I am trying to implement a method that takes a matrix from the matrix class i've defined and returns a triagonal matrix using gaussian elimination. Consider the following matrix:
m1 = [[2, -3, -4],
[-1, 4, 5],
[1, -3, -4]]
Basically i need to add to each row, a multiple of another previous row, until i end up with a matrix which has 0 in all places below the main diagonal. Following this process, i should have the following matrix:
m2 = [[2, -3, -4],
[0, 5/2, 3],
[0, 0, -1/5]]
The problem is that fractions like 1/3 will often come up and i wouldn't want to lose precision by using floats. So is there any way to represent fractions? Will i have to define special behaviour for those? For the sake of doing it by myself i don't want to use any external modules.
There is a class that does exactly what you want: fractions.Fraction:
>>> from fractions import Fraction
>>> print(Fraction(5, 6))
5/6
Fractions behave like regular numbers in most situations:
>>> print(Fraction(5, 6) + 6)
41/6
>>> print(Fraction(5, 6) + Fraction(1, 2))
4/3
>>> print(Fraction(5, 6) + 17.445)
18.278333333333332
The last example shows that the fraction gets converted to a float if the other operand is a float. This makes sense, since you would not expect a float of undetermined precision to be converted to a Fraction.