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Very large time of evaluation of the ImplicitRegion

Discussion in 'Mathematics' started by John Taylor, Oct 8, 2018.

  1. John Taylor

    John Taylor Guest

    I have a following implicit region:

    Cosalpha[x_, y_, cosz_] = cosz*Sin[x]*Sin[y] + Cos[x]*Cos[y];
    Cosalphamin[E1_, m1_, m2_] =
    1/(2*m2)*Sqrt[4 E1^2 m2^2 - m2^4 - 2 m2^2 m1^2 - m1^4]/
    Sqrt[E1^2 - m1^2]
    E1crit[m1_, m2_] = (m1^2 + m2^2)/(2*m2);
    coszmin[m1_, E1_, m2_, x_, y_] =
    If[E1 > E1crit[m1, m2],
    cosz /. Solve[Cosalpha[x, y, cosz] - cosalphamin == 0,
    cosz][[1]] /. cosalphamin -> Cosalphamin[E1, m1, m2], -1]
    Regionxy[m1_, E1_, m2_] :=
    coszmin[m1, E1, m2, x, y] <= 1, {{x, 0, Pi}, {y, 0, Pi}}]

    When I try to visualize the region using RegionPlot for E1 > E1crit, Mathematica stucks:

    RegionPlot[Regionxy[2, 5*E1crit[2, 6.3], 6.3]]

    I don't understand why it fails. Is there some qualitative reason, or it is simply numerical? Anyway, is there some way to make the evaluation faster?

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