In the computational topology literature, the reduction algorithm for computing the Smith normal form of a boundary matrix uses the notation $b_j > 1 \: \text{ and }\: b_j\mid b_{j+1}$ in the context of the diagonal elements of the Smith matrix. Can anyone give me an idea for what it means?
What does $b_i\mid b_{i+1}$ mean in this context?
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linear-algebra
abstract-algebra
algebraic-topology
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2yes, it's standard notation in this context. – 2010-12-31
1 Answers
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The $b_i$ are integers and $|$ stands for "divides."
-Qiaochu Yuan
Yes, it's standard notation in this context.
-lhf
See also Wikipedia's "List of mathematical symbols" and "Vertical bar."