假定

A module which implements predicates and assumption context.

class sympy.assumptions.assume.AppliedPredicate(predicate, *args)

The class of expressions resulting from applying Predicate to the arguments. AppliedPredicate merely wraps its argument and remain unevaluated. To evaluate it, use the ask() function.

实例

>>> from sympy import Q, ask
>>> Q.integer(1)
Q.integer(1)

The function attribute returns the predicate, and the arguments attribute returns the tuple of arguments.

>>> type(Q.integer(1))
<class 'sympy.assumptions.assume.AppliedPredicate'>
>>> Q.integer(1).function
Q.integer
>>> Q.integer(1).arguments
(1,)

Applied predicates can be evaluated to a boolean value with ask:

>>> ask(Q.integer(1))
True

property arg

返回此假设使用的表达式。

实例

>>> from sympy import Q, Symbol
>>> x = Symbol('x')
>>> a = Q.integer(x + 1)
>>> a.arg
x + 1

property arguments

Return the arguments which are applied to the predicate.

property function

Return the predicate.

class sympy.assumptions.assume.AssumptionsContext

Set containing default assumptions which are applied to the ask() function.

解释

它用于表示全局假设，但也可以使用此类创建自己的本地假设上下文。它基本上是Python集合的一个瘦包装器，因此请参阅其文档以了解高级用法。

实例

The default assumption context is global_assumptions, which is initially empty:

>>> from sympy import ask, Q
>>> from sympy.assumptions import global_assumptions
>>> global_assumptions
AssumptionsContext()

You can add default assumptions:

>>> from sympy.abc import x
>>> global_assumptions.add(Q.real(x))
>>> global_assumptions
AssumptionsContext({Q.real(x)})
>>> ask(Q.real(x))
True

And remove them:

>>> global_assumptions.remove(Q.real(x))
>>> print(ask(Q.real(x)))
None

The clear() method removes every assumption:

>>> global_assumptions.add(Q.positive(x))
>>> global_assumptions
AssumptionsContext({Q.positive(x)})
>>> global_assumptions.clear()
>>> global_assumptions
AssumptionsContext()

参见

assuming

add(*assumptions)

Add assumptions.

class sympy.assumptions.assume.Predicate(*args, **kwargs)

Base class for mathematical predicates. It also serves as a constructor for undefined predicate objects.

解释

Predicate is a function that returns a boolean value [1].

Predicate function is object, and it is instance of predicate class. When a predicate is applied to arguments, AppliedPredicate instance is returned. This merely wraps the argument and remain unevaluated. To obtain the truth value of applied predicate, use the function ask.

Evaluation of predicate is done by multiple dispatching. You can register new handler to the predicate to support new types.

Every predicate in SymPy can be accessed via the property of Q. For example, Q.even returns the predicate which checks if the argument is even number.

To define a predicate which can be evaluated, you must subclass this class, make an instance of it, and register it to Q. After then, dispatch the handler by argument types.

If you directly construct predicate using this class, you will get UndefinedPredicate which cannot be dispatched. This is useful when you are building boolean expressions which do not need to be evaluated.

实例

Applying and evaluating to boolean value:

>>> from sympy import Q, ask
>>> ask(Q.prime(7))
True

You can define a new predicate by subclassing and dispatching. Here, we define a predicate for sexy primes [2] as an example.

>>> from sympy import Predicate, Integer
>>> class SexyPrimePredicate(Predicate):
...     name = "sexyprime"
>>> Q.sexyprime = SexyPrimePredicate()
>>> @Q.sexyprime.register(Integer, Integer)
... def _(int1, int2, assumptions):
...     args = sorted([int1, int2])
...     if not all(ask(Q.prime(a), assumptions) for a in args):
...         return False
...     return args[1] - args[0] == 6
>>> ask(Q.sexyprime(5, 11))
True

Direct constructing returns UndefinedPredicate, which can be applied but cannot be dispatched.

>>> from sympy import Predicate, Integer
>>> Q.P = Predicate("P")
>>> type(Q.P)
<class 'sympy.assumptions.assume.UndefinedPredicate'>
>>> Q.P(1)
Q.P(1)
>>> Q.P.register(Integer)(lambda expr, assump: True)
Traceback (most recent call last):
  ...
TypeError: <class 'sympy.assumptions.assume.UndefinedPredicate'> cannot be dispatched.

工具书类

[R5]

https://en.wikipedia.org/wiki/Predicate_%28mathematical_logic%29

[R6]

https://en.wikipedia.org/wiki/Sexy_prime

eval(args, assumptions=True)

Evaluate self(*args) under the given assumptions.

这只使用直接解析方法，不使用逻辑推理。

handler = <dispatched AskPredicateHandler>

classmethod register(*types, **kwargs)

Register the signature to the handler.

classmethod register_many(*types, **kwargs)

Register multiple signatures to same handler.

class sympy.assumptions.assume.UndefinedPredicate(name, handlers=None)

Predicate without handler.

解释

This predicate is generated by using Predicate directly for construction. It does not have a handler, and evaluating this with arguments is done by SAT solver.

实例

>>> from sympy import Predicate, Q
>>> Q.P = Predicate('P')
>>> Q.P.func
<class 'sympy.assumptions.assume.UndefinedPredicate'>
>>> Q.P.name
Str('P')

sympy.assumptions.assume.assuming(*assumptions)

Context manager for assumptions.

实例

>>> from sympy import assuming, Q, ask
>>> from sympy.abc import x, y
>>> print(ask(Q.integer(x + y)))
None
>>> with assuming(Q.integer(x), Q.integer(y)):
...     print(ask(Q.integer(x + y)))
True