(* ::Package:: *)

(************************************************************************)\012(* This file was generated automatically by the Mathematica front end.  *)\012(* It contains Initialization cells from a Notebook file, which         *)\012(* typically will have the same name as this file except ending in      *)\012(* ".nb" instead of ".m".                                               *)\012(*                                                                      *)\012(* This file is intended to be loaded into the Mathematica kernel using *)\012(* the package loading commands Get or Needs.  Doing so is equivalent   *)\012(* to using the Evaluate Initialization Cells menu command in the front *)\012(* end.                                                                 *)\012(*                                                                      *)\012(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)\012(* automatically each time the parent Notebook file is saved in the     *)\012(* Mathematica front end.  Any changes you make to this file will be    *)\012(* overwritten.                                                         *)\012(************************************************************************)\012\012

(* ::Input::Initialization:: *)
SetDirectory["C:\\drorbn\\AcademicPensieve\\Talks\\CUMC-200820"];
SetOptions[Graphics, ImageSize->{200,200}];
PRoot[name_, a_, n_] := PRoot[name, n] = If[NumberQ[PRoot[name, n]],
MinimalBy[
N[a^(1/n)]Table[E^(2\[Pi] 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]};


(* ::Input::Initialization:: *)
Import["Quintic-Handout.pdf"][[1]]


(* ::Input::Initialization::Plain:: *)
Module[{a0,b0,c0,a,b,c,\[CapitalDelta],\[Delta],r},
{a0,b0,c0}={{1,0},{0,0},{0,1/3}};
LocatorPane[Dynamic[{a0,b0,c0}],InputBackground, Appearance -> {"a", "b", "c"}]
->Dynamic[Graphics[{OutputBackground,
a={1,I} . a0; b={1,I} . b0; c={1,I} . c0;
\[CapitalDelta]=b^2-4 a c;
Text["\[CapitalDelta]",{Re[\[CapitalDelta]], Im[\[CapitalDelta]]}]
}, PlotRange->All, PlotLabel -> "\[CapitalDelta]=\!\(\*SuperscriptBox[\(b\), \(2\)]\)-4ac"]]
->Dynamic[Graphics[{OutputBackground,
\[Delta]=PRoot["\[CapitalDelta][2]", \[CapitalDelta],2];
Text["\[Delta]", {Re[\[Delta]], Im[\[Delta]]}]
}, PlotRange->All, PlotLabel -> "\[Delta]=\!\(\*SqrtBox[\(\[CapitalDelta]\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,PointSize[Large],
r=(-b+\[Delta])/(2a);
Point[{Re[r], Im[r]}]
}, PlotRange->All, PlotLabel -> "r=(-b+\[Delta])/(2a)"]]
]


(* ::Input::Initialization::Plain:: *)
DynamicModule[{\[Lambda]1,\[Lambda]2,x,a,b,c,\[CapitalDelta],\[Delta],r},
{\[Lambda]1,\[Lambda]2}={{1,1}/2, {1,-1}/2};
LocatorPane[Dynamic[{\[Lambda]1,\[Lambda]2}],InputBackground, Appearance -> {"\!\(\*SubscriptBox[\(\[Lambda]\), \(1\)]\)", "\!\(\*SubscriptBox[\(\[Lambda]\), \(2\)]\)"}]
-> Dynamic[Graphics[{OutputBackground,
{c,b,a}=CoefficientList[(x-{1,I} . \[Lambda]1)(x-{1,I} . \[Lambda]2), x];
Text["a", {Re[a],Im[a]}], Text["b", {Re[b],Im[b]}], Text["c",{Re[c],Im[c]}]
}, PlotRange->All, PlotLabel -> "(x-\!\(\*SubscriptBox[\(\[Lambda]\), \(1\)]\))(x-\!\(\*SubscriptBox[\(\[Lambda]\), \(2\)]\))=\!\(\*SuperscriptBox[\(ax\), \(2\)]\)+bx+c"]]
-> Dynamic[Graphics[{OutputBackground,
\[CapitalDelta]=b^2-4 a c;
Text["\[CapitalDelta]",{Re[\[CapitalDelta]], Im[\[CapitalDelta]]}]
}, PlotRange->All, PlotLabel -> "\[CapitalDelta]=\!\(\*SuperscriptBox[\(b\), \(2\)]\)-4ac"]]
-> Dynamic[Graphics[{OutputBackground,
\[Delta]=PRoot["\[CapitalDelta][2]", \[CapitalDelta],2];
Text["\[Delta]", {Re[\[Delta]], Im[\[Delta]]}]
}, PlotRange->All, PlotLabel -> "\[Delta]=\!\(\*SqrtBox[\(\[CapitalDelta]\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,PointSize[Large],
r=(-b+\[Delta])/(2a);
Point[{Re[r], Im[r]}]
}, PlotRange->All, PlotLabel -> "r=(-b+\[Delta])/(2a)"]]
]


