Re: [Haskell-cafe] Equivalence of two expressions
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 ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Equivalence of two expressions
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. Can we decide weather these two expressions are equivalent? If there is such an algorithm, where can I find something in Haskell about it? If there is no such algorithm for a ring, maybe there is for a field? ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Equivalence of two expressions
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
