Linear system solution with fractions in numpy

Question

I have matrix A and a right-hand-side vector y expressed in terms of fractions.Fraction objects:

import random, fractions, numpy as np

A = np.zeros((3, 3), dtype=fractions.Fraction)
y = np.zeros((3, 1), dtype=fractions.Fraction)
for i in range(3):
    for j in range(3):
        A[i, j] = fractions.Fraction(np.random.randint(0, 4), np.random.randint(1, 6))
    y[i] = fractions.Fraction(np.random.randint(0, 4), np.random.randint(1, 6))

I would like to solve the system A*x = y using the provided functions in numpy and get a result expressed in fraction objects, but unfortunately the basic x = np.linalg.solve(A, y) returns the result in standard floating point values:

>>> np.linalg.solve(A, y)

array([[-1.5245283 ],
       [ 2.36603774],
       [ 0.56352201]])

Is there a way of getting the exact result with fraction objects?

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EDIT

What I would like to do is just not feasible with the built-in functionalities of numpy (as of version 1.10 - see Mad Physicist's answer). What one could do is implementing his/her own linear solver based on Gauss elimination, which relies on sum, subtraction, multiplication and division, all of which are well-defined and executed exactly with fraction objects (as long as the numerators and denominators fit in the data type, which I think is arbitrarily long).

If you are really interested in having this, just implement a solver yourself, it will be easy and fast to do (follow one of the many tutorials online). I'm not that much interested, so I will stick to the floating point result.

Answer 1

It does not appear to be possible to invert a matrix of rationals using pure numpy according to this thread on the python mailing list. The response suggests that you can use sympy for matrices of rationals up to size 4x4. If you are tied to numpy for some reason, you can consider taking and using the inverse of a 3x3 matrix "manually". Step by step tutorials on how to do this can be found on http://www.mathsisfun.com/algebra/matrix-inverse-minors-cofactors-adjugate.html, as well as a large multitude of other tutorials on matrix inversion.