With arbitrary presentations of the ring allowed, this problem has as a corner case the word problem for groups ( http://en.wikipedia.org/wiki/Word_problem_for_groups). We take the ring to be K = CG, the group algebra over C of a group G. Then take the two elements in K to be the images under the natural inclusion of G in CG of two elements of G.
Regards, Michael On Sat, Jul 10, 2010 at 10:09 PM, Roman Beslik <ber...@ukr.net> wrote: > Hi. > > On 10.07.10 21:40, Grigory Sarnitskiy wrote: > >> I'm not very familiar with algebra and I have a question. >> >> Imagine we have ring K. We also have two expressions formed by elements >> from K and binary operations (+) (*) from K. >> > In what follows I assume "elements from K" ==> "variables" > > Can we decide weather these two expressions are equivalent? If there is >> such an algorithm, where can I find something in Haskell about it? >> > Using distributivity of ring you convert an expression to a normal form. "A > normal form" is "a sum of products". If normal forms are equal (up to > associativity and commutativity of ring), expressions are equivalent. I am > not aware whether Haskell has a library. > > -- > Best regards, > Roman Beslik. > > > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe >
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