Rational class
A Rational class instance represents a rational number.
Initialisation
A new Rational requires a numerator and denominator.
For example, to create the rational number 2/3:
two_thirds = Rational(2, 3) # 2/3
From a floating-point number
A Rational can also be created from a float by calling from_float.
two_and_a_half = Rational.from_float(2.5) # 5/2
From a string
Finally, a Rational can also be created by passing a string to from_string.
The string is expected to be either:
- a fraction in the form
x/yor-x/y, or: - a decimal in the form
x,-x,x.yor-x.y, where.is your local culture's decimal marker.
two_thirds = Rational.from_string("2/3") # 2/3
two_and_a_half = Rational.from_string("2.5") # 5/2
Mathematic operations
The following operations can be performed between a Rational and:
intfloatstr- other
Rationalinstances
Addition
Rational(1, 3) + Rational(1, 4) # 7/12
Rational(1, 3) + 0.25 # 7/12
Rational(1, 3) + "0.25" # 7/12
Rational(1, 3) + "1/4" # 7/12
Subtraction
Rational(2, 3) - Rational(1, 4) # 5/12
Rational(2, 3) - 0.25 # 5/12
Rational(2, 3) - "0.25" # 5/12
Rational(2, 3) - "1/4" # 5/12
Multiplication
Rational(2, 4) * Rational(3, 6) # 1/4
Rational(2, 4) * 0.5 # 1/4
Rational(2, 4) * "0.5" # 1/4
Rational(2, 4) * "4/8" # 1/4
True division
Rational(20, 4) / Rational(17, 8) # 40/17
Rational(20, 4) / 2.125 # 40/17
Rational(20, 4) / "2.125" # 40/17
Rational(20, 4) / "17/8" # 40/17
Floor division
Floor division returns a Rational that describes the integral result of the division.
Rational(20, 4) // Rational(17, 8) # 2/1
Rational(20, 4) // 2.125 # 2/1
Rational(20, 4) // "2.125" # 2/1
Rational(20, 4) // "17/8" # 2/1
Comparison
Equality
Rational(2, 4) == Rational(3, 6) # True
Rational(2, 4) == 0.5 # True
Rational(2, 4) == "0.5" # True
Rational(2, 4) == "4/8" # True
Greater than
Rational(2, 3) > Rational(1, 4) # True
Rational(2, 3) > 0.25 # True
Rational(2, 3) > "0.25" # True
Rational(2, 3) > "1/4" # True
Greater than or equal to
Rational(2, 3) >= Rational(1, 4) # True
Rational(2, 3) >= 0.25 # True
Rational(2, 3) >= "0.25" # True
Rational(2, 3) >= "1/4" # True
Less than
Rational(2, 3) < Rational(1, 4) # False
Rational(2, 3) < 0.25 # False
Rational(2, 3) < "0.25" # False
Rational(2, 3) < "1/4" # False
Less than or equal to
Rational(2, 3) <= Rational(1, 4) # False
Rational(2, 3) <= 0.25 # False
Rational(2, 3) <= "0.25" # False
Rational(2, 3) <= "1/4" # False
Integral and fractional parts
The integral property returns the integral part of the number, and fractional returns the fractional part.
For example, given 3/2, the integral part is 1 (i.e. 2/2) and the fractional part is 1/2.
Decimal string
The decimal function returns the Rational as a decimal string.
Rational(33, 8).decimal() # "4.125"
By default, decimal will return no more than 100 decimal places. To adjust this, set the max_dp argument. This is limited only by your available memory and patience.
Rational(355, 113).decimal(max_dp=6) # "3.141592"
By default, decimal will monitor for recurring digits and represent them with an overhead dot.
Rational(1, 3).decimal() # "0.̇3"
If you prefer, you can disable recursion tracking by setting recursion=False.
Rational(1, 3).decimal(max_dp=6, recursion=False) # "0.333333"
Also, if you prefer, you can change the overhead dot to any string by setting recurring_prefix. For example, \u0305 is an overhead line.
Rational(1, 3).decimal(recurring_prefix="\u0305") # "0.̅3"
Tip
To get the true floating-point value of a Rational, convert it to a float via Python's built-in float() function.
float(Rational(4, 3)) # 1.3333333333333333
Reciprocals
The reciprocal property returns the reciprocal of the Rational.
Rational(1, 3).reciprocal # 3/1
Reduction
The reduced property returns the Rational in its most-simplified form.
Rational(25767, 34356).reduced # 3/4
Converting to floating-point and integer numbers
To get the true floating-point value of a Rational, convert it to a float via Python's built-in float() function.
float(Rational(4, 3)) # 1.3333333333333333
Likewise, use the built-in int() function to get the integral value as an int.
int(Rational(4, 3)) # 1