(* ::Input::Initialization:: *)
b1={{1,0}};
{LocatorPane[Dynamic[b1],InputBackground], 
Dynamic[Graphics[{OutputBackground, PointSize[Large],Point[r=Power[b1[[1,1]]+I b1[[1,2]], (2)^-1]; {Re[r], Im[r]}]}, PlotRange->All, PlotLabel -> "A Square Root"]],Dynamic[Graphics[{OutputBackground, PointSize[Large],Point[r=PRoot["ex",b1[[1,1]]+I b1[[1,2]],2]; {Re[r], Im[r]}]}, PlotRange->All, PlotLabel -> "A Persistent Square Root"]]
}


(* ::Input::Initialization:: *)
Button["Play", SystemOpen["../../2015-01/Commutators/LeadingQuestions.mp4"]]


(* ::Input::Initialization:: *)
DynamicModule[{a0,b0,c0,d0,a,b,c,d,x,\[CapitalDelta],\[Delta],\[CapitalGamma],\[Gamma],r},
{a0,b0,c0,d0}={{0,-1/3},{0,0},{1/3,0},{-1/3,0}};
LocatorPane[Dynamic[{a0,b0,c0,d0}],InputBackground,Appearance -> {"a", "b", "c", "d","e"}]
-> Dynamic[Graphics[{OutputBackground,
a={1,I} . a0; b={1,I} . b0; c={1,I} . c0; d={1,I} . d0;
\[CapitalDelta]= -18a b c d+4b^3 d-b^2 c^2+4a c^3+27a^2 d^2;
Text["\[CapitalDelta]", {Re[\[CapitalDelta]],Im[\[CapitalDelta]]}]
}, PlotRange->All, PlotLabel ->"\[CapitalDelta]"]]
-> Dynamic[Graphics[{OutputBackground,
\[Delta]=PRoot["3\[CapitalDelta]",\[CapitalDelta],2];
Text["\[Delta]", {Re[\[Delta]],Im[\[Delta]]}]
}, PlotRange->All, PlotLabel ->"\[Delta]=\!\(\*SqrtBox[\(\[CapitalDelta]\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,
\[CapitalGamma]= 2b^3-9a b c+27a^2 d+3Sqrt[3]a \[Delta];
Text["\[CapitalGamma]", {Re[\[CapitalGamma]],Im[\[CapitalGamma]]}]
}, PlotRange->All, PlotLabel -> "\[CapitalGamma]"]]
-> Dynamic[Graphics[{OutputBackground,
\[Gamma]=PRoot["\[CapitalGamma]",\[CapitalGamma]/2,3];
Text["\[Gamma]", {Re[\[Gamma]],Im[\[Gamma]]}]
}, PlotRange->All, PlotLabel -> "\[Gamma]=\!\(\*RadicalBox[\(\[CapitalGamma]/2\), \(3\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,
r=-(b+\[Gamma]+(b^2-3a c)/\[Gamma])/(3a);
Text[Style["r",Bold, Large], {Re[r], Im[r]}]
}, PlotRange->All, PlotLabel->"r"]]
]


