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I am using Mathematica to perform Newton quasi-linearization of the non-linear terms during discretization of PDEs for numerical solution. These expressions can involve tens of terms (depending on the PDE system), which I then have to carefully translate into code. It will help me if in a large expression I can automatically highlight or color terms containing a certain variable. For example, if my expression is stored in 'SEupwind', and I am collecting terms as below

Collect[SEupwind, {Subscript[\[Phi], k], Subscript[\[Phi], k - 1], 
Subscript[\[Phi], k + 1], Subscript[m, k], Subscript[m, k - 1], 
Subscript[m, k - 2], Subscript[m, k + 1], Subscript[m, k + 2]}] 

is there a way to automatically highlight or color the terms containing my collected variables?

Here is a simple example case. Say I have two functions defined like

A1[x_] := A11 x + A12 /x
A2[x_] := A21 x + A22 /x

I then define an expression

TestExpr = A1[Subscript[x, k]] A2[Superscript[x, g]] + 
A1[Superscript[x, g]] A2[Subscript[x, k]]

Then I want to collect coefficients of the variable 'x_k'

Collect[TestExpr, {Subscript[x, k]}]

This produces the output

Subscript[x,k] (A21 (A12/Superscript[x,g] + A11 Superscript[x,g]) + 
A11 (A22/Superscript[x,g] + A21 Superscript[x,g])) + (
A22 (A12/Superscript[x,g] + A11 Superscript[x,g]) + 
A12 (A22/Superscript[x,g] + A21 Superscript[x,g]))/Subscript[x, k]

I would like to highlight or color the coefficients of 'x_k' that I collected (the first term) and display in traditional form. For complex expressions, this will be quite useful while translating to code in another language.

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In addition to the nice answer of Edmund, if you do not mind to highlight also the factor (such as Subscript[x,k] you might use a bit shorter approach. Let us first introduce two functions, any of them may be used for your purposes:

    colored[x_, term_] := If[MemberQ[x, term], Style[x, Red], x];

highlighted[x_, term_] :=If[MemberQ[x, term],Style[x, 14, Red, Bold, Background -> LightYellow], x];

and now let us apply it to your expression (provided it has already been evaluated):

    Map[colored[#, Subscript[x, k]] &, p]
Map[highlighted[#, Subscript[x, k]] &, p]

enter image description here

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You can use Coefficient.

p = Collect[TestExpr, {Subscript[x, k]}];
p /. {\[FormalT] : Coefficient[p, Subscript[x, k]] :> Style[\[FormalT], Blue]} // TraditionalForm

enter image description here

Hope this helps.

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  • $\begingroup$ Thank you. It worked great. I am accepting Alexei's answer since it is easier to use. $\endgroup$ – GreenEye Jan 29 '16 at 23:52

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