Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it. As an example, we show how we have detected an error of Mathematica computing determinants of matrices of integer numbers: not only it computes the determinants wrongly, but also it produces different results if one evaluates the same determinant twice.

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For two weights u, w on In, we show that w E Ap,. (the Muckenhoupt class of weights) if and only if wu Ap and wu-p Ap, under the assumption that u E A,. for every r > 1. We also prove a rather general result on pasting weights on E that satisfy the Ap condition.