VPM-B: use an analytic solution for nucleon inner pressure instead of binary root search

According to mathematica

In[4]:= f[x_] := x^3 - b x^2 - c

In[18]:= Solve[f[x] == 0, x]

Out[18]= {{x ->
   1/3 (b + (
      2^(1/3) b^2)/(2 b^3 + 27 c + 3 Sqrt[3] Sqrt[4 b^3 c + 27 c^2])^(
      1/3) + (2 b^3 + 27 c + 3 Sqrt[3] Sqrt[4 b^3 c + 27 c^2])^(1/3)/
      2^(1/3))}, {x ->
   b/3 - ((1 + I Sqrt[3]) b^2)/(
    3 2^(2/3) (2 b^3 + 27 c + 3 Sqrt[3] Sqrt[4 b^3 c + 27 c^2])^(
     1/3)) - ((1 - I Sqrt[3]) (2 b^3 + 27 c +
       3 Sqrt[3] Sqrt[4 b^3 c + 27 c^2])^(1/3))/(6 2^(1/3))}, {x ->
   b/3 - ((1 - I Sqrt[3]) b^2)/(
    3 2^(2/3) (2 b^3 + 27 c + 3 Sqrt[3] Sqrt[4 b^3 c + 27 c^2])^(
     1/3)) - ((1 + I Sqrt[3]) (2 b^3 + 27 c +
       3 Sqrt[3] Sqrt[4 b^3 c + 27 c^2])^(1/3))/(6 2^(1/3))}}

For the values of b and c encounterd in the algorithm, the first solution is in fact the
only real one that we are after. So we can use this solution instead of doing a binary
search for the root of the cubic.

Signed-off-by: Robert C. Helling <helling@atdotde.de>
Signed-off-by: Jan Darowski <jan.darowski@gmail.com>

0 files changed, 0 insertions, 0 deletions