Dear,

Could you explain me how does the slot works in the command bellow? I also show the complete code lower. This code is from

__http://demonstrations.wolfram.com/CubicEquation/.nb file.__ The "Download Author Code »(preview »)" is wrong and I had to get the code from the .nb file.

COMMAND

(If[Flatten[#1] === {}, {},

(Point[{#1,

Function[x$, a3*x$^3 + a2*x$^2 + a1*x$ + a0][#1]}] & ) /@

(x /. #1)] & )[{ToRules[

Quiet[Reduce[a3*x^3 + a2*x^2 + a1*x + a0 == 0, x,

Reals]]]}]

(*Entire Code*)

Manipulate[

Plot[a3*x^3 + a2*x^2 + a1*x + a0, {x, -2, 2}, PlotRange -> 10,

PlotLabel ->

2 3

a0 + a1 x + a2 x + a3 x

, PlotStyle -> Thickness[0.005], Epilog -> {PointSize[0.015],

{RGBColor[1, 0.26, 0.], Point[{1.2, 7}]},

Text[Style["zeros", 12, Italic],

{1.3, 7}, {-1, 0}], {RGBColor[0.12, 0.61, 0.78],

Point[{1.2, 6}]},

Text[

Style["critical points", 12, Italic], {1.3, 6}, {-1, 0}],

{RGBColor[0.67, 0.75, 0.15], Point[{1.2, 5}]},

Text[

Style["inflection points", 12, Italic], {1.3, 5}, {-1, 0}],

RGBColor[1, 0.26, 0.], (If[Flatten[#1] === {}, {},

(Point[{#1,

Function[x$, a3*x$^3 + a2*x$^2 + a1*x$ + a0][#1]}] & ) /@

(x /. #1)] & )[{ToRules[

Quiet[Reduce[a3*x^3 + a2*x^2 + a1*x + a0 == 0, x,

Reals]]]}], RGBColor[0.12, 0.61, 0.78],

(If[Flatten[#1] === {}, {},

(Point[{#1,

Function[x$, a3*x$^3 + a2*x$^2 + a1*x$ + a0][#1]}] & ) /@

(x /. #1)] & )[{ToRules[

Quiet[Reduce[(3*x^2)*a3 + (2*a2)*x + a1 == 0, x,

Reals]]]}], RGBColor[0.67, 0.75, 0.15],

(If[Flatten[#1] === {}, {},

(Point[{#1,

Function[x$, a3*x$^3 + a2*x$^2 + a1*x$ + a0][#1]}] & ) /@

(x /. #1)] & )[{ToRules[

Quiet[Reduce[(6*x)*a3 + 2*a2 == 0, x,

Reals]]]}]}, ImageSize -> {500, 400}], {a3, -5.,

5.}, {a2, -5., 5.},

{a1, -5., 5.}, {a0, -5., 5.}, ControllerLinking -> True]

Thank you,

Ana