(* ::Input::Initialization:: *)
DynamicModule[{\[Lambda]1,\[Lambda]2,\[Lambda]3,a,b,c,d,x,\[CapitalDelta],\[Delta],\[CapitalGamma],\[Gamma],r},
{\[Lambda]1,\[Lambda]2,\[Lambda]3}=1/2 {{1,1}, {1,-1}, {-1,1}};
LocatorPane[Dynamic[{\[Lambda]1,\[Lambda]2,\[Lambda]3}],InputBackground(*,Appearance \[Rule] {"Subscript[\[Lambda], 1]", "Subscript[\[Lambda], 2]", "Subscript[\[Lambda], 3]"}*)]
-> Dynamic[Graphics[{OutputBackground,
{d,c,b,a}=CoefficientList[(x-{1,I} . \[Lambda]1)(x-{1,I} . \[Lambda]2)(x-{1,I} . \[Lambda]3), x];
Text["a", {Re[a],Im[a]}], Text["b", {Re[b],Im[b]}], Text["c",{Re[c],Im[c]}],Text["d",{Re[d],Im[d]}]
}, PlotRange->All, PlotLabel -> "a,b,c,d"]]
-> Dynamic[Graphics[{OutputBackground,
\[CapitalDelta]= -18a b c d+4b^3 d-b^2 c^2+4a c^3+27a^2 d^2;
Text["\[CapitalDelta]", {Re[\[CapitalDelta]],Im[\[CapitalDelta]]}]
}, PlotRange->All, PlotLabel ->"\[CapitalDelta]"]]
-> Dynamic[Graphics[{OutputBackground,
\[Delta]=PRoot["3\[CapitalDelta]",\[CapitalDelta],2];
Text["\[Delta]", {Re[\[Delta]],Im[\[Delta]]}]
}, PlotRange->All, PlotLabel ->"\[Delta]=\!\(\*SqrtBox[\(\[CapitalDelta]\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,
\[CapitalGamma]= 2b^3-9a b c+27a^2 d+3Sqrt[3]a \[Delta];
Text["\[CapitalGamma]", {Re[\[CapitalGamma]],Im[\[CapitalGamma]]}]
}, PlotRange->All, PlotLabel -> "\[CapitalGamma]"]]
-> Dynamic[Graphics[{OutputBackground,
\[Gamma]=PRoot["\[CapitalGamma]",\[CapitalGamma]/2,3];
Text["\[Gamma]", {Re[\[Gamma]],Im[\[Gamma]]}]
}, PlotRange->All, PlotLabel -> "\[Gamma]=\!\(\*RadicalBox[\(\[CapitalGamma]/2\), \(3\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,
r=-(b+\[Gamma]+(b^2-3a c)/\[Gamma])/(3a);
Text[Style["r",Bold, Large], {Re[r], Im[r]}]
}, PlotRange->All, PlotLabel->"r"]]
]


