Re: Pisot numbers When the third edition of the Mathematica Book came out in 1996, it included this neat example in its Formula Gallery: http://reference.wolfram.com/legacy/v4/MainBook/G.1.2.html For the most recent version of Mathematica, a Pisot sampler is relegated to a "neat example" for Root and an application for FractionalPart. And for the function AlgebraicIntegerQ we learn how to recognize a Pisot number: In[1]:= pisotNumberQ[a_] := AlgebraicIntegerQ[a] && Element[a, Reals] && (a > 1) && (Count[ List @@ (Last /@ Roots[MinimalPolynomial[a, x] == 0, x]), _?(Abs[#] > 1 &)] == 1) So, to borrow Bill's tribonacci constant… In[2]:= pisotNumberQ[1/3 (1 + (19 - 3 Sqrt[33])^(1/3) + (19 + 3 Sqrt[33])^(1/3))] Out[2]= True