Thanks, Warren, Mike, Neil. I should have known that. Duh to me! At 09:24 AM 8/22/2012, Neil Sloane wrote:

Sure, use a version of Lagrange interpolation. Make a list (a generalized truth table) of all the values the function takes at all possible arguments. Then write a monomial for each term and add them up. E.g. if you want the value 7 at x=3, y=4, z=5, the monomial is Prod_{a!=3}(x-a) Prod_{b!=4} (y-b) Prod_{c!=5) (z-c) 7/d, where d is the appropriate constant.

On Wed, Aug 22, 2012 at 12:06 PM, Henry Baker <hbaker1@pipeline.com> wrote:

...

It appears that all functions over GF(2) can be synthesized using only polynomials:

E.g.,

f()=0, f()=1

f(x)=0, f(x)=1, f(x)=x, f(x)=1+x

not(x)=1+x, and(x,y)=x*y, or(x,y)=x+y+x*y, etc.

Q: Can all functions over _any_ finite field by synthesized using only polynomials, and is there a simple synthesis procedure?

-- Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com