Return equality from Mathematica function

Question

I have a function that returns equalities, which I want to print, for example, x==y, or 2x+5==10. These usually have no meaning for mathematica, it cannot simplify it furhter.

Answer 1

Usually one uses HoldForm for this sort of thing. HoldForm is a head that works like Hold, in that it doesn't evaluate its contents, but it's not displayed when it's printed as output, like so:

In[1]:= HoldForm[x == 3]
Out[1]= x == 3

In[2]:= HoldForm[x == x]
Out[2]= x == x

As with Hold, you can interpolate things into a HoldForm using With or function argument substitution, like so:

In[3]:= PrintableEqual[x_, y_] := HoldForm[x == y]

In[4]:= PrintableEqual[x, x]
Out[4]= x == x

However, this will mean that the arguments are evaluated before substitution, like so:

In[5]:= PrintableEqual[x + x, 2 x]
Out[5]= 2 x == 2x

If you don't want this to happen, you can use SetAttributes and HoldAll:

In[6]:= SetAttributes[PrintableEqual, {HoldAll}]

In[7]:= PrintableEqual[x + x, 2 x]
Out[7]= x + x == 2 x

Note that HoldForm is always there, it's just not displayed in output form:

In[8]:= PrintableEqual[x, x] // InputForm
Out[8]= HoldForm[x == x]

If you want to evaluate things, use ReleaseHold:

In[9]:= ReleaseHold@PrintableEqual[x, x]
Out[9]= True