Some more of the minimal Pisot types beyond the pentic:
(* Mathematica: sequence of minimal Pisots and near minimal Pisots*)
Clear[p, \
q]
(* list of probable minimal Pisot polynomials*)
p = {-1, x - 1, x^2 - x - 1,
x^3 - x - 1,
x^4 - x^3 - 1, -1 + x^2 - x^3 - x^4 + x^5, -1 + x^2 - x^4 - x^5 + x^6, -1 +
x^2 - x^5 - x^6 + x^7, -1 + x^2 - x^6 - x^7 + x^8, -1 + x^2 - x^7 - x^8 +
x^9, -1 + x^2 - x^8 - x^9 + x^10, -1 + x^2 - x^9 - x^10 + x^11, -1 + x^2 -
x^10 - x^11 + x^12, -1 + x^2 - x^11 - x^12 + x^13, -1 + x^2 - x^12 - x^13 +
x^14, -1 + x^2 - x^13 - x^14 + x^15, -1 + x^2 - x^14 - x^15 + x^16, -1 +
x^2 - x^15 - x^16 + x^17, -1 + x^2 - x^16 - x^17 + x^18, -1 + x^2 - x^17 -
x^18 + x^19, -1 + x^2 - x^18 - x^19 + x^20}
Clear[q]
q[x_, i_] := ExpandAll[x^(i - 1)*(p[[i]] /. x -> 1/x)] TableForm[Table[CoefficientList[p[[i]], x], {i, Length[p]}]]
Table[Apply[Plus, CoefficientList[p[[i]], x]], {i, Length[p]}] TableForm[Table[CoefficientList[Expand[q[x, i]], x], {i, Length[p]}]]
aa = Table[{Re[x], Im[x]} /. NSolve[p[[i]] == 0, x], {i, 2, Length[p]}] ListPlot[Flatten[aa, 1], PlotStyle -> Red]
(* end*)
(*Mathematica*)
p8 = x /. NSolve[-1 + x^2 - x^6 - x^7 + x^8 == 0, x][[8]]
p[x_] = -1 + x^2 - x^6 - x^7 + x^8
q[x_] = ExpandAll[x^8*p[1/x]]
toRGBs[h_] :=
If[h >= 0.,(*Color function*)List @@ Blend["DarkRainbow", h](*outside*),
List @@ Blend["CMYKColors", -h]] (*inside*);
wrongbrot =
Compile[{{x, _Real}, {y, _Real}},
Module[{ct = 0, t, c = x + y I, z = x + y I, min = 10., count = 0},
While[Abs[z] < 32 && ct++ <= 32^2, z = N[Exp[I*2*Pi*p8]]*z^2*p[z]/q[z];
If[Abs[z] < min, min = Abs[z]; count = ct]];
If[ct <= 200,
Mod[Abs[Arg[x + I*y]]/(2*Pi)*Log[ct + 1],
1], -Mod[Abs[Arg[x + I*y]/(4*Pi)]*count*Sqrt[8.], 1.]]]];
center = {-0.5, .0}; size = {3., 3.};
xres = 1501; dx = dy = 2*size[[1]]/(xres - 1);
{{xl, yl}, {xh, yh}} = {{-1.45001, -1.85}, {2.25, 1.85}};
cols = Table[
toRGBs[Log[1 + wrongbrot[x, y]]], {y, yl, yh, dy}, {x, xl, xh, dx}];
g = Graphics[Raster[cols], ImageSize -> 1500]
(*end*)
https://scontent-lax3-1.xx.fbcdn.net/v/t1.0-9/20229347_10155517592961499_2088088800225894885_n.jpg?oh=d3a40318a68e3309237e943b56f44f4c&oe=5A04D46D
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
