Dear Alexander Konovalov,
Thank you very much for your help!
> Yes, precisely! This is dynamic polymorphism. The method selected depends on
> types of all arguments, and objects may change their type during their
> lifetime.
>
> For example, if there is a faster algorithm for a group for which it is known
> that is has some attribute X, you may install a generic method for IsGroup and
> a specific for IsGroup and HasX. Then for a group without X a generic method
> will be called, while for the group for which X is known a specific method
> will
> be called. This will not automatically enforce the calculation of X which may
> be expensive.
>
> This may be seen in the method that implements the Feit–Thompson theorem from
> my mail yesterday:
>
> InstallImmediateMethod( IsSolvableGroup, IsGroup and HasSize, 10,
> function( G )
> G:= Size( G );
> if IsInt( G ) and G mod 2 = 1 then
> return true;
> fi;
> TryNextMethod();
> end );
>
> - it will be applied (automatically, since it is *immediate*) only if the Size
> is already known, what is checked with HasSize.
Thank you very much for explanation, I can understand it because your
explanation is great.
I am re-createing the myIsSolvable for practice.
$ grep IsSolvable /usr/share/gap/lib/* | grep Declare
There was codes of IsSolvable family also in "lib/overload.g" and "lib/ctbl.gd".
And,I made a myIsSolvable with the Feit-Thompson theorem.
But, I do not write the source code here, because It has some bugs.
> You might be interested in the following paper which describes this in more
> details:
>
> @inproceedings{Breuer:1998:GTS:281508.281540,
> author = {Breuer, Thomas and Linton, Steve},
> title = {The GAP 4 Type System: Organising Algebraic Algorithms},
> booktitle = {Proceedings of the 1998 International Symposium on Symbolic and
> Algebraic Computation},
> series = {ISSAC '98},
> year = {1998},
> isbn = {1-58113-002-3},
> location = {Rostock, Germany},
> pages = {38--45},
> numpages = {8},
> url = {http://doi.acm.org/10.1145/281508.281540},
> doi = {10.1145/281508.281540},
> acmid = {281540},
> publisher = {ACM},
> address = {New York, NY, USA},
> }
Thank you very much for this information.
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: 2014/9/18, Thu 19:27
> Subject: Re: [GAP Forum] Is it possible to step through the program, like GNU
> GDB debugger, against built-in functions(ex. DerivedSubgroup,
> ClosureSubgroupNC )?
>
>
> On 18 Sep 2014, at 02:47, buynnnm...@yahoo.co.jp wrote:
>
>> Dear Alexander Konovalov,
>>
>> Thank you very much for your description with some execution examples!
>>
>> I tried to run Copy and paste the example of you.It's very interesting.
>>
>> I have not read the document you taught me yet, but I understand the point.
>> I think that is similar to polymorphism of object-oriented programming
> languages.
>
> Yes, precisely! This is dynamic polymorphism. The method selected depends on
> types of all arguments, and objects may change their type during their
> lifetime.
>
> For example, if there is a faster algorithm for a group for which it is known
> that is has some attribute X, you may install a generic method for IsGroup and
> a specific for IsGroup and HasX. Then for a group without X a generic method
> will be called, while for the group for which X is known a specific method
> will
> be called. This will not automatically enforce the calculation of X which may
> be expensive.
>
> This may be seen in the method that implements the Feit–Thompson theorem from
> my mail yesterday:
>
> InstallImmediateMethod( IsSolvableGroup, IsGroup and HasSize, 10,
> function( G )
> G:= Size( G );
> if IsInt( G ) and G mod 2 = 1 then
> return true;
> fi;
> TryNextMethod();
> end );
>
> - it will be applied (automatically, since it is *immediate*) only if the Size
> is already known, what is checked with HasSize.
>
> You might be interested in the following paper which describes this in more
> details:
>
> @inproceedings{Breuer:1998:GTS:281508.281540,
> author = {Breuer, Thomas and Linton, Steve},
> title = {The GAP 4 Type System: Organising Algebraic Algorithms},
> booktitle = {Proceedings of the 1998 International Symposium on Symbolic and
> Algebraic Computation},
> series = {ISSAC '98},
> year = {1998},
> isbn = {1-58113-002-3},
> location = {Rostock, Germany},
> pages = {38--45},
> numpages = {8},
> url = {http://doi.acm.org/10.1145/281508.281540},
> doi = {10.1145/281508.281540},
> acmid = {281540},
> publisher = {ACM},
> address = {New York, NY, USA},
> }
>
> Best wishes
> Alexander
>
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