Why Mathematica 12.1 is taking so long time in solving non-linear equations

Question

I tried to implement simple non-relativistic and relativistic elastic collisions between two masses in one dimension, they are 2 non-linear, equations for two unknowns. I give it a try on Mathematica 12.1 since I bought a new licence. It took too much time (didn't end in case of relativistic collision)

The code of non-relativistic:

    Solve[m1*v1 + m2*v2 == m1*u1 + m2*u2 && 
  m1*v1^2 + m2*v2^2 == m1*u1^2 + m2*u2^2, {u1, u2}]

The code of relativistic:

    FullSimplify[
 Solve[m1*v1*(1/Sqrt (1 - (v1/C)^2)) + m2*v2*(1/Sqrt (1 - (v2/C)^2)) ==
     m1*u1*(1/Sqrt (1 - (u1/C)^2)) + m2*u2*(1/Sqrt (1 - (u2/C)^2)) && 
   m1*C^2*(1/Sqrt (1 - (v1/C)^2)) + m2*C^2*(1/Sqrt (1 - (v2/C)^2)) == 
    m1*C^2*(1/Sqrt (1 - (u1/C)^2)) + 
     m2*C^2*(1/Sqrt (1 - (u2/C)^2)) , {u1, u2}]]

Thanks for help

AbsoluteTiming yields {0.005526, {{u1 -> v1, u2 -> v2}, {u1 -> (m1 v1 - m2 v1 + 2 m2 v2)/(m1 + m2), u2 -> (2 m1 v1 - m1 v2 + m2 v2)/(m1 + m2)}}} on 12.1.1 for Linux x86 (64-bit) (June 19, 2020) — Acus, Sep 17 '20 at 17:10
Maybe because I am working in multiple Notebooks in parallel. I will try to restart the software and work only in this notebook — Ahmed Kamal Kassem, Sep 17 '20 at 17:23
Weird!! When I closed all sheets and restarted the software it solved it in less than second. Thanks for your help — Ahmed Kamal Kassem, Sep 17 '20 at 17:24
What about the relativistic collision, I will add it in the question — Ahmed Kamal Kassem, Sep 17 '20 at 17:34
The relativistic expression requires approximately 11 seconds to solve on my machine. Win7 x64 running 12.0. — eyorble, Sep 17 '20 at 17:59
@eyorble I find such expressions, do you know the meaning?
Root[{#1^2 + 1 &, -6 #1 #2^3 - 6 #1 #2^2 + 19 #1 #2 + 32 #1 + #2^5 + 2 #2^4 - 2 #2^3 - 10 #2^2 - 4 #2 - 2 &}, {2, 1}]^2 — Ahmed Kamal Kassem, Sep 17 '20 at 18:25
When you work in multiple notebooks they all use the same kernel unless you have started each with its own session. This means they share symbol definitions. — David Keith, Sep 17 '20 at 18:37
@AhmedKamalKassem See: https://mathematica.stackexchange.com/questions/13767/how-do-i-work-with-root-objects/126156#126156 for a short-ish explanation of Root objects. They're solutions to polynomials, in this case in two variables. #1 and #2 are anonymized names for the variables of those polynomials, see anonymous functions (& in the documentation should be a decent start). — eyorble, Sep 17 '20 at 19:37
The square roots are missing brackets. Was that a transcription error or is that the actual code? — Daniel Lichtblau, Sep 17 '20 at 23:10
Sqrt (1 - (v2/C)^2) how is missing a bracket? you mean it should be [ ... ] bracket? It is in the original code — Ahmed Kamal Kassem, Sep 18 '20 at 02:31

Why Mathematica 12.1 is taking so long time in solving non-linear equations

The code of non-relativistic:

The code of relativistic:

0 Answers0