Irreducible factorization 
Mmx]  
use "factorix"
 
Mmx]  
help irreducible_factorization

irreducible_factorization : Rational -> Vector (Irreducible_factor (Rational))
(Native)
irreducible_factorization : Integer -> Vector (Irreducible_factor (Integer))
(Native)
irreducible_factorization : Modular (Integer) -> Vector (Irreducible_factor (Modular (Integer)))
(Native)
irreducible_factorization : Ffe (Modular (Integer)) -> Vector (Irreducible_factor (Ffe (Modular (Integer))))
(Native)
irreducible_factorization : Polynomial (Integer) -> Vector (Irreducible_factor (Polynomial (Integer)))
(Native)
irreducible_factorization : Polynomial (Rational) -> Vector (Irreducible_factor (Polynomial (Rational)))
(Native)
irreducible_factorization : Polynomial (Modular (Integer)) -> Vector (Irreducible_factor (Polynomial (Modular (Integer))))
(Native)
irreducible_factorization : Polynomial (Polynomial (Integer)) -> Vector (Irreducible_factor (Polynomial (Polynomial (Integer))))
(Native)
irreducible_factorization : Polynomial (Polynomial (Rational)) -> Vector (Irreducible_factor (Polynomial (Polynomial (Rational))))
(Native)
irreducible_factorization : Polynomial (Series (Rational)) -> Vector (Irreducible_factor (Polynomial (Series (Rational))))
(Native)
irreducible_factorization : Polynomial (Polynomial (Modular (Integer))) -> Vector (Irreducible_factor (Polynomial (Polynomial (Modular (Integer)))))
(Native)
irreducible_factorization : Polynomial (Ffe (Modular (Integer))) -> Vector (Irreducible_factor (Polynomial (Ffe (Modular (Integer)))))
(Native)
irreducible_factorization : Polynomial (Series (Modular (Integer))) -> Vector (Irreducible_factor (Polynomial (Series (Modular (Integer)))))
(Native)
irreducible_factorization : Polynomial (Polynomial (Ffe (Modular (Integer)))) -> Vector (Irreducible_factor (Polynomial (Polynomial (Ffe (Modular (Integer))))))
(Native)
irreducible_factorization : Polynomial (Series (Ffe (Modular (Integer)))) -> Vector (Irreducible_factor (Polynomial (Series (Ffe (Modular (Integer))))))
(Native) 

Mmx]  
irreducible? 35164639
 

Mmx]  
irreducible_factorization 100!
 

Mmx]  
x == polynomial (0, 1)
 

Mmx]  
irreducible_factorization (15*(x-1)^10 * (x-2)^2)
 

Mmx]  
irreducible_factorization (-(x-1)^10 * (x-2)^2)
 

Mmx]  
irreducible_factorization ((x-1)^10 * (x-2)^2 mod modulus 5)
 

Mmx]  
irreducible_factorization (1000640091 * 9 * (x^10-1)^3 * (x-2)^2)
 

Mmx]  
irreducible_factorization ((x^10-1)^3 * (x-2)^2 mod modulus 11)
 

Mmx]  
y == polynomial (polynomial (0 :> Rational), polynomial (1 :> Rational));
 
Mmx]  
irreducible_factorization ((y - x - 1) * (y^2 - x^10 - 2 * x +1))
 

Mmx]  
p == modulus 3;
 
Mmx]  
x == polynomial (0, 1) mod p;
 
Mmx]  
q == irreducible_polynomial (x, 3)
 

Mmx]  
a == ffe (x, q);
 
Mmx]  
set_variable_name (a, 'a);
 
Mmx]  
x == polynomial (ffe (polynomial (0) mod p, q),
                 ffe (polynomial (1) mod p, q))
 

Mmx]  
zero == ffe (polynomial (0) mod p, q);
one  == ffe (polynomial (1) mod p, q);
 
Mmx]  
irreducible_factorization (x^27-x)
 

Mmx]  
y == polynomial (polynomial zero, polynomial one);
 
Mmx]  
f == (y - x - a)^2 * (y^7 - x^6 - x + one)
 

Mmx]  
irreducible_factorization f

© 2013 Grégoire Lecerf
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU General Public License. If you don't have this file, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.