# How to simplify expression and use HoldForm at the same time?

Hopefully a simple problem for the experts here.

I have a need many times to build a symbolic expression for an equation (say a PDE) to use for plot labels in a low level function inside Manipulate, and so I make a function that I call to build the pde in symbolic form, so I can use it for a plot label. I pass the PDE parameters to this function, and the function uses HoldForm to build it.

But when one of the parameters is 1 (or even zero), and because of HoldForm, these remain stuck there and do not simplify away, and I'd like to remove them.

Currently I use If statement to check for these cases. But I have a feeling there is a better way.

Here is the function (example)

f[c_] := Module[{},
HoldForm[c* D["u"["x", "t"], {"x", 2}] == "f"["x", "t"]]
]


now, when I call it like this

f[1]


it returns

So now I do

f[c_] := Module[{},
If[c == 1,
HoldForm[ D["u"["x", "t"], {"x", 2}] == "f"["x", "t"] ],
HoldForm[c* D["u"["x", "t"], {"x", 2}] == "f"["x", "t"] ],
]
]


and now f[1] returns

I tried many things, (Defer, Simplify, Evaluate, etc...) and nothing works, other than by doing this manual check before using HoldForm.

And about the use of strings there, I had to do it this way :). Too many problems if I use actual symbols. Long story. May be for another topic I can explain why, but for the above works ok for me now other than those extra checks I have to do manually.

question is: is there a trick to do what I am doing about without the If check (I have few parameters to check, and have to do many checks for 1's and 0's as well). Not a big problem for me to do the checks, just wondering if there is a trick I am overlooking.

thanks

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Nasser, in passing, why do you keep using Module[{}, ...]? – Mr.Wizard Jan 19 '12 at 16:13
Nasser, I fear I have received that answer before; my apologies for not remembering. In a compiled language I believe the empty module would not affect speed, but in Mathematica it does. The hit is small, but in cases of fast and simple functions it is significant. I would personally prefer that you leave the extraneous Module out of your questions as IMHO it obscures the function, and also results in propagation of the empty Module to answers. – Mr.Wizard Jan 20 '12 at 4:11

## 1 Answer

Why don't you use HoldForm only on the part that actually needs to be held? For example:

f[c_] := Module[{},
c HoldForm[D["u"["x", "t"], {"x", 2}]] == "f"["x", "t"]]


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