Re: record intermediate steps

*To*: mathgroup at smc.vnet.net*Subject*: [mg73294] Re: record intermediate steps*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Fri, 9 Feb 2007 23:41:04 -0500 (EST)*References*: <acbec1a40702030708s788e8d9eyb42dbca0941a061c@mail.gmail.com>

On Feb 9, 9:38 am, "dimitris" <dimmec... at yahoo.com> wrote: > 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- Hide quoted text - > > - Show quoted text - Oooops! I meant "Can you provide me with some examples of application of the trap method of your own?" that is,examples instead of advances (I really don't know what I was thinking when I wrote the last post!) Dimitris