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plotting - Why do I have to put Evaluate[] here


I wanted to draw some contours. I succeeded with this:


W1 = {p, -2, 2, 0.5};
W2 = {p, -10, 10, 1};
P = W1; ContourPlot[ 
 Evaluate[Union[Table[y^2 == 2 p*x, Evaluate[P]], 

   Table[x^2 == 2 p*y, Evaluate[P]]]], {x, -5, 5}, {y, -5, 5}]
P = W2;
ContourPlot[Evaluate[
  Union[Table[y^2 == 2 p*x, Evaluate[ P]], 
   Table[x^2 == 2 p*y, Evaluate[P]]]], {x, -5, 5}, {y, -5, 5}]

I don't like this solution. I used Evaluate[] a few times and I feel like it is unnecessary although without the function I get errors. Could anyone explain me that. I find the reference unhelpful (maybe that's my lack of language?) "causes expr to be evaluated even if it appears as the argument of a function whose attributes specify that it should be held unevaluated.".



Answer



ContourPlot has the attribute HoldAll. That means that it receives its arguments before they are evaluated. So, if you put as a first argument, something that evaluates to a list but it's not a list, it won't fit with the overloaded version of ContourPlot that expects a list. The same happens with the second argument of Table. Whether they end up not evaluating, using another overload, giving a warning, or simply taking more time than they should, that depends on the particular case at hand


Evaluate is something that makes the containing function behave temporarily as non-holding. Try



SetAttributes[f, HoldAll];
f[x_]:=Hold[x];
f[2+2]
f[Evaluate[2+2]]

If you don't find this neat, what's usually done is use With


With[{P = P},
 With[{lists = Union[Table[y^2 == 2 p*x, P], Table[x^2 == 2 p*y, P]]},
   ContourPlot[lists, {x, -5, 5}, {y, -5, 5}]
  ]

 ]

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