two trace Pseudo-Pisot:

Based on the 3x3 SL(3,R) matrix:

m = {{0, (4/3)^(1/3), 0}, {0, 0, (Sqrt[3]/2)^(1/3)}, {(Sqrt[3]/2)^(1/3), (Sqrt[3]/2)^(1/3), 0}}

CharacteristicPolynomial[m, x]
1 + (3^(1/3) x)/2^(2/3) - x^3

The Pseudo-Pisot polynomial solved to two traces:

r[i_] := -x /. NSolve[1 + (3^(1/3) x)/2^(2/3) - x^3 == 0, x][[i]]
t1 = r[1] + 1/r[1]
(*first trace*)
t2 = r[2] + 1/r[2]
(*second trace *)

In general the Pseudo-Pisot has a lower Eigenvalue at: 1.2961723106869747

than the Minimal Pisot at:1.324717957244746

Mathematica:

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Tags:#Minimal Pisot,#two trace,#polynomial,#kleinian group,#roger bagula