(* ::Input::Initialization:: *)
DynamicModule[{a0,b0,c0,d0,e0,a,b,c,d,e,x,\[CapitalDelta],\[Delta],Q,S,q,s,u,v,\[CapitalGamma],\[Gamma],r},
{a0,b0,c0,d0,e0}={{0,-1/3},{0,0},{1/3,0},{-1/3,0},{0,1/3}};
LocatorPane[Dynamic[{a0,b0,c0,d0,e0}],InputBackground,Appearance -> {"a", "b", "c", "d","e"}]
-> Dynamic[Graphics[{OutputBackground,
a={1,I} . a0; b={1,I} . b0; c={1,I} . c0; d={1,I} . d0; e={1,I} . e0;
Subscript[\[CapitalDelta], 0]=c^2-3b d+12a e;
Subscript[\[CapitalDelta], 1]=2c^3-9b c d+27b^2 e+27a d^2-72a c e;
Subscript[\[CapitalDelta], 2]=(-4 Subscript[\[CapitalDelta], 0]^3+Subscript[\[CapitalDelta], 1]^2)/27;
u=(8 a c-3b^2)/(8a^2);
v=(b^3-4a b c+8a^2 d)/(8a^3);
Text["\!\(\*SubscriptBox[\(\[CapitalDelta]\), \(0\)]\)", Pt@Subscript[\[CapitalDelta], 0]], Text["\!\(\*SubscriptBox[\(\[CapitalDelta]\), \(1\)]\)", Pt@Subscript[\[CapitalDelta], 1]], Text["\!\(\*SubscriptBox[\(\[CapitalDelta]\), \(2\)]\)", Pt@Subscript[\[CapitalDelta], 2]], Text["u", Pt@u], Text["v", Pt@v]
}, PlotRange->All, PlotLabel ->"a,\!\(\*SubscriptBox[\(\[CapitalDelta]\), \(0\)]\),\!\(\*SubscriptBox[\(\[CapitalDelta]\), \(1\)]\),\!\(\*SubscriptBox[\(\[CapitalDelta]\), \(2\)]\),u,v"]]
-> Dynamic[Graphics[{OutputBackground,
Subscript[\[Delta], 2]=PRoot["4\[CapitalDelta]",Subscript[\[CapitalDelta], 2],2];
Text["\!\(\*SubscriptBox[\(\[Delta]\), \(2\)]\)", Pt@Subscript[\[Delta], 2]]
}, PlotRange->All, PlotLabel ->"\!\(\*SubscriptBox[\(\[Delta]\), \(2\)]\)=\!\(\*SqrtBox[SubscriptBox[\(\[CapitalDelta]\), \(2\)]]\)"]]
-> Dynamic[Graphics[{OutputBackground,
Q=(Subscript[\[CapitalDelta], 1]+3Sqrt[3] Subscript[\[Delta], 2])/2;
Text["Q", Pt@Q]
}, PlotRange->All, PlotLabel ->"Q"]]
-> Dynamic[Graphics[{OutputBackground,
q=PRoot["Q",Q,3];
Text["q", Pt@q]
}, PlotRange->All, PlotLabel ->"q=\!\(\*RadicalBox[\(Q\), \(3\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,
S=-u/6+(q+Subscript[\[CapitalDelta], 0]/q)/(12a);
Text["S", Pt@S]
}, PlotRange->All, PlotLabel ->"S"]]
-> Dynamic[Graphics[{OutputBackground,
s=PRoot["S",S,2];
Text["s", Pt@s]
}, PlotRange->All, PlotLabel ->"s=\!\(\*SqrtBox[\(S\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,
\[CapitalGamma]=-4S-2u-v/s;
Text["\[CapitalGamma]", Pt@\[CapitalGamma]]
}, PlotRange->All, PlotLabel ->"\[CapitalGamma]"]]
-> Dynamic[Graphics[{OutputBackground,
\[Gamma]=PRoot["\[CapitalGamma]4",\[CapitalGamma],2];
Text["\[Gamma]", Pt@\[Gamma]]
}, PlotRange->All, PlotLabel ->"\[Gamma]=\!\(\*SqrtBox[\(\[CapitalGamma]\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,
r=-b/(4a)+s+\[Gamma]/2;
Text[Style["r",Bold, Large], Pt@r]
}, PlotRange->All, PlotLabel ->"\[Gamma]"]]
]


