Assignments don't apply in scoping constructs

Questions
1

Hello guys

I created the procedure below assigning values to variables a, b and c, so that they are protected. When I apply WU, the values assigned to variables a,b and c are not applied. Within the WU procedure, I used the With and Block functions, but to no avail.

WU[ex_] := Module[{a, b, c, ex1, sk},
  a = x + y;
  b = x - y;
  c = x*y;
  ex1 = ex;
  sk[t_] := Sin[t];
  Return[sk[ex1]]]

{WU[a*b/c], WU[a - b - c]}
{Sin[(a b)/c], Sin[a - b - c]}

I’m grateful if anyone can help.

Regards,

Sinval

2

What makes you think they were not assigned? Since those assigned objects are not actually used, there is no evidence one way or the other.

3

It would help if you provided expected output. I suspect that you’re trying to do some sort of change of variables, maybe something like this;

{Sin[(a b)/c], Sin[a - b - c]} /. {a -> x + y, b -> x - y, c -> x*y}

{Sin[((x - y)*(x + y))/(x*y)], Sin[2*y - x*y]}

If that’s the case, then to understand why it didn’t work you need to understand how Mathematica does scoping in constructs like Module. So, modify your WU function like this:

WU[ex_] :=
 Module[
  {a, b, c, ex1, sk},
  Print[SymbolName[a]];
  a = x + y;
  b = x - y;
  c = x*y;
  ex1 = ex;
  sk[t_] := Sin[t];
  Return[sk[ex1]]]

Now evaluate WU[a*b/c]. Notice that what appears as a inside the Module actually has a more complicated name. Before going into a lengthy explanation, I think it would be easier if you explained exactly what you’re trying to do, what you intend for WU to do, what your objective is, what your expected outputs are, etc. We can probably help you get to where you want to be without diving too deeply into scoping rules.

4

Hi Daniel
Thank you for your attention. I made the procedure work using the Block function.

WU[ex_] := Module[{sk},
  sk[t_] := Sin[t];
  Block[{a = x + y, b = x - y, c = x*y}, sk[ex]]]

The result I wanted is shown below.

In[19]:= {WU[a*b/c], WU[a - b - c]}

Out[19]= {Sin[((x - y) (x + y))/(x y)], Sin[2 y - x y]}

Any additional information will be welcome.

5

Thank you for your attention, Eric. The expected result is in the post above.

6

Sinval, check this;

WU[ex_]:=Block[{a,b,c,ex1,sk},
  a=x+y;
  b=x-y;
  c=x*y;
  ex1=ex;
  sk[t_]:=Sin[t];
  sk[ex1]
]

In[2]:= {WU[a*b/c], WU[a - b - c]}
Out[2]= {Sin[((x - y) (x + y))/(x y)], Sin[2 y - x y]}
7

Yes Hans, it worked as expected. I am also grateful for your contribution.