irreducibility test

Hi all,

I would like to ask you, about the function irreducible.. http://www.mathworks.com/help/toolbox/mupad/stdlib/irreducible.html

I want to check if a polynomial is irreducible, but I have problem on how to declare the polynomial..I tried the examples o the abov link but matlab returns " ??? Undefined function or variable 'x'."..

Answer 1

[Walter Roberson]

syms x
evalin(symengine, 'irreducible', x^2 - 2)

Answer 2

[Stefan Wehmeier]

You have to declare it as a polynomial over GaloisField, e.g.

F = evalin(symengine, 'poly(x^2-2, Dom::GaloisField(5^7)))
feval(symengine, 'irreducible', F)

[mmavrop]

thanks a lot!

[sqw]

hi I want use this function for a loop of polynomial but I cant change the polynomial with symbolic variableas.

for example i want this: syms x z=x^a(n,1)+x^a(n,2)+1 for i=1 we have z=x^19+x^12+1 %%a is a vector and change base for i=1:n i want check the z polynomial is irreducible or not?

F = evalin(symengine, 'poly(z,Dom::GaloisField(2))') F =

poly(z, [z], Dom::GaloisField(2, 1, poly(X7, [X7], IntMod(2)))) feval(symengine, 'irreducible', F)

ans =

TRUE

 but this polynomial in not irreducible

the mistake of this answer come from [z] instead of [x]!!!!

please help me to solve it

Answer 3

[mmavrop]

thank you Walter! I tried your answer and matlab returned "`proc irreducible(p) ... end`" in both cases, (x^2 - 2) and (x^2 + 2).. What am I doing wrong? I am using matlab R2009b..

[Walter Roberson]

Hmmm.... Say, are you perhaps using the Maple symbolic engine? That was still possible in R2009b even though MuPAD was the default. Your ending of the procedure with "end" is a clue, in that MuPAD ends its procedures with "end_proc" but Maple ends with "end".

The internal Maple name for the procedure was irreduc so you could _try_

feval(symengine, 'irreduc', x^2 - 2)

If that doesn't work, go back to irreducible but with feval

[Alexander]

feval did the trick for me:

>> syms x

>> feval(symengine, 'irreducible', x^2 + 2)

ans =

TRUE

Answer 4

[mmavrop]

Thank you so much both! it works! May I ask an other question? Is there a way to find out if a polynomial over galois field is irreducible?