Re: record intermediate steps

• To: mathgroup at smc.vnet.net
• Subject: [mg73129] Re: [mg73095] record intermediate steps
• From: dimitris anagnostou <dimmechan at yahoo.com>
• Date: Sun, 4 Feb 2007 07:01:15 -0500 (EST)

Hello Chris,

Thanks for your response!

It will be very good to suceed in your attempts!

I used Robby Villegas' trap method on some examples; very interesting indeed but I doubt if I will ever can understand it completely or write it down on my own!

Doing my first steps on this area of Mathematica (figuring out what is going/called etc) I tried to use something like

On[];
FullSimplify[Cos[2*(Pi/7)]*Cos[4*(Pi/7)]*Cos[8*(Pi/7)]]
Off[];

But the process during the (Full)Simplification are too "internal" to be "reported" by this elementary setting.

Best Regards
Dimitris

Chris Chiasson <chris at chiasson.name> wrote:
Dimitris,
I tried using Robby Villegas' trap method in an automated fashion on
most of the functions in the System` context to see if I could figure
out what is being called. Unfortunately, it breaks FullSimplify and
doesn't reveal what functions were called. However, I am not yet ready
to give up on this method.

Also, it is possible to get 1/8 by using
RootReduce@TrigFactor@tr

Anyway, here is the automated trapping code:
In[1]:=
nameTrapBin={};
In[2]:=
nameTrap[symb_Symbol]/;FreeQ[Attributes@symb,Locked]:=
Module[{trap=True},Unprotect@Unevaluated@symb;
g_symb/;trap:=
Block[{trap=False},
If[nameTrapCount>0,nameTrapCount--;
nameTrapBin={nameTrapBin,HoldForm@g}];g]]
In[3]:=
nameTrap[str_String]:=ToExpression[str,InputForm,nameTrap]
In[4]:=
nameSet=DeleteCases[Names["System`*"],
Alternatives@@
Union[Join[
ToString/@
Cases[DownValues@nameTrap,_Symbol,{0,Infinity},
Names["System`*Box*"],Names["System`*Abort*"],
Names["System`*Trace*"],Names["System`*Dialog*"],
Names["System`*Message*"],Names["System`*\$*"],
Names["System`*Message*"],{"Apply"}]]];
In[5]:=
((*Print@#;*)nameTrap@#)&/@nameSet;
In[6]:=
Block[{nameTrapCount=10},tr=Cos[2*Pi/7]*Cos[4*Pi/7]*Cos[8*Pi/7]]
In[7]:=
FullSimplify@tr
In[8]:=
Block[{nameTrapCount=10},BetaRegularized[1,2,3]]
In[9]:=
Flatten@nameTrapBin

On 2/3/07, dimitris wrote:
> 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
>
>

--
http://chris.chiasson.name/

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