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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1909.0. "Polynomials only" by EVTSG8::ESANU (Au temps pour moi) Fri Nov 18 1994 12:03

Let  p  be prime,  Zp  be the field of the residues modulo  p  and
f: (Zp)^n --> Zp. Then  f  is polynomial.

(The only functions defined on the direct product n times  Zp  and taking
values in  Zp  are the polynomials - for prime  p ).

Mihai.
T.RTitleUserPersonal
Name		DateLines
1909.1CSC32::D_DERAMODan D'Eramo, Customer Support CenterFri Nov 18 1994 20:2114
        Hint:
        
        Let p=7, n=3, and consider the function
        
                           { 1        if x = 3, y = 2, z = 6
        	f(x,y,z) = {
                           { 0        otherwise
        
        Then f(x,y,z) is the polynomial function
        
        	(1 - (x-3)^6)(1 - (y-2)^6)(1 - (z-6)^6)
        
        Dan