(* ::Input::Initialization:: *)
DynamicModule[{\[Lambda]1,\[Lambda]2,\[Lambda]3,\[Lambda]4,a,b,c,d,e,x,\[CapitalDelta],\[Delta],Q,S,q,s,u,v,\[CapitalGamma],\[Gamma],r},
{\[Lambda]1,\[Lambda]2,\[Lambda]3,\[Lambda]4}=1/2 {{1,1}, {1,-1}, {-1,1},{-1,-1}};
LocatorPane[Dynamic[{\[Lambda]1,\[Lambda]2,\[Lambda]3,\[Lambda]4}],InputBackground(*,Appearance \[Rule] {"Subscript[\[Lambda], 1]", "Subscript[\[Lambda], 2]", "Subscript[\[Lambda], 3]", "Subscript[\[Lambda], 4]"}*)]
-> Dynamic[Graphics[{OutputBackground,
{e, d,c,b,a}=CoefficientList[(x-{1,I} . \[Lambda]1)(x-{1,I} . \[Lambda]2)(x-{1,I} . \[Lambda]3)(x-{1,I} . \[Lambda]4), x];
Text["a", {Re[a],Im[a]}], Text["b", {Re[b],Im[b]}], Text["c",{Re[c],Im[c]}],Text["d",{Re[d],Im[d]}], Text["e",{Re[e],Im[e]}]
}, PlotRange->All]]
-> Dynamic[Graphics[{OutputBackground,
Subscript[\[CapitalDelta], 0]=c^2-3b d+12a e;
Subscript[\[CapitalDelta], 1]=2c^3-9b c d+27b^2 e+27a d^2-72a c e;
Subscript[\[CapitalDelta], 2]=(-4 Subscript[\[CapitalDelta], 0]^3+Subscript[\[CapitalDelta], 1]^2)/27;
u=(8 a c-3b^2)/(8a^2);
v=(b^3-4a b c+8a^2 d)/(8a^3);
Text["\!\(\*SubscriptBox[\(\[CapitalDelta]\), \(0\)]\)", Pt@Subscript[\[CapitalDelta], 0]], Text["\!\(\*SubscriptBox[\(\[CapitalDelta]\), \(1\)]\)", Pt@Subscript[\[CapitalDelta], 1]], Text["\!\(\*SubscriptBox[\(\[CapitalDelta]\), \(2\)]\)", Pt@Subscript[\[CapitalDelta], 2]], Text["u", Pt@u], Text["v", Pt@v]
}, PlotRange->All]]
-> Dynamic[Graphics[{OutputBackground,
Subscript[\[Delta], 2]=PRoot["4\[CapitalDelta]",Subscript[\[CapitalDelta], 2],2];
Text["\!\(\*SubscriptBox[\(\[Delta]\), \(2\)]\)", Pt@Subscript[\[Delta], 2]]
}, PlotRange->All, PlotLabel ->"\!\(\*SubscriptBox[\(\[Delta]\), \(2\)]\)=\!\(\*SqrtBox[SubscriptBox[\(\[CapitalDelta]\), \(2\)]]\)"]]
-> Dynamic[Graphics[{OutputBackground,
Q=(Subscript[\[CapitalDelta], 1]+3Sqrt[3] Subscript[\[Delta], 2])/2;
Text["Q", Pt@Q]
}, PlotRange->All]]
-> Dynamic[Graphics[{OutputBackground,
q=PRoot["Q",Q,3];
Text["q", Pt@q]
}, PlotRange->All, PlotLabel ->"q=\!\(\*RadicalBox[\(Q\), \(3\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,
S=-u/6+(q+Subscript[\[CapitalDelta], 0]/q)/(12a);
Text["S", Pt@S]
}, PlotRange->All]]
-> Dynamic[Graphics[{OutputBackground,
s=PRoot["S",S,2];
Text["s", Pt@s]
}, PlotRange->All, PlotLabel ->"s=\!\(\*SqrtBox[\(S\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,
\[CapitalGamma]=-4S-2u-v/s;
Text["\[CapitalGamma]", Pt@\[CapitalGamma]]
}, PlotRange->All]]
-> Dynamic[Graphics[{OutputBackground,
\[Gamma]=PRoot["\[CapitalGamma]4",\[CapitalGamma],2];
Text["\[Gamma]", Pt@\[Gamma]]
}, PlotRange->All, PlotLabel ->"\[Gamma]=\!\(\*SqrtBox[\(\[CapitalGamma]\)]\)"]]
-> Dynamic[Graphics[{OutputBackground,
r=-b/(4a)+s+\[Gamma]/2;
Text[Style["r",Bold, Large], Pt@r]
}, PlotRange->All]]
]


(* ::Input::Initialization:: *)
b1={{1,0}};
{LocatorPane[Dynamic[b1],InputBackground], 
Dynamic[Graphics[{OutputBackground, PointSize[Large],Point[r=PRoot["ex10",b1[[1,1]]+I b1[[1,2]],10]; {Re[r], Im[r]}]}, PlotRange->All, PlotLabel -> "A Persistent 10th Root"]]
}


(* ::Input::Initialization:: *)
Import["Proof.png"]


(* ::Input::Initialization:: *)
Import["Dance.png"]



