davimon

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These are replies submitted by davimon

@dharr Thanks!

So this would be the procedure for calculating the root of an element in G. Actually I need this step later on in my algorithm so now I am prepared for this.

The equation we discussed was actually a first example. In the first step I have to solve the equation

L²+L= (element in G)   or    L²+L + (element in G) = 0

with L as lambda. This one really needs a solve command. Otherwise I would have to use a quadratic formula for fields with characteristik 2 and calculate it this way.

@dharr

"Solving lambda^2-(number in G) = 0 means solving a polynomial whose coefficient field is G."

So as far as I understood, Maple cannot recognize where to solve the equation? This seems to be kind of format issue.

Btw. I tried the "use" command outside and inside a procedure and got different warnings (see sheet Algorithmus.mw):

use G in
  solve(lambda^2+x2=0,lambda)
end use;

OUTSIDE: Error, (in ^) modp1: invalid arguments to function Powmod

INSIDE: Error, (in algo) no bindings were specified or implied

Why does it behave differently within a procedure?

@dharr Now I have a subsequent question:

I want to solve an equation in G:=GF(2,4,p) for lambda using

solve(G:-`^`(lambda,2) = G:-`+`(x2,coeffa),lambda)    #x2 and coeffa are converted elements in G, so the sum is calculated correctly

I get: Error, (in ^) modp1: invalid arguments to function Powmod

I think it's because lambda is not explicitly from G. How can I declare lambda as a variable in G? If this is not working, how can I solve an equation in G in general?

BR, David

Algorithmus.mw

@dharr Thank you very much! This workaround helped a lot :)

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