Pensieve header: Not solving the quintic in MAT 1750 - background matter.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2015-04\\Commutators"];
PRoot[name_, a_, n_] := PRoot[name, n] = If[NumberQ[PRoot[name, n]],
MinimalBy[N[(a^(1/n))]Table[(E^(2π I k/n)), {k,n}],Abs[#-PRoot[name,n]]&][[1]],
(a^(1/n))];
InputBackground=Graphics[{Pink, Disk[],Red, Point[{0,0}],
Table[{Line[{{t,-1},{t,1}}], Line[{{-1,t},{1,t}}]}, {t,-1,1,2/3}]}];
OutputBackground = {LightBlue, Disk[],Blue, Point[{0,0}],
Table[{Line[{{t,-1},{t,1}}], Line[{{-1,t},{1,t}}]}, {t,-1,1,2/3}],
Black};
Pt@c_ := {Re[c],Im[c]};

Import["Commutators-Handout_800.png"]

Decommute = p[j_,k_,m_] :>  Module[{i,l},
{i,l}=Complement[Range[5],{j,k,m}];
c[p[i,j,k],p[k,l,m]]];
Format[p[i_,j_,k_]] := "("<>ToString[i]<>ToString[j]<>ToString[k]<>")";
Format[c[a_,b_]] := "["<>ToString[a]<>","<>ToString[b]<>"]";
Column[{p[2,3,5] /. Decommute, dc= p[1,2,3] /. Decommute,
dc=dc/.Decommute,dc=dc/.Decommute,dc=dc/.Decommute}]

Button["Play", SystemOpen["../../2015-01/Commutators/SwordFight.mp4"]]

Module[{λ1,λ2,x,a,b,c,Δ,δ,r},
{λ1,λ2}={{1,1}/2, {1,-1}/2};
GraphicsGrid[Partition[#,3]& @ {
LocatorPane[Dynamic[{λ1,λ2}],InputBackground, Appearance -> {"(Subscript[λ, 1])", "(Subscript[λ, 2])"}],
Dynamic[Graphics[{OutputBackground,
{c,b,a}=CoefficientList[(x-{1,I}.λ1)(x-{1,I}.λ2), x];
Text["a", {Re[a],Im[a]}], Text["b", {Re[b],Im[b]}], Text["c",{Re[c],Im[c]}]
}, PlotRange->All, PlotLabel -> "(x-(Subscript[λ, 1]))(x-(Subscript[λ, 2]))=(ax^2)+bx+c"]],
Dynamic[Graphics[{OutputBackground,
Δ=(b^2)-4 a c; Text["Δ",{Re[Δ], Im[Δ]}]
}, PlotRange->All, PlotLabel -> "Δ=(b^2)-4ac"]],
Dynamic[Graphics[{OutputBackground,
δ=PRoot["Δ[2]", Δ,2]; Text["δ", {Re[δ], Im[δ]}]
}, PlotRange->All, PlotLabel -> "δ=(Sqrt[Δ])"]],
Dynamic[Graphics[{OutputBackground,
r=(-b+δ)/(2a); Point[{Re[r], Im[r]}]
}, PlotRange->All, PlotLabel -> "r=(-b+δ)/(2a)"]],
Null }] ]