Dual numbers are mathematically modeled using square matrices. Let J be the n×n matrix with 1 above the main diagonal and 0 everywhere else. We have

Jk ≠ Jm for 0 ≤ k < m < n,

so they provide a model of dual numbers of order n.

The software implementation represents the dual number d = d0 I + ⋅⋅⋅ + dn - 1/(n - 1)! Jn - 1 as a C++ std::array d = {d0, ..., dn - 1}.

Last edited Nov 14, 2011 at 12:25 AM by keithalewis, version 1

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