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If I have a function:

f[x_, y_, z_, d_] = 4 x + y + z + d;

and made lists for f for different values of the free parameters x,y,z,d, by

T := Table[f[x, y, z, d], {x, 2, 5, 1}, {y, 2, 6, 2}, {z, 5, 10, 1}, {d, 3, 7, 1}]

How to plot f[x, y, z, d] versus any coulomb of the table, i.e., x, y, z or d ..

** Edit **

So why ListPlot dosn't work if I one more than two varibles change, i.e., for

T = Table[{x, If[-50 < DC[x, y] < 50, sigma[x, y, z, d]]}, {x, -5, -2, 1}, {y, 2, 6, 1}, {z, 6, 9, 1}, {d, 2, 9, 1}];

ListPlot[T] stuck ..

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    $\begingroup$ Table[ { x, Table[ f[x, y, z, d] } ... ]? $\endgroup$
    – Kuba ♦
    Jun 8, 2016 at 5:48
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    $\begingroup$ Just to explain @Kuba 's comment datax = Table[ { x, Table[ f[x, y0, z0, d0] }, {x,2,5,1} ] and you have to use specific value y0,z0,d0 for y,z,d. Then use ListPlot[datax]. Since you have an analytical expression you can also use Plot[f[x,y0,z0,d0],{x,2,5}]. $\endgroup$
    – Sumit
    Jun 8, 2016 at 9:57

2 Answers 2

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You can plot your stuff like so:

Manipulate[ContourPlot3D[Norm[{4 x + y + z + d}], 
{x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
ContourStyle -> (Directive[Opacity[.3, #]] & /@ {Red, Green, Cyan}),
Contours -> {1, 2, 3}, MeshStyle -> None], {d, -1, 1}]

enter image description here

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  • $\begingroup$ Please see my question, I edit .. $\endgroup$
    – S.S.
    Jun 8, 2016 at 14:20
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Description

Below you will find two examples.

  • Example No.1 shows how to process function using a set of lists as
    input parameters (per column basis).

  • Example No.2 shows how to process function using all possible
    combinations of passed parameters; in your example it is {x,y,z,d}

Example 1:

(*data*)
x = {2, 5, 1};
y = {2, 6, 2};
z = {5, 10, 1};
d = {3, 7, 1};

(*operation*)
Thread[f[x, y, z, d]];

Example 2:

(*operation*)
Outer[f, x, y, z, d];
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  • $\begingroup$ So, you want to plot a function of 4 independent variables in 3D space ? The only way seems to be by ListContourPlot3D $\endgroup$
    – Lotus
    Jun 8, 2016 at 9:57

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