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
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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