Numeric Types

Sympy library has the numeric types Rational and Real. The Rational class represents a rational number as a pair of two integers: the numerator and the denominator, so Rational(1,4) represents 1/4, Rational(5,2) represents 5/2:

>>> a = sympy.Rational(1,10)
>>> a
1/10
>>> b = sympy.Rational(45,46)
>>> b
45/46
>>> a*b
9/92
>>> a-b
-101/115
>>> a+b
124/115

Rational class works with rational expressions exactly. This is in contrast to Python’s standard float data type which uses floating point representation to approximate numbers. We can convert the sympy.Rational type into a Python floating point variable using float or the evalf method of the Rational object. The evalf method can take an argument that specifies how many digits should be computed for the floating point approximation.

>>> c = sympy.Rational(5,6)
>>> c
5/6
>>> float(c)
0.8333333333333334
>>> c.evalf()
0.833333333333333
>>> c.evalf(20)
0.83333333333333333333