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  1. Equivalent definitions for $BMO$

    The space of functions of bounded mean oscillation $BMO$ is defined by the BMO norm \begin{equation} \label{norm} ||f||_{BMO} = \sup_{\text{cubes }Q} \frac{1}{|Q|} \int_Q |u(y) - u_Q| dy \end{equation}

    But an equivalent definition is to take the sup over balls instead of cubes ...

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  2. The space $BMO$

    Introducing $BMO$

    The space of functions of bounded mean oscillation or $BMO$ arises when studying the space of functions whos deviation from the mean over cubes is bounded. In ways $BMO$ is similar to $L^\infty$, and it is often used as a replacement, however functions in $BMO$ may be ...

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  3. GMPY_CFFI mpz speed

    gmpy_cffi is slow

    Today I released version 0.1 of gmpy_cffi, a PyPy compatible implementation of gmpy. The problem is that my implementation is quite a bit slower.

    gmpy_mpz.png

    As you can see, the time taken to initialize an mpz instance is about 10x slower under gmpy_cffi when compared to gmpy ...

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  4. Scoping in Python 3

    Introduction

    Recently I was working on porting my Python2 library gmpy_cffi to work under Python3 as well. I'm using py.test to organise and run my tests. Each test module is in it's own class, and so we have code that looks something like this

    import sys
    import ...
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