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MathGroup Archive 2007

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Re: record intermediate steps

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73275] Re: record intermediate steps
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Fri, 9 Feb 2007 02:25:13 -0500 (EST)
  • References: <acbec1a40702030708s788e8d9eyb42dbca0941a061c@mail.gmail.com>

On Feb 6, 9:35 am, "Chris Chiasson" <c... at chiasson.name> wrote:
> The trap method is pretty straightforward and elegant, at least when
> one isn't trying to use it on all functions at once or limit the
> number of function calls recorded:
>
> The first idea is to take a function name (which is a symbol) and then
> assign a very specific DownValue to it, causing that DownValue to
> "jump the queue" and be executed before the symbol's internal
> DownValues.
>
> The second idea is that the right hand side of this specific DownValue
> then sets the condition to be False, Prints or otherwise records the
> function call, and then executes the built in DownValues by performing
> the same function call again. The condition must be set to false in
> order to avoid infinite tail recursion.
>
> On 2/3/07, dimitris anagnostou <dimmec... at yahoo.com> wrote:
>
>
>
>
>
> > 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 <c... 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},
> > Heads\[Rule]True],Names["System`*Packet*"],
> > Names["System`*Box*"],Names["System`*Abort*"],
> > Names["System`*Trace*"],Names["System`*Dialog*"],
> > Names["System`*Message*"],Names["System`*$*"],
> > Names["System`*Link*"],Names["System`*Set*"],
> > 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[{name TrapCount=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/
>
> >  ________________________________
> > We won't tell. Get more on shows you hate to love
> > (and love to hate): Yahoo! TV's Guilty Pleasures list.
>
> --http://chris.chiasson.name/- Hide quoted text -
>
> - Show quoted text -

Hello again!

Can you provide me with some advances of application of the trap
method of your own?

Thanks a lot!

Dimitris



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