Dear Alexander Konovalov, Thank you very much for your help.
> Not really - the method for IsSolvable did not evolve from the code similar > to > myIsSolvable at all. > > Perhaps the key is to read about GAP method selection and learn the concept > of > methods as bundles of functions: > > http://www.gap-system.org/Manuals/doc/tut/chap8.html#X7AEED9AB824CD4DA > > - that is, IsSolvable(G) will select the best available method to apply to G, > taking into account what's known about G at the moment. With myIsSolvable, > you enforce the calculation of DerivedSeries, while some of the methods may > need > not to know the derived series at all to give an answer. The profile below > just > illustrates this, since the number of methods involved in the calls to GAP's > IsSolvable is much smaller. IsSolvable in lib/grp.gi is the same as the method for determining whether or not solvable group I have learned . I'll try to understand that the method for determining whether or not solvable group I have learned is the same the built-in IsSolvable function. I think it will be the good study of group theory . I'll try to be able to understand "Operations and Methods of GAP" with the document, too. Thank you very much for your help. With best regards buynnnmmm1 ----- Original Message ----- > From: Alexander Konovalov <al...@mcs.st-andrews.ac.uk> > To: buynnnm...@yahoo.co.jp > Cc: GAP Forum <fo...@gap-system.org> > Date: 2014/9/17, Wed 22:07 > Subject: Re: [GAP Forum] Is it possible to step through the program, like GNU > GDB debugger, against built-in functions(ex. DerivedSubgroup, > ClosureSubgroupNC )? > > > On 17 Sep 2014, at 13:57, buynnnm...@yahoo.co.jp wrote: > >> Dear Alexander Konovalov, >> >> Thank you very much for your help. >> I will be able to do what I would like to do with the way you taught me, > embeded Err("Message")s in codes. >> >>> What is does is that it calls TryPcgsPermGroup and then checks if it > returns the >>> object which is IsPcgs (polycyclic generating system, see >>> http://www.gap-system.org/Manuals/doc/ref/chap45.html). If that > calculation is >>> not successful, the group is not solvable, otherwise it is. Now you may > be >>> interested to find the (undocumented!) function TryPcgsPermGroup which > does the >>> actual job, see for any comments in the code, etc. >> >> >> I have not try to read the source TryPcgsPermGroup and IsPcgs yet. >> >> Source code of IsSolvable was also included in the lib / grp.gi and lib / > grp.gd. >> It is very easy to understand for me. >> >> myIsSolvable:=function ( x ) >> local d; >> d := DerivedSeries( x ); >> return IsTrivial( d[Size( d )] ); >> end >> >> >> gap> List([1..30], x -> myIsSolvable(SymmetricGroup(x))) = > List([1..30], x -> IsSolvable(SymmetricGroup(x))); >> true >> >> For Symmetric Group, the same results have been obtained. >> So I'm going to try to do withmyIsSolvable function that uses the > DerivedSeries function. >> >> There was a difference of more than twice the run time to IsSolvable of > built-in and myIsSolvable Taking the profile. >> >> Built-in IsSolved Would has become the source code I hard to understand in > order to increase the execution speed? >> >> > > Not really - the method for IsSolvable did not evolve from the code similar > to > myIsSolvable at all. > > Perhaps the key is to read about GAP method selection and learn the concept > of > methods as bundles of functions: > > http://www.gap-system.org/Manuals/doc/tut/chap8.html#X7AEED9AB824CD4DA > > - that is, IsSolvable(G) will select the best available method to