SymPy - Numbers

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 class represents a floating point number of arbitrary precision.
>>> from sympy import Float 
>>> Float(6.32)

The output for the above code snippet is as follows −
6.32
SymPy can convert an integer or a string to float.
>>> Float(10)

10.0
Float('1.33E5')# scientific notation

133000.0
While converting to float, it is also possible to specify number of digits for precision as given below −
>>> Float(1.33333,2)

The output for the above code snippet is as follows −
1.3
A representation of a number (p/q) is represented as object of Rational class with q being a non-zero number.
>>> Rational(3/4)

The output for the above code snippet is as follows −
34
If a floating point number is passed to Rational() constructor, it returns underlying value of its binary representation
>>> Rational(0.2)

The output for the above code snippet is as follows −
360287970189639718014398509481984
For simpler representation, specify denominator limitation.
>>> Rational(0.2).limit_denominator(100)

The output for the above code snippet is as follows −
15
When a string is passed to Rational() constructor, a rational number of arbitrary precision is returned.
>>> Rational("3.65")

The output for the above code snippet is as follows −
7320
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))

The output for the above code snippet is as follows −
3/5
numerator:3, denominator:5
>>> a

The output for the above code snippet is as follows −
35
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)

The output for the above code snippet is as follows −
10
>>> Integer(3.4)

The output for the above code snippet is as follows −
3
>>> Integer(2/7)

The output for the above code snippet is as follows −
0
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

The output is as follows −
0
>>> S.One

The output is as follows −
1
Other predefined Singleton number objects are Half, NaN, Infinity and ImaginaryUnit
>>> from sympy import S 
>>> print (S.Half)

The output is as follows −
1⁄2
>>> print (S.NaN)

The output is as follows −
nan
Infinity is available as oo symbol object or S.Infinity
>>> from sympy import oo 
>>> oo

The output for the above code snippet is as follows −
∞
>>> S.Infinity

The output for the above code snippet is as follows −
∞
ImaginaryUnit number can be imported as I symbol or accessed as S.ImaginaryUnit and represents square root of -1
>>> from sympy import I 
>>> I

When you execute the above code snippet, you get the following output −
i
>>> S.ImaginaryUnit

The output of the above snippet is as follows −
i
>>> from sympy import sqrt 
>>> i=sqrt(-1) 
>>> i*i

When you execute the above code snippet, you get the following output −
-1
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