Sympy 简明教程
SymPy - Numbers
SymPy 包中的核心模块包含表示原子数的数字类。该类有两个子类：Float 和 Rational 类。Rational 类由 Integer 类进一步扩展。
The core module in SymPy package contains Number class which represents atomic numbers. This class has two subclasses: Float and Rational class. Rational class is further extended by Integer class.
Float 类表示任意精度的浮点数。
Float class represents a floating point number of arbitrary precision.
>>> from sympy import Float
>>> Float(6.32)上述代码段的输出如下：
The output for the above code snippet is as follows −
6.32
6.32
SymPy 可以将整数或字符串转换为浮点数。
SymPy can convert an integer or a string to float.
>>> Float(10)10.0
10.0
Float('1.33E5')# scientific notation133000.0
133000.0
在转换为浮点数的同时，也可以根据如下内容指定用于精度的数字：
While converting to float, it is also possible to specify number of digits for precision as given below −
>>> Float(1.33333,2)上述代码段的输出如下：
The output for the above code snippet is as follows −
1.3
1.3
数字 (p/q) 的表示形式通过 Rational 类对象表示，而 q 是非零数字。
A representation of a number (p/q) is represented as object of Rational class with q being a non-zero number.
>>> Rational(3/4)上述代码段的输出如下：
The output for the above code snippet is as follows −
$\frac{3}{4}$
$\frac{3}{4}$
如果将浮点数传递给 Rational() 构造函数，它将返回其二进制表示的底层值
If a floating point number is passed to Rational() constructor, it returns underlying value of its binary representation
>>> Rational(0.2)上述代码段的输出如下：
The output for the above code snippet is as follows −
$\frac{3602879701896397}{18014398509481984}$
$\frac{3602879701896397}{18014398509481984}$
为了更简单的表示，指定分母限制。
For simpler representation, specify denominator limitation.
>>> Rational(0.2).limit_denominator(100)上述代码段的输出如下：
The output for the above code snippet is as follows −
$\frac{1}{5}$
$\frac{1}{5}$
当字符串传给 Rational() 构造函数时，将返回任意精度的有理数。
When a string is passed to Rational() constructor, a rational number of arbitrary precision is returned.
>>> Rational("3.65")上述代码段的输出如下：
The output for the above code snippet is as follows −
$\frac{73}{20}$
$\frac{73}{20}$
如果传递两个数字参数，也可以获得有理数对象。分子和分母部分作为属性提供。
Rational object can also be obtained if two number arguments are passed. Numerator and denominator parts are available as properties.
>>> a=Rational(3,5)
>>> print (a)
>>> print ("numerator:{}, denominator:{}".format(a.p, a.q))上述代码段的输出如下：
The output for the above code snippet is as follows −
3/5
3/5
numerator:3, denominator:5
numerator:3, denominator:5
>>> a上述代码段的输出如下：
The output for the above code snippet is as follows −
$\frac{3}{5}$
$\frac{3}{5}$
SymPy 中的 Integer 类表示任何大小的整数。构造函数可以接受 Float 或 Rational 数，但会舍弃分数部分。
Integer class in SymPy represents an integer number of any size. The constructor can accept a Float or Rational number, but the fractional part is discarded
>>> Integer(10)上述代码段的输出如下：
The output for the above code snippet is as follows −
10
10
>>> Integer(3.4)上述代码段的输出如下：
The output for the above code snippet is as follows −
3
3
>>> Integer(2/7)上述代码段的输出如下：
The output for the above code snippet is as follows −
0
0
SymPy 有一个 RealNumber 类，充当 Float 的别名。SymPy 还将 Zero 和 One 定义为单例类，分别可以通过 S.Zero 和 S.One 访问，如下所示：
SymPy has a RealNumber class that acts as alias for Float. SymPy also defines Zero and One as singleton classes accessible with S.Zero and S.One respectively as shown below −
>>> S.Zero输出如下 −
The output is as follows −
0
0
>>> S.One输出如下 −
The output is as follows −
1
1
其他预定义单例数字对象包括 Half、NaN、Infinity 和 ImaginaryUnit。
Other predefined Singleton number objects are Half, NaN, Infinity and ImaginaryUnit
>>> from sympy import S
>>> print (S.Half)输出如下 −
The output is as follows −
½
½
>>> print (S.NaN)输出如下 −
The output is as follows −
nan
nan
可以将 Infinity 表示为 oo 符号对象或 S.Infinity
Infinity is available as oo symbol object or S.Infinity
>>> from sympy import oo
>>> oo上述代码段的输出如下：
The output for the above code snippet is as follows −
$\infty$
$\infty$
>>> S.Infinity上述代码段的输出如下：
The output for the above code snippet is as follows −
$\infty$
$\infty$
可以将 ImaginaryUnit 数字导入为 I 符号，或者以 S.ImaginaryUnit 为索引符号进行访问，它表示 -1 的平方根
ImaginaryUnit number can be imported as I symbol or accessed as S.ImaginaryUnit and represents square root of -1
>>> from sympy import I
>>> I执行上述代码片段时，你将获得以下输出 −
When you execute the above code snippet, you get the following output −
i
i
>>> S.ImaginaryUnit上述片段的输出如下 −
The output of the above snippet is as follows −
i
i
>>> from sympy import sqrt
>>> i=sqrt(-1)
>>> i*i执行上述代码片段时，你将获得以下输出 −
When you execute the above code snippet, you get the following output −
-1
-1