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MathGroup Archive 2007

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Re: Re: record intermediate steps

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80667] Re: [mg73649] Re: record intermediate steps
  • From: "Chris Chiasson" <chris at chiasson.name>
  • Date: Tue, 28 Aug 2007 02:17:15 -0400 (EDT)
  • References: <200702161021.FAA09937@smc.vnet.net> <erc1vu$mm5$1@smc.vnet.net>

I was tracing (and graphing) the FullSimplify; look what I found:

Developer`TrigToRadicals[Cos[2*(Pi/7)]*Cos[4*(Pi/7)]*Cos[8*(Pi/7)]]//Together//Apart//Expand//Factor

Simplify`SimplifyTrigAlgebraicConstant[Cos[2*(Pi/7)]*Cos[4*(Pi/7)]*Cos[8*(Pi/7)]]

Also, this one is kind interesting, but doesn't give the 1/8th:
FactorSquareFree[Cos[2*(Pi/7)]*Cos[4*(Pi/7)]*Cos[8*(Pi/7)],Trig->True]


On 2/23/07, dimitris <dimmechan at yahoo.com> wrote:
> Hello Chris.
>
> I have a question regarding your code.
>
> Consider for example the thread with title
> Showing that ArcSinh[2]/ArcCsch[2] is 3
> from here:
> http://groups.google.gr/group/comp.soft-sys.math.mathematica/browse_thread/
> thread/e3a54d0fff7b596f/040152a96625a9df?hl=el#040152a96625a9df
>
> Dana DeLouis' answer was
>
> equ = TrigToExp[ArcSinh[2]/ArcCsch[2]];
> avoid = Count[{#1}, _ArcSinh | _ArcCsch | _Log,
>      Infinity] & ;
> FullSimplify[equ, ComplexityFunction -> avoid]
> 3
>
> So let use your code in order to get a list of
> symbols called from the System` context during the simplification
> process.
>
> Quit;
>
> equ = TrigToExp[ArcSinh[2]/ArcCsch[2]];
> avoid = Count[{#1}, _ArcSinh | _ArcCsch | _Log,
> Infinity] & ;
>
> lst1 = Block[{$Output = {OpenWrite["C:\\msgStream.m"]}},
> TracePrint[FullSimplify[equ, ComplexityFunction -> avoid],
>       TraceInternal -> True]; Close /@ $Output];
> Thread[Union[Cases[ReadList["C:\\msgStream.m",
> HoldComplete[Expression]],
>     symb_Symbol /; AtomQ[Unevaluated[symb]] &&
> Context[Unevaluated[symb]] === "System`" :> HoldComplete[symb], {0,
> Infinity},
>     Heads -> True]], HoldComplete]
>
> Here we use FullSimplify with the default settings
>
> Developer`ClearCache []
>
> lst2 = Block[{$Output = {OpenWrite["C:\\msgStream.m"]}},
> TracePrint[FullSimplify[equ], TraceInternal -> True];
>      Close /@ $Output];
> Thread[Union[Cases[ReadList["C:\\msgStream.m",
> HoldComplete[Expression]],
>     symb_Symbol /; AtomQ[Unevaluated[symb]] &&
> Context[Unevaluated[symb]] === "System`" :> HoldComplete[symb], {0,
> Infinity},
>     Heads -> True]], HoldComplete]
>
> How can someone "use" Complement, Union, Intersection in lst1, lst2 in
> order to see e.g. symbols called
> during both processes?
>
> Best Regards
> Dimitris
>
>
> =CF/=C7 Chris Chiasson =DD=E3=F1=E1=F8=E5:
> > Also, if you make two lists of results, one from FullSimplify and one
> > from Simplify, you can eliminate some functions to try, assuming one
> > of the function names can simplify the expression in one step. Don't
> > forget Developer`ClearCache between the two runs to cull out more
> > functions.
> >
> > DeleteCases[Sequence@@HoldComplete@@@list1,HoldPattern@@Alternatives@@@li=
> st2]
> >
> > On 2/19/07, Chris Chiasson <chris at chiasson.name> wrote:
> > > If the list of expressions returned by TracePrint TraceInteral->True
> > > is relatively complete, here is a method that will return a list of
> > > symbols called from the System` context during the simplification.
> > >
> > > This code could easily be modified to assign the list of expressions
> > > encountered during the evaluation to a variable, from which the
> > > aforementioned list of symbols could be cross referenced (to see how
> > > they were called)
> > >
> > > Block[{$Output=List@OpenWrite["C:\\msgStream.m"]},
> > > TracePrint[FullSimplify[Cos[2*Pi/7]*Cos[4*Pi/7]*Cos[8*Pi/7]],TraceInter=
> nal->True];
> > > Close/@$Output];
> > >
> > > Thread[Union@Cases[ReadList["C:\\msgStream.m",
> > > HoldComplete[Expression]],symb_Symbol/;AtomQ@Unevaluated@symb&&
> > > Context@Unevaluated@symb==="System`":>HoldComplete@symb,{0,Infini=
> ty},Heads->True],
> > > HoldComplete]
> > >
> > >
> > > --
> > > http://chris.chiasson.name/
> > >
> >
> >
> > --
> > http://chris.chiasson.name/
>
>
>


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


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