Re: "UnFullForm"ing an Expression?

• To: mathgroup at smc.vnet.net
• Subject: [mg13271] Re: "UnFullForm"ing an Expression?
• From: "Allan Hayes" <hay at haystack.demon.cc.uk>
• Date: Fri, 17 Jul 1998 03:18:05 -0400
• References: <6ocrqt\$h03@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```AES wrote in message <6ocrqt\$h03 at smc.vnet.net>...
>I recently posted a query noting that if you enter the following
>
>   f1[a_,x_] :=a Cos[x] + a^2 Sin[x]
>
>   f2[a_,x_] := D[f1[a,x],x]
>
>you can make a Table[ ] of f1[a,x] but not of f2[a,x].
>
>If I look at the FullForms for these, e.g.
>
>   f1[a,x] //  FullForm
>
>   f2[a,x] // FullForm
>
>they both look like simple functions to me (i.e., f2[a,x] shows no
>visible memory of having originated from a derivative), except the f2
>is inside a "FullForm[ ]" wrapper and f1 isn't.
>
>Is there a way to "UnFillForm" f2 ? If so, would f2 from then on act
>like f1 ?  Does this query make any sense?
>
>I'd like to understand the situation here.
>
>Thanks   siegman at ee.stanford.edu
>

I get

In[1]:=
f1[a_,x_] :=a Cos[x] + a^2 Sin[x]
f2[a_,x_] := D[f1[a,x],x]
f1[a,x] // FullForm
f2[a,x] // FullForm

Out[3]//FullForm=
Plus[Times[a, Cos[x]], Times[Power[a, 2], Sin[x]]]

Out[4]//FullForm=
Plus[Times[Power[a, 2], Cos[x]], Times[-1, a, Sin[x]]]

Which tell us that we are seeing Out[3] and Out[4] displayed in
FullForm. This fits in with the fact that Out[3] and Out[4] themselves
do not involve FullForm, for example

In[5]:=
%4
Out[5]=
2
a  Cos[x] - a Sin[x]

(the mechanism is that FullForm is stripped off before Out[4] is set)

However, with

In[6]:=
fff2 = FullForm[f2[a,x]]

Out[6]//FullForm=
Plus[Times[Power[a, 2], Cos[x]], Times[-1, a, Sin[x]]]

FullForm is  part of the stored value of fff2

In[7]:=
?fff2

Global`fff2
fff2 = FullForm[a^2*Cos[x] - a*Sin[x]]

So, evaluating fff2 gives the same as evaluating FullForm[a^2*Cos[x] -
a*Sin[x]]

In[8]:=
fff2
Out[8]//FullForm=
Plus[Times[Power[a, 2], Cos[x]], Times[-1, a, Sin[x]]]

We can show that fff2 includes FullForm In[9]:=
FullForm[fff2]

Out[9]//FullForm=
FullForm[Plus[Times[Power[a, 2], Cos[x]],

Times[-1, a, Sin[x]]]]

and
In[10]:=
Last[fff2]

Out[10]=
2
a  Cos[x] - a Sin[x]

whereas

In[11]:=
Last[%6]
Out[11]=
-(a Sin[x])

A variant of the above that lets us see the FullForm without including
FullForm in the stored value of fff2 is In[12]:=
FullForm[fff2 = f2[a,x]]

Out[12]//FullForm=
Plus[Times[Power[a, 2], Cos[x]], Times[-1, a, Sin[x]]]

In[13]:=
fff2

Out[13]=
2
a  Cos[x] - a Sin[x]

------------------------------------------------------------- Allan
Hayes
Training and Consulting
Leicester UK
http://www.haystack.demon.co.uk
hay at haystack.demon.co.uk
voice: +44 (0)116 271 4198
fax: +44(0)116 271 8642

```

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