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?
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
>
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