Mathematica Part of complex plot disappears [mathematica]

1. Apr 19, 2017

illuminates

I have a very large expression:

Code (Text):

j - Sqrt[q^2 + qp^2 -
2 q qp Cos[\[Theta]]] - \[Sqrt](qp^2 +
1/2 (16 m5^2 + ma^2 + mp^2 -
Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0

where
Code (Text):

\[Theta] = Pi/6; ma = 980; mp = 139;
j = \[Sqrt](q^2 +
1/2 (16 m5^2 + ma^2 + mp^2 +
Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
4 (ma^2 mp^2 - 16 m5^2 q^2)]))

And qp, m5, q is real and positive.

There is two method to solve it, but they give some different result.
Namely, let's look at both methods

First solution

Code (Text):

eqn = j -
Sqrt[q^2 + qp^2 -
2 q qp Cos[\[Theta]]] - \[Sqrt](qp^2 +
1/2 (16 m5^2 + ma^2 + mp^2 -
Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0;
With[{gensol = Solve[eqn , qp]},
Block[{\[Theta] = Pi/6, ma = 980, mp = 139,
j},(*subs vals when gensol is evaluated*)
j = \[Sqrt](q^2 +
1/2 (16 m5^2 + ma^2 + mp^2 +
Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
4 (ma^2 mp^2 - 16 m5^2 q^2)]));
sols = gensol]];
qpC13 = Compile[{{q, _Complex}, {m5, _Complex}},
Evaluate[qp /. sols[[3]]],
RuntimeOptions -> "EvaluateSymbolically" -> False] ;
Plot3D[Re@qpC13[q, m5], {q, 0, 10000}, {m5, 0, 2000},
AxesLabel -> Automatic]

Second solution

Code (Text):

eqn = j -
Sqrt[q^2 + qp^2 -
q qp Cos[\[Theta]]] - \[Sqrt](qp^2 +
1/2 (16 m5^2 + ma^2 + mp^2 -
Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0;

With[{gensol = Solve[eqn, qp]},
Block[{\[Theta] = Pi/6, ma = 980, mp = 139, j},
j = \[Sqrt](q^2 +
1/2 (16 m5^2 + ma^2 + mp^2 +
Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
4 (ma^2 mp^2 - 16 m5^2 q^2)]));
sols = gensol]];
opt = Experimental`OptimizeExpression[qp /. sols[[3]]];
Block[{\[Theta] = Pi/6, f},
f[q0_, m50_] :=
Block[{q = SetPrecision[q0, 40], m5 = SetPrecision[m50, 40], qp},
qp = First@opt;
Re@qp /; Im@qp == 0];
Plot3D[f[q, m5], {q, 0, 10000}, {m5, 0, 1000}, MaxRecursion -> 3,
AxesLabel -> Automatic]]

The part of plot disappears in second solution! Why is this happening?

Last edited: Apr 19, 2017
2. Apr 24, 2017

PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.