# how to use a variable in finite field

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ling on 6 Apr 2024
Answered: Paul on 6 Apr 2024
sym a;
I want y=gf(3,8)*a, but it did not work.
ling on 6 Apr 2024
The polynomial can be easily reconstructed using Lagrange interpolation in GF(p),where p is a primer.
Manikanta Aditya on 6 Apr 2024
Yeah

John D'Errico on 6 Apr 2024
Edited: John D'Errico on 6 Apr 2024
g = gf(3, 8)
g = GF(2^8) array. Primitive polynomial = D^8+D^4+D^3+D^2+1 (285 decimal) Array elements = 3
whos g
Name Size Bytes Class Attributes g 1x1 92 gf
g is a gf object. But g is not compatible for multiplication by a symbolic parameter. These are two independent (and unfortunately, incompatible) toolboxes. They don't talk to or with each other. This is why when you do try to multiply g with a symbolic object, it fails.
syms a
g*a
Error using gf
Expected input x to be one of these types:

double, single, uint8, uint16, uint32, uint64, int8, int16, int32, int64

Error in gf (line 191)
validateattributes(x,{'numeric'}, {'integer', ...

Error in gf>areCompatible (line 1481)
if ~isa(b,'gf'), b=gf(b,a.m,a.prim_poly); return; end

Error in * (line 931)
[x,y]=areCompatible(x,y,'mtimes');
As the error message says, the only things you can multiply a gf object by are in that list of numeric classes. A sym is not one of the allowed classes for that operation.
You could possibly write your own set of tools that would work as you wish, essentially rewriting the gf class. Since a sym can take on any value, and it MUST be discrete for that operation to make any sense at all, it might take some work on your part to do so in a valid way.

Paul on 6 Apr 2024
How about something along these lines?
y = @(a) gf(3,8)*a;
y(1)
ans = GF(2^8) array. Primitive polynomial = D^8+D^4+D^3+D^2+1 (285 decimal) Array elements = 3
y(2)
ans = GF(2^8) array. Primitive polynomial = D^8+D^4+D^3+D^2+1 (285 decimal) Array elements = 6