Sympy 简明教程

SymPy - Querying

SymPy 程序包中的假设模块包含用于提取有关表达式的信息的工具。该模块为此目的定义了 ask() 函数。

The assumptions module in SymPy package contains tools for extracting information about expressions. The module defines ask() function for this purpose.

sympy.assumptions.ask(property)

以下属性提供了有关表达式的有用信息 −

Following properties provide useful information about an expression −

algebraic(x)

为了成为代数数，一个数必须是有理系数的非零多项式方程的根。√2 是代数数，因为 √2 是 x2 − 2 = 0 的解。

To be algebraic, a number must be a root of a non-zero polynomial equation with rational coefficients. √2 because √2 is a solution to x2 − 2 = 0, so it is algebraic.

complex(x)

复数谓词。当且仅当 x 属于复数集时，它为真。

Complex number predicate. It is true if and only if x belongs to the set of complex numbers.

composite(x)

ask(Q.composite(x)) 返回的复合数谓词当且仅当 x 为正整数，并且除了 1 和该数本身外，至少有一个正除数时为真。

Composite number predicate returned by ask(Q.composite(x)) is true if and only if x is a positive integer and has at least one positive divisor other than 1 and the number itself.

even, odd

ask() 分别返回 x 在偶数集中和奇数集中的真值。

The ask() returns true of x is in the set of even numbers and set of odd numbers respectively.

imaginary

此属性表示虚数谓词。当 x 可以表示为一个实数乘以虚数单位 I 时，它为真。

This property represents Imaginary number predicate. It is true if x can be written as a real number multiplied by the imaginary unit I.

integer

Q.integer(x) 返回的此属性返回 x 属于偶数集的真值。

This property returned by Q.integer(x) returns true of x belong to set of even numbers.

rational, irrational

Q.irrational（x）成立当且仅当 x 是任何不能表示为整数比的实数。例如，π 是一个无理数。

Q.irrational(x) is true if and only if x is any real number that cannot be expressed as a ratio of integers. For example, pi is an irrational number.

positive, negative

检查数字是正还是负的谓词

Predicates to check if number is positive or negative

zero, nonzero

检查数字是否为零的谓词

Predicates to heck if a number is zero or not

>>> from sympy import *
>>> x=Symbol('x')
>>> x=10
>>> ask(Q.algebraic(pi))
False
>>> ask(Q.complex(5-4*I)), ask( Q.complex(100))
(True, True)
>>> x,y=symbols("x y")
>>> x,y=5,10
>>> ask(Q.composite(x)), ask(Q.composite(y))
(False, True)
>>> ask(Q.even(x)), ask(Q.even(y))
(False, True)
>>> x,y= 2*I, 4+5*I
>>> ask(Q.imaginary(x)), ask(Q.imaginary(y))
(True, False)
>>> x,y=5,10
>>> ask(Q.even(x)), ask(Q.even(y)), ask(Q.odd(x)), ask(Q.odd(y))
(False, True, True, False)
>>> x,y=5,-5
>>> ask(Q.positive(x)), ask(Q.negative(y)), ask(Q.positive(x)), ask(Q.negative(y))
(True, True, True, True)
>>> ask(Q.rational(pi)), ask(Q.irrational(S(2)/3))
(False, False)
>>> ask(Q.zero(oo)), ask(Q.nonzero(I))
(False, False)