I've made modifications in https://github.com/sympy/sympy/pull/267 

When I run the matrices.txt file alone all tests pass. When I run the full 
doctest suite I get the failure below for QR decomposition. When I shut
caching off and run the suite, it passes. How can caching give a wrong
answer? It's not just different, it's wrong as shown below.

    **********************************************************************
    File "c:\documents and settings\chris\sympy\doc\src\modules\matrices.txt", 
line
    374, in matrices.txt
    Failed example:
        Q
    Expected:
        [  ___     ___     ___]
        [\/ 6   -\/ 3   -\/ 2 ]
        [-----  ------  ------]
        [  6      3       2   ]
        [                     ]
        [  ___     ___    ___ ]
        [\/ 6   -\/ 3   \/ 2  ]
        [-----  ------  ----- ]
        [  6      3       2   ]
        [                     ]
        [  ___    ___         ]
        [\/ 6   \/ 3          ]
        [-----  -----     0   ]
        [  3      3           ]
    Got:
        [  ___             ___]
        [\/ 6        -11*\/ 2 ]
        [-----  2/3  ---------]
        [  6             18   ]
        [                     ]
        [  ___            ___ ]
        [\/ 6        -5*\/ 2  ]
        [-----  2/3  -------- ]
        [  6            18    ]
        [                     ]
        [  ___            ___ ]
        [\/ 6        -2*\/ 2  ]
        [-----  1/3  -------- ]
        [  3            9     ]
    **********************************************************************
    File "c:\documents and settings\chris\sympy\doc\src\modules\matrices.txt", 
line
    389, in matrices.txt
    Failed example:
        R
    Expected:
        [           ___         ]
        [  ___  4*\/ 6       ___]
        [\/ 6   -------  2*\/ 6 ]
        [          3            ]
        [                       ]
        [          ___          ]
        [        \/ 3           ]
        [  0     -----      0   ]
        [          3            ]
        [                       ]
        [                   ___ ]
        [  0       0      \/ 2  ]
    Got:
        [           ___         ]
        [  ___  4*\/ 6       ___]
        [\/ 6   -------  2*\/ 6 ]
        [          3            ]
        [                       ]
        [  0       1        4   ]
        [                       ]
        [                    ___]
        [  0       0     3*\/ 2 ]
    **********************************************************************
    1 items had failures:
       2 of  97 in matrices.txt
    ***Test Failed*** 2 failures.
    doc\src\modules\matrices.txt [97]                                           
 [2]

This wouldn't be so bad, but Q*R doesn' even equal the original matrix, giving

    h[2] >>> pprint(Q)
    [  ___             ___]
    [\/ 6        -11*\/ 2 ]
    [-----  2/3  ---------]
    [  6             18   ]
    [                     ]
    [  ___            ___ ]
    [\/ 6        -5*\/ 2  ]
    [-----  2/3  -------- ]
    [  6            18    ]
    [                     ]
    [  ___            ___ ]
    [\/ 6        -2*\/ 2  ]
    [-----  1/3  -------- ]
    [  3            9     ]
    h[2] >>> pprint(R)
    [           ___         ]
    [  ___  4*\/ 6       ___]
    [\/ 6   -------  2*\/ 6 ]
    [          3            ]
    [                       ]
    [  0       1        4   ]
    [                       ]
    [                    ___]
    [  0       0     3*\/ 2 ]
    h[2] >>> Q*R
    [1, 2, 1]
    [1, 2, 3]
    [2, 3, 4]

Q*R should be
    [1, 1, 1]
    [1, 1, 3]
    [2, 3, 4]

Does anyone have any idea what the problem might be? I don't even 
know how to go about debuging this?

/c

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