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Let's assume you have the following points a-f, which form the line segments ab and cd and ef. a = {0, 0}; b = {3, 3}; c = {1, .5}; d = {2, 1.5}; e = {0, 2}; f = {2, 0}; In order to test whether they intersect you can use RegionIntersection. First form lines from your points, then use RegionIntersection on the two lines. Compare the intersection to an ...


1

This expression, designated exp for convenience, can be simplified substantially as follows. num = Map[FullSimplify[#] &, Numerator[exp]]; Map[FullSimplify[#, θ[_] ∈ Reals && ϕ[_] ∈ Reals] &, Denominator[exp] /. Abs[z_]^2 :> FullSimplify[Abs[z]^2, θ[_] ∈ Reals && ϕ[_] ∈ Reals]; /. Abs[z_]^2 :> z^2] den = ...



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