apply to G, > taking into account what's known about G at the moment. With myIsSolvable, > you enforce the calculation of DerivedSeries, while some of the methods may > need > not to know the derived series at all to give an answer. The profile below > just > illustrates this, since the number of methods involved in the calls to GAP's > IsSolvable is much smaller. > > Best wishes > Alexander > > > > > >> gap> ProfileGlobalFunctions( true ); >> gap> ProfileOperationsAndMethods( true ); >> gap> List( [1..30], x -> IsSolvable(SymmetricGroup(x))) ; >> [ true, true, true, true, false, false, false, false, false, false, false, > false, false, false, false, false, false, false, false, >> false, false, false, false, false, false, false, false, false, false, > false ] >> gap> ProfileGlobalFunctions( false ); >> gap> ProfileOperationsAndMethods( false ); >> gap> DisplayProfile(); >> count self/ms chld/ms stor/kb chld/kb package function > >> 56 0 32 6 786 GAP TryPcgsPermGroup > >> 56 0 32 9 794 (oprt.) IsSolvableGroup > >> 30 0 32 0 804 (oprt.) IsSolvable > >> 28 0 32 0 794 GAP IsSolvableGroup: for > permgrp >> 156491 40 0 741 15 (oprt.) Add > >> 3 52 0 70 0 SortParallel: for two > dense and mutable lists >> 574 16 40 2043 988 GAP List > >> 4 4 80 96 213 (oprt.) Sortex > >> 4 60 52 72 70 (oprt.) SortParallel > >> 2028 272 0 0 0 (oprt.) Position > >> 72 2324 OTHER > >> 516 5365 TOTAL > >> gap> ProfileGlobalFunctions( true ); >> gap> ProfileOperationsAndMethods( true ); >> gap> List( [1..30], x -> myIsSolvable(SymmetricGroup(x))) ; >> [ true, true, true, true, false, false, false, false, false, false, false, > false, false, false, false, false, false, false, false, >> false, false, false, false, false, false, false, false, false, false, > false ] >> gap> ProfileGlobalFunctions( false ); >> gap> ProfileOperationsAndMethods( false ); >> gap> DisplayProfile(); >> count self/ms chld/ms stor/kb chld/kb package function > >> 11686 0 0 0 0 CanComputeIsSubset: > default: no, unless identical >> 12708 4 4 198 0 GAP IsOne: for a > multiplicative-element-with-one >> 18151 8 4 0 0 (oprt.) > Tester(IsAssociative) >> 12708 20 0 0 198 (oprt.) IsOne > >> 15776 12 4 0 0 OneImmutable: system > getter >> 21144 16 4 29 0 > GeneratorsOfMagmaWithInverses: system getter >> 17646 12 12 18 173 (oprt.) Representative: for > magma-with-one with known one >> 382 0 32 5 269 (oprt.) Setter(ParentAttr) > >> 21144 16 16 18 29 (oprt.) > FreeGeneratorsOfFpGroup: for a free group >> 1 0 32 70 70 GAP Sortex: for a mutable > list >> 3391 8 24 92 191 GAP SmallestMovedPoint: > for a collection of permutations >> 382 0 32 7 12 GAP Setter(ParentAttr): > method that calls 'UseSubsetRelation' >> 8681 4 40 0 337 (oprt.) SmallestMovedPoint > >> 43634 16 36 1985 382 GAP ForAll > >> 185602 52 0 863 2 (oprt.) Add > >> 757 44 16 17 0 GAP UseSubsetRelation: > default method that checks maintenances and then returns * >> 757 0 60 7 17 (oprt.) UseSubsetRelation > >> 53823 68 4 11517 0 GAP > InverseRepresentative >> 3 76 0 70 0 SortParallel: for two > dense and mutable lists >> 9945 20 72 194 12950 GAP in: for a > permutation, and a permutation group >> 5564 44 60 3915 2410 GAP ChooseNextBasePoint > >> 4 0 108 113 254 (oprt.) Sortex > >> 224034 116 0 0 0 (oprt.) NumberOp: for a dense > list >> 5564 84 60 498 168 GAP > AddGeneratorsExtendSchreierTree >> 5 76 76 113 70 (oprt.) SortParallel > >> 12526 280 4 0 0 (oprt.) Position > >> 94315 472 8 89804 0 GAP SiftedPermutation > >> 5564 184 804 8789 94952 GAP StabChainStrong > >> 265 8 1104 77 107182 GAP ClosureGroup: > permgroup, elements, options >> 265 4 1112 0 107259 (oprt.) ClosureGroup > >> 62 0 1296 0 122301 (oprt.) DerivedSubgroup > >> 56 12 1284 162 122086 GAP DerivedSubgroup: > permgrps >> 30 0 1316 5 122489 GAP DerivedSeriesOfGroup: > generic method for groups >> 30 0 1316 0 122505 (oprt.) DerivedSeries > >> 30 0 1316 0 122505 (oprt.) DerivedSeriesOfGroup > >> 26 36 1324 2853 122729 GAP List > >> 160 6531 OTHER > >> 1852 127963 TOTAL > >> >> >> With best regards >> buynnnmmm1 >> >> >> >> ----- Original Message ----- >>> From: Alexander Konovalov <al...@mcs.st-andrews.ac.uk> >>> To: buynnnm...@yahoo.co.jp >>> Cc: GAP Forum <fo...@gap-system.org> >>> Date: 2014/9/17, Wed 20:19 >>> Subject: Re: [GAP Forum] Is it possible to step through the program, > like GNU GDB debugger, against built-in functions(ex. DerivedSubgroup, > ClosureSubgroupNC )? >>> >>> On 16 Sep 2014, at 22:52, buynnnm...@yahoo.co.jp wrote: >>> >>>> Dear GAP forum, >>>> >>>> Is it possible to set break points against built-in functions (ex. >>> DerivedSubgroup)？ >>>> >>>> Is it possible to step through the program, like GNU GDB debugger, > against >>> built-in functions(ex. DerivedSubgroup, ClosureSubgroupNC )? >>>> >>>> Because I am a beginner the group theory , I would to examine in > detail >>> what functions are doing in what procedure . >>>> >>>> I check http://www.gap-system.org/Manuals/doc/ref/chap7.html, but I > cannot >>> find the function that set break points or step through the function. >>> >>> No, there is no such functionality, but there are workarounds and > alternatives. >>> >>> First, you can add the line like >>> >>> Error("Break point some text which you want to display..."); >>> >>> in the code, and then you will be able to investigate local variables > from the >>> break loop - see http://www.gap-system.org/Manuals/doc/ref/chap6.html >>> >>> Second, you already know from your previous post how to find the code > of the >>> function. Since GAP is an interpreted language, you may try to paste > the code of >>> the function into your session line by line and see what happens. >>> >>> Finally, YMMV (your mileage may vary): looking at the method below for >>> IsSolvableGroup itself will likely not give an insight into the > solvability of >>> groups, it will just point to some other procedure: >>> >>>> gap> g := SymmetricGroup(5); >>>> Sym( [ 1 .. 5 ] ) >>>> gap> ApplicableMethod(IsSolvableGroup,[g]); >>>> function( G ) ... end >>>> gap> f := last; >>>> function( G ) ... end >>>> gap> Print(f); >>>> function ( G ) >>>> local pcgs; >>>> pcgs := TryPcgsPermGroup( G, false, false, true ); >>>> if IsPcgs( pcgs ) then >>>> SetIndicesEANormalSteps( pcgs, pcgs!.permpcgsNormalSteps > ); >>>> SetIsPcgsElementaryAbelianSeries( pcgs, true ); >>>> if not HasPcgs( G ) then >>>> SetPcgs( G, pcgs ); >>>> fi; >>>> if not HasPcgsElementaryAbelianSeries( G ) then >>>> SetPcgsElementaryAbelianSeries( G, pcgs ); >>>> fi; >>>> return true; >>>> else >>>> return false; >>>> fi; >>>> return; >>>> end >>> >>> >>> What is does is that it calls TryPcgsPermGroup and then checks if it > returns the >>> object which is IsPcgs (polycyclic generating system, see >>> http://www.gap-system.org/Manuals/doc/ref/chap45.html). If that > calculation is >>> not successful, the group is not solvable, otherwise it is. Now you may > be >>> interested to find the (undocumented!) function TryPcgsPermGroup which > does the >>> actual job, see for any comments in the code, etc. >>> >>> Best wishes >>> Alexander >>> > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
