In[18]:= y = Integrate[z, z]
Out[18]= z^2/2
In[19]:= fu[u_] := y /. z -> u
In[20]:= fs[3]
Out[20]= 9/2
In[21]:= fz[z_] := y
In[22]:= fz[3]
Out[22]= z^2/2
why doesn’t fz[3] evaluate and how can I force it?
Hi,
sorry, I do not get the question. Why do you say that fz[3] does not evaluate? Doesn’t Mathematica do exactly what you would expect it to do?
By definition fz does not depend on z. So I would expect it to evaluate to y. But input 18 defines y as \frac{z^2}{2}. So after fz evaluates to y this is substituted by \frac{z^2}{2}. So Mathematica’s result is as expected. I understand that this is not the result you expect. Would you have expected something like this?
ClearAll["Global`*"]
y[z_] := Evaluate[Integrate[z, z]]
fz[z_] := y[z]
fz[3]
This evaluates to \frac{9}{2}. By using the delayed evaluations I have changed to order of evaluations.
Cheers,
Marco
Thanks, my beef is that I have y=z^2/2 the equal sign should sybstitute z^2/2 whenever y is encountered right?
However when I use y in the function fz definition it seems to substitute for y after evaluating the function.
I guess Evaluate forces it:
In[13]:= y = Integrate[z, z]
Out[13]= z^2/2
In[14]:= fz[z_] := Evaluate[y]
In[15]:= fz[3]
Out[15]= 9/2
maybe I’m just foggy about rules here - why do I need evaluate here?
When you do
y = z^2/2;
fz[z_] := y;
fz[3]
the delayed evaluation f[z_]:=y means that the right-hand side is memorized verbatim. You can check with ?fz
When you then call f[3], the replacement z->3 is done in the frozen y, resulting in no replacement at all, since the verbatim y does not contain z.
After this useless replacement y/.z->3 is done, the result is unfrozen, and the outside rule y=z^2/2 gets finally applied.