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Add arclength #20

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dlfivefifty opened this issue Jul 26, 2018 · 3 comments
Open

Add arclength #20

dlfivefifty opened this issue Jul 26, 2018 · 3 comments

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@dlfivefifty
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I'm not sure what the conclusion was what to call it, but there should be some version of arclength for an interval.

It could be called lebesguemeasure, though that's a bit confusing for intervals embedded in the complex plane, as the measure with respect to dx*dy would be zero....

@daanhb
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daanhb commented Jul 26, 2018

I'm fine with arclength, but the cases you mention can also be distinguished. Any Interval{T} where T <: Real has non-zero Lebesgue measure, and the current way to embed an interval in the complex plane is to explicitly use an embedding: i = embedding_map(Float64, Complex128) * interval(). (Nicer syntax would be welcome.) One could probably make it so that the lebesgue measure of i is zero in this case, since the embedding map knows the difference in dimension of the spaces.

@dlfivefifty
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I usre Segment(a::Complex,b::Complex) for line segments in the complex plane, so don't need embedding_map.

@dlfivefifty
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IntervalSets.jl uses width(d), which I think is fine.

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