Implementation of hemireal arithmetic for Julia
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2 Years Ago
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December 2015


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A hemireal number z can be written

z = r ++

where r, m, and n are real, and the special numbers μ, ν satisfy

μ*μ = ν*ν = 0, μ*ν = ν*μ = 1.

Addition, subtraction, and any operation involving real numbers are defined "the obvious way," and the conjugate of z is just z. Multiplication of general hemireals is commutative but not associative. Hemireals with ν=0 are the same as dual numbers.

The motivation for inventing/rediscovering (?) the hemireals was to solve, using finite numbers, what would otherwise be singular equations.