matrix - How to represent fractions in python -

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i trying implement method takes matrix matrix class i've defined , returns triagonal matrix using gaussian elimination. consider following matrix:

m1 = [[2, -3, -4],       [-1, 4, 5],       [1, -3, -4]]

basically need add each row, multiple of previous row, until end matrix has 0 in places below main diagonal. following process, should have following matrix:

m2 = [[2, -3, -4],       [0, 5/2, 3],       [0, 0, -1/5]]

the problem fractions 1/3 come , wouldn't want lose precision using floats. there way represent fractions? have define special behaviour those? sake of doing myself don't want use external modules.

there class want: fractions.fraction:

>>> fractions import fraction >>> print(fraction(5, 6)) 5/6

fractions behave regular numbers in 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 fraction gets converted float if other operand float. makes sense, since not expect float of undetermined precision converted fraction.


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