Re: record intermediate steps

*To*: mathgroup at smc.vnet.net*Subject*: [mg73649] Re: record intermediate steps*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Fri, 23 Feb 2007 04:50:36 -0500 (EST)*References*: <200702161021.FAA09937@smc.vnet.net><erc1vu$mm5$1@smc.vnet.net>

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/

**References**:**Re: Re: record intermediate steps***From:*"Chris Chiasson" <chris@chiasson.name>