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In the computational topology literature, the reduction algorithm for computing the Smith normal form of a boundary matrix uses the notation $b_j > 1 \: \text{and}\: b_j|b_{j+1}$ in the context of the diagonal elements of the Smith matrix. Can anyone give me an idea for what it means?

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The b_i are integers and | stands for "divides." –  Qiaochu Yuan Dec 31 '10 at 12:45
Ahhh. Thanks very much. That makes perfect sense. I assume this is standard notation, perhaps in algebra or number theory? –  niale Dec 31 '10 at 12:47
yes, it's standard notation in this context. –  lhf Dec 31 '10 at 17:22

1 Answer 1

The $b_i$ are integers and $|$ stands for "divides."

-Qiaochu Yuan

Yes, it's standard notation in this context.


See also Wikipedia's "List of mathematical symbols" and "Vertical bar."

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