> <\body> <\session|mathemagix|default> <\input> <|input> use "factorix" <\unfolded-io> <|unfolded-io> help separable_factorization <|unfolded-io> <\text> Vector (Separable_factor (Polynomial (Integer)))>> Vector (Separable_factor (Polynomial (Rational)))>> Vector (Separable_factor (Polynomial (Modular (Integer))))>> Vector (Separable_factor (Polynomial (Polynomial (Integer))))>> Vector (Separable_factor (Polynomial (Polynomial (Rational))))>> Vector (Separable_factor (Polynomial (Polynomial (Modular (Integer)))))>> Vector (Separable_factor (Polynomial (Ffe (Modular (Integer)))))>> Vector (Separable_factor (Polynomial (Polynomial (Ffe (Modular (Integer))))))>> <\input> <|input> x == polynomial (0 :\ Rational, 1 :\ Rational); <\unfolded-io> <|unfolded-io> separable_factorization ((x-1)^10 * (x-2)^2) <|unfolded-io> *> <\input> <|input> x == polynomial (0 :\ Integer, 1 :\ Integer); <\unfolded-io> <|unfolded-io> separable_factorization ((x-1)^10 * (x-2)^2) <|unfolded-io> *> <\unfolded-io> <|unfolded-io> v == separable_factorization ((x-1)^10 * (x-2)^2 mod modulus 5) <|unfolded-io> *+4|)>> <\unfolded-io> <|unfolded-io> factor (v[1]) <|unfolded-io> <\unfolded-io> <|unfolded-io> ideg (v[1]) <|unfolded-io> <\unfolded-io> <|unfolded-io> mul (v[1]) <|unfolded-io> <\unfolded-io> <|unfolded-io> separable? ((x - 1)^10 - 1) <|unfolded-io> <\input> <|input> y == polynomial (polynomial (0 :\ Rational), polynomial (1 :\ Rational)); <\unfolded-io> <|unfolded-io> f == (y - x - 1) * (y^2 - x^10 - 2 * x +1) <|unfolded-io> +*y+-2*x+1|)>*y+x+x+2*x+x-1> <\unfolded-io> <|unfolded-io> separable_factorization f <|unfolded-io> +*y+-2*x+1|)>*y+x+x+2*x+x-1> <\input> <|input> y == polynomial (polynomial (0 :\ Integer), polynomial (1 :\ Integer)); <\unfolded-io> <|unfolded-io> f == (y - x - 1) * (y^2 - x^10 - 2 * x +1) <|unfolded-io> +*y+-2*x+1|)>*y+x+x+2*x+x-1> <\unfolded-io> <|unfolded-io> separable_factorization f <|unfolded-io> +*y+-2*x+1|)>*y+x+x+2*x+x-1> <\unfolded-io> <|unfolded-io> separable_factorization (f mod modulus 2) <|unfolded-io> *+x+1|)>> <\input> <|input> p == modulus 2; <\input> <|input> x == polynomial (0, 1) mod p; <\unfolded-io> <|unfolded-io> q == irreducible_polynomial (x, 8) <|unfolded-io> +x+x+x+1> <\unfolded-io> <|unfolded-io> a == ffe (x, q) <|unfolded-io> <\input> <|input> set_variable_name (a, 'a) <\unfolded-io> <|unfolded-io> a <|unfolded-io> <\unfolded-io> <|unfolded-io> x == polynomial (ffe (polynomial (0) mod p, q), \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ffe (polynomial (1) mod p, q)) <|unfolded-io> <\input> <|input> zero == ffe (polynomial (0) mod p, q); one \ == ffe (polynomial (1) mod p, q); <\unfolded-io> <|unfolded-io> separable_factorization ((x-one)^10 * (x^2+x+one)^2) <|unfolded-io> |)>+x+1|)>*+1|)>> . If you don't have this file, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.> >