Hi, all, To Eric Allen Wohlstadter's (wohlstad@cs.ucdavis.edu) : Are there any Haskell libraries or programs related to group theory? I am : taking a class and it seems like Haskell would be a good programming : language for exploring/reasoning about group theory. What I had in mind : was perhaps you could have a function which takes a list(set) and a : function with two arguments(binary operator) and checks to see whether or : not it is a group. I think it might be a fun exercies to write myself but : I'd like to see if it's already been done or what you guys think about it. Marc van Dongen <dongen@cs.ucc.ie> writes
I think Sergey Mechveliani's docon (algebraic DOmain CONstructor) has facilities for that. Have a look at:
Sorry, DoCon (<http://www.botik.ru/pub/local/Mechveliani/docon/2.01/>) really supports the Commutative Rings, but provides almost nothing for the Group theory. For example, for the domain (Integer,Integer) it would set automatically (IsGroup,Yes) for the Additive semigroup and (IsGroup,No) for the Multiplicative semigroup. For the additive case, it would also set the group generator list [(1,0),(0,1)]. In both cases, it would also set cardinality = Infinity. Similar attributes are formed for the constructors of Permutation, Vector, Matrix, Polyninomial, Fraction, ResidueRing. And that is all. It does not provide so far any real algorithmic support for the Group theory, except some operations on permutations. But one may develop the program by adding the needed algorithms and introducing new attributes. : What I had in mind : was perhaps you could have a function which takes a list(set) and a : function with two arguments(binary operator) and checks to see whether or : not it is a group. I think it might be a fun exercies to write myself but : I'd like to see if it's already been done or what you guys think about it. I never programmed this. It looks like some exercise in algorithms. There are also books on the combinatorial group theory, maybe, they say something about efficient procedures for this. Regards, ------------------ Sergey Mechveliani mechvel@botik.ru
S.D.Mechveliani wrote:
Hi, all,
To Eric Allen Wohlstadter's
: Are there any Haskell libraries or programs related to group theory?
...
Marc van Dongen <dongen@cs.ucc.ie> writes
I think Sergey Mechveliani's docon (algebraic DOmain CONstructor) has facilities for that. ...
Sorry, DoCon (<http://www.botik.ru/pub/local/Mechveliani/docon/2.01/>)
really supports the Commutative Rings, but provides almost nothing for the Group theory.
EAW again:
: ... I think it might be a fun exercies to write myself but : I'd like to see if it's already been done or what you guys : think about it.
SM:
I never programmed this. It looks like some exercise in algorithms. There are also books on the combinatorial group theory, maybe, they say something about efficient procedures for this.
== "Some exercise in algorithms". Hm. There is more to that than this... This issue has been recently stirred a bit in the comp.functional newsgroup, in a larger context, general Math, not necessarily the group theor. There are at least two people *interested* in it, although they didn't do much yet (for various reasons...) Suggestion: Take GAP! ( http://www-history.mcs.st-and.ac.uk/~gap/ ) Plenty of simply coded algorithms, specifically in this domain. I coded just for fun a few simple things in Haskell some time ago, and it was a real pleasure. The code is cleaner and simpler. Its presentation is also much cleaner than the original algorithms written in GAP language. But I discarded all this stuff, thinking that I would have never time enough to get back to it... This is a nice project, and I would participate with pleasure in it, although the time factor is still there... Dima Pasechnik (<d.pasechnik@twi.tudelft.nl>; does he read it?) - apparently - as well. Jerzy Karczmarczuk Caen, France
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Jerzy Karczmarczuk -
S.D.Mechveliani