My plotting comes out to be gray not coloured using AbsArgPlot function in Mathematica. What is the reason for not getting a coloured graph??h

Question

My graph comes out to be gray, not coloured using AbsArgPlot function in Mathematica. What is the reason for not getting a coloured graph or what I can deduce from it about the complex function that I considered. Basically I am using a complex Lagrange interpolating polynomial. I am including the graph. The Exp[z] gives a good coloured graph given below.

z = Cos[j] + I*Sin[j];
AbsArgPlot[{Exp[z]}, {j, 0, 2 Pi}, Filling -> Axis]

The interpolating polynomial that I created using the nodes on the unit circle produces the below graph which comes out to be gray.

z = Cos[j] + I*Sin[j];
AbsArgPlot[{LR}, {j, 0, 2 Pi}, Filling -> Axis]

,

where LR is the interpolatory polynomial I created. My interpolating polynomial approximates Exp[z] nicely as the graph turns out to be similar. but what can I deduce with this gray colour coming .

Answer 1

This is meant to be an extensive comment.

The main point is that there might be an issue with the definition of LR in your code. The reason that I am suggesting this, is that I tried to plot an interpolating polynomial and AbsArgPlot works fine. Let me show you what I have tried.

To begin with, I have taken the definition of the Lagrange interpolation from this answer

We have

lagrangeInterpolation[values_, var_] := 
 Module[{xvalues = values\[Transpose][[1, All]], 
   yvalues = values\[Transpose][[2, All]], subs, complements, 
   nominators, denominators}, 
  subs = Subsets[xvalues, {Length@xvalues - 1}];
  complements = Flatten[Complement[xvalues, #] & /@ subs];
  nominators = Times @@ (# - x) & /@ subs;
  denominators = 
   Table[Times @@ (subs[[i]] - complements[[i]]), {i, 1, Length@subs}];
  Reverse[nominators/denominators].yvalues]

Ok, so now my logic is quite simple. Create a list of data points {x,y}. Not that for the y-points I have used your expression $e^z=e^{\cos j + i \sin j}$

xvalues = Join[{0}, Range@6]
yvalues = Table[Exp[Cos[j] + I*Sin[j]], {j, 0, 2 Pi}] // N
data = Transpose[{xvalues, yvalues}];

Since we have a a way of obtaining the Lagrange polynomial we can use

poly = Expand[lagrangeInterpolation[data, x]]

and then we can plot

AbsArgPlot[{poly}, {x, 0, 2 Pi}, Filling -> Axis]

which gives

As it has already been pointed out it would be very helpful to give us the expression for the LR that you used.

Edit: following the documentation I think that the best way to understand the different colours is the following

AbsArgPlot[{poly}, {x, 0, 2 Pi}, PlotLegends -> Automatic] 

and observe what you get next to your plot