# [Haskell-cafe] Equivalence of two expressions

Sun Jul 11 20:21:14 EDT 2010

```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 <beroal at 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.
>
>
> _______________________________________________