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Fixed `pl = Plot[Arg[exp], {a, x0, x1}` into `pl = Plot[Arg[exp], {x, x0, x1}`
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Rojo
Rojo
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For a continuous function you could do something like this:

SetAttributes[argPlot, HoldAll];
Options[argPlot] = Options[Plot];

argPlot[exp_, {x_, x0_, x1_}, opt : OptionsPattern[argPlot]] :=
 Module[{pts, pl},
  pl = Plot[Arg[exp], {ax, x0, x1}, PlotRange -> All, 
    PlotPoints -> OptionValue[PlotPoints]];
  pts = SortBy[Cases[pl, Line[pts_] :> pts, Infinity], #[[1, 1]] &];
  pts = Reap[Fold[Module[{ptsn},
         ptsn = #2;
         ptsn[[All, 2]] -= Round[ptsn[[1, 2]] - #1, 2 Pi];
         Sow[ptsn];
         ptsn[[-1, 2]]] &, 0, pts];][[2, 1]];      
  ListLinePlot[Flatten[pts, 1], opt]]

argPlot[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)], {a, -8, 8}]

Mathematica graphics

Compared to an ordinary plot of the Arg[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)]]

Plot[Arg[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)]], {a, -8, 8}, PlotRange -> All]

Mathematica graphics

For a continuous function you could do something like this:

SetAttributes[argPlot, HoldAll];
Options[argPlot] = Options[Plot];

argPlot[exp_, {x_, x0_, x1_}, opt : OptionsPattern[argPlot]] :=
 Module[{pts, pl},
  pl = Plot[Arg[exp], {a, x0, x1}, PlotRange -> All, 
    PlotPoints -> OptionValue[PlotPoints]];
  pts = SortBy[Cases[pl, Line[pts_] :> pts, Infinity], #[[1, 1]] &];
  pts = Reap[Fold[Module[{ptsn},
         ptsn = #2;
         ptsn[[All, 2]] -= Round[ptsn[[1, 2]] - #1, 2 Pi];
         Sow[ptsn];
         ptsn[[-1, 2]]] &, 0, pts];][[2, 1]];      
  ListLinePlot[Flatten[pts, 1], opt]]

argPlot[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)], {a, -8, 8}]

Mathematica graphics

Compared to an ordinary plot of the Arg[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)]]

Plot[Arg[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)]], {a, -8, 8}, PlotRange -> All]

Mathematica graphics

For a continuous function you could do something like this:

SetAttributes[argPlot, HoldAll];
Options[argPlot] = Options[Plot];

argPlot[exp_, {x_, x0_, x1_}, opt : OptionsPattern[argPlot]] :=
 Module[{pts, pl},
  pl = Plot[Arg[exp], {x, x0, x1}, PlotRange -> All, 
    PlotPoints -> OptionValue[PlotPoints]];
  pts = SortBy[Cases[pl, Line[pts_] :> pts, Infinity], #[[1, 1]] &];
  pts = Reap[Fold[Module[{ptsn},
         ptsn = #2;
         ptsn[[All, 2]] -= Round[ptsn[[1, 2]] - #1, 2 Pi];
         Sow[ptsn];
         ptsn[[-1, 2]]] &, 0, pts];][[2, 1]];      
  ListLinePlot[Flatten[pts, 1], opt]]

argPlot[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)], {a, -8, 8}]

Mathematica graphics

Compared to an ordinary plot of the Arg[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)]]

Plot[Arg[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)]], {a, -8, 8}, PlotRange -> All]

Mathematica graphics

Source Link
Heike
Heike
  • 36.1k
  • 3
  • 110
  • 157

For a continuous function you could do something like this:

SetAttributes[argPlot, HoldAll];
Options[argPlot] = Options[Plot];

argPlot[exp_, {x_, x0_, x1_}, opt : OptionsPattern[argPlot]] :=
 Module[{pts, pl},
  pl = Plot[Arg[exp], {a, x0, x1}, PlotRange -> All, 
    PlotPoints -> OptionValue[PlotPoints]];
  pts = SortBy[Cases[pl, Line[pts_] :> pts, Infinity], #[[1, 1]] &];
  pts = Reap[Fold[Module[{ptsn},
         ptsn = #2;
         ptsn[[All, 2]] -= Round[ptsn[[1, 2]] - #1, 2 Pi];
         Sow[ptsn];
         ptsn[[-1, 2]]] &, 0, pts];][[2, 1]];      
  ListLinePlot[Flatten[pts, 1], opt]]

argPlot[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)], {a, -8, 8}]

Mathematica graphics

Compared to an ordinary plot of the Arg[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)]]

Plot[Arg[3 + 2 Exp[3 I a] + Exp[(1 - I a^2)]], {a, -8, 8}, PlotRange -> All]

Mathematica graphics