SymPy - Numbers

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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 −

$\frac{3}{4}$

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 −

$\frac{3602879701896397}{18014398509481984}$

For simpler representation, specify denominator limitation.

>>> Rational(0.2).limit_denominator(100)

The output for the above code snippet is as follows −

$\frac{1}{5}$

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 −

$\frac{73}{20}$

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 −

$\frac{3}{5}$

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 −

½

>>> 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 −

$\infty$

>>> S.Infinity

The output for the above code snippet is as follows −

$\infty$

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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