` if you want the negation of being zero without any real
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assumptions.
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A few important facts about nonzero numbers:
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- ``Q.nonzero`` is logically equivalent to ``Q.positive | Q.negative``.
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- See the documentation of ``Q.real`` for more information about
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related facts.
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Examples
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========
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>>> from sympy import Q, ask, symbols, I, oo
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>>> x = symbols('x')
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>>> print(ask(Q.nonzero(x), ~Q.zero(x)))
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None
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>>> ask(Q.nonzero(x), Q.positive(x))
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True
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>>> ask(Q.nonzero(x), Q.zero(x))
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False
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>>> ask(Q.nonzero(0))
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False
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>>> ask(Q.nonzero(I))
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False
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>>> ask(~Q.zero(I))
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True
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>>> ask(Q.nonzero(oo))
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False
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"""
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name = 'nonzero'
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handler = Dispatcher(
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"NonZeroHandler",
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doc=("Handler for key 'zero'. Test that an expression is not identically"
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" zero.")
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)
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class ZeroPredicate(Predicate):
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"""
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Zero number predicate.
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Explanation
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===========
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``ask(Q.zero(x))`` is true iff the value of ``x`` is zero.
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Examples
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========
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>>> from sympy import ask, Q, oo, symbols
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>>> x, y = symbols('x, y')
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>>> ask(Q.zero(0))
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True
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>>> ask(Q.zero(1/oo))
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True
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>>> print(ask(Q.zero(0*oo)))
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None
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>>> ask(Q.zero(1))
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False
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>>> ask(Q.zero(x*y), Q.zero(x) | Q.zero(y))
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True
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"""
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name = 'zero'
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handler = Dispatcher(
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"ZeroHandler",
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doc="Handler for key 'zero'."
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)
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class NonPositivePredicate(Predicate):
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"""
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Nonpositive real number predicate.
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Explanation
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===========
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``ask(Q.nonpositive(x))`` is true iff ``x`` belongs to the set of
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negative numbers including zero.
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- Note that ``Q.nonpositive`` and ``~Q.positive`` are *not* the same
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thing. ``~Q.positive(x)`` simply means that ``x`` is not positive,
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whereas ``Q.nonpositive(x)`` means that ``x`` is real and not
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positive, i.e., ``Q.nonpositive(x)`` is logically equivalent to
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`Q.negative(x) | Q.zero(x)``. So for example, ``~Q.positive(I)`` is
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true, whereas ``Q.nonpositive(I)`` is false.
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Examples
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========
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>>> from sympy import Q, ask, I
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>>> ask(Q.nonpositive(-1))
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True
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>>> ask(Q.nonpositive(0))
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True
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>>> ask(Q.nonpositive(1))
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False
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>>> ask(Q.nonpositive(I))
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False
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>>> ask(Q.nonpositive(-I))
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False
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"""
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name = 'nonpositive'
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handler = Dispatcher(
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"NonPositiveHandler",
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doc="Handler for key 'nonpositive'."
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)
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class PositivePredicate(Predicate):
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r"""
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Positive real number predicate.
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Explanation
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===========
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``Q.positive(x)`` is true iff ``x`` is real and `x > 0`, that is if ``x``
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is in the interval `(0, \infty)`. In particular, infinity is not
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positive.
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A few important facts about positive numbers:
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- Note that ``Q.nonpositive`` and ``~Q.positive`` are *not* the same
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thing. ``~Q.positive(x)`` simply means that ``x`` is not positive,
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whereas ``Q.nonpositive(x)`` means that ``x`` is real and not
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positive, i.e., ``Q.nonpositive(x)`` is logically equivalent to
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`Q.negative(x) | Q.zero(x)``. So for example, ``~Q.positive(I)`` is
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true, whereas ``Q.nonpositive(I)`` is false.
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- See the documentation of ``Q.real`` for more information about
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related facts.
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Examples
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========
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>>> from sympy import Q, ask, symbols, I
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>>> x = symbols('x')
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>>> ask(Q.positive(x), Q.real(x) & ~Q.negative(x) & ~Q.zero(x))
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True
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>>> ask(Q.positive(1))
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True
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>>> ask(Q.nonpositive(I))
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False
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>>> ask(~Q.positive(I))
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True
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"""
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name = 'positive'
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handler = Dispatcher(
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"PositiveHandler",
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doc=("Handler for key 'positive'. Test that an expression is strictly"
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" greater than zero.")
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)
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class ExtendedPositivePredicate(Predicate):
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r"""
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Positive extended real number predicate.
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Explanation
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===========
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``Q.extended_positive(x)`` is true iff ``x`` is extended real and
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`x > 0`, that is if ``x`` is in the interval `(0, \infty]`.
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Examples
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========
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>>> from sympy import ask, I, oo, Q
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>>> ask(Q.extended_positive(1))
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True
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>>> ask(Q.extended_positive(oo))
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True
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>>> ask(Q.extended_positive(I))
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False
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"""
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name = 'extended_positive'
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handler = Dispatcher("ExtendedPositiveHandler")
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class ExtendedNegativePredicate(Predicate):
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r"""
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Negative extended real number predicate.
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Explanation
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===========
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``Q.extended_negative(x)`` is true iff ``x`` is extended real and
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`x < 0`, that is if ``x`` is in the interval `[-\infty, 0)`.
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Examples
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========
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>>> from sympy import ask, I, oo, Q
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>>> ask(Q.extended_negative(-1))
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True
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>>> ask(Q.extended_negative(-oo))
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True
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>>> ask(Q.extended_negative(-I))
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False
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"""
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name = 'extended_negative'
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handler = Dispatcher("ExtendedNegativeHandler")
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class ExtendedNonZeroPredicate(Predicate):
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"""
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Nonzero extended real number predicate.
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Explanation
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===========
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``ask(Q.extended_nonzero(x))`` is true iff ``x`` is extended real and
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``x`` is not zero.
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Examples
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========
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>>> from sympy import ask, I, oo, Q
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>>> ask(Q.extended_nonzero(-1))
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True
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>>> ask(Q.extended_nonzero(oo))
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True
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>>> ask(Q.extended_nonzero(I))
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False
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"""
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name = 'extended_nonzero'
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handler = Dispatcher("ExtendedNonZeroHandler")
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class ExtendedNonPositivePredicate(Predicate):
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"""
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Nonpositive extended real number predicate.
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Explanation
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===========
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``ask(Q.extended_nonpositive(x))`` is true iff ``x`` is extended real and
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``x`` is not positive.
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Examples
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========
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>>> from sympy import ask, I, oo, Q
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>>> ask(Q.extended_nonpositive(-1))
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True
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>>> ask(Q.extended_nonpositive(oo))
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False
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>>> ask(Q.extended_nonpositive(0))
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True
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>>> ask(Q.extended_nonpositive(I))
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False
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"""
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name = 'extended_nonpositive'
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handler = Dispatcher("ExtendedNonPositiveHandler")
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class ExtendedNonNegativePredicate(Predicate):
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"""
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Nonnegative extended real number predicate.
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Explanation
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===========
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``ask(Q.extended_nonnegative(x))`` is true iff ``x`` is extended real and
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``x`` is not negative.
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Examples
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========
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>>> from sympy import ask, I, oo, Q
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>>> ask(Q.extended_nonnegative(-1))
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False
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>>> ask(Q.extended_nonnegative(oo))
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True
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>>> ask(Q.extended_nonnegative(0))
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True
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>>> ask(Q.extended_nonnegative(I))
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False
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"""
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name = 'extended_nonnegative'
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handler = Dispatcher("ExtendedNonNegativeHandler")
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