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record intermediate steps

• To: mathgroup at smc.vnet.net
• Subject: [mg73095] record intermediate steps
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Sat, 3 Feb 2007 03:47:58 -0500 (EST)

I know that Mathematica's implementated algorithms in most cases (for
e.g. indefinite integration) do not follow the "human way" (e.g.
integration by parts, substitution etc).

But sometimes it is quite interesting to "record on the side" the
intermediate tranformations
rules followed in the course of arriving in the result.

So, consider the following expression:

In[6]:=
tr = Cos[2*Pi/7]*Cos[4*Pi/7]*Cos[8*Pi/7]

Out[6]=
Cos[(2*Pi)/7]*Cos[(4*Pi)/7]*Cos[(8*Pi)/7]

It is very easy to show that tr is actually equal to 1/8.

In Mathematica you can demonstrate this with the command

In[7]:=
FullSimplify[tr]

Out[7]=
1/8

I believe (but I am not sure!) that Mathematica more or less in this
example follow the "human way" of applying the transformation rules.

So, I would like to see/know them (i.e. the transformation rules)
applied by mathematica to reach this result and further record on the
side (regardless if they actually have any resemblence with the way a
human will work in this example!).

I personally tried

In[8]:=
Trace[FullSimplify[tr], TraceInternal -> True]

but this is not the case here!

Thanks in advance for any kind of response.

Dimitris

• Follow-Ups:
  • Re: Re: record intermediate steps
    • From: "Chris Chiasson" <chris@chiasson.name>
  • Re: record intermediate steps
    • From: "Chris Chiasson" <chris@chiasson.name>