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 <beroal@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.

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