> <\body> <\session|mathemagix|default> <\input> <|input> use "factorix" <\unfolded-io> <|unfolded-io> help squarefree_factorization <|unfolded-io> <\text> Vector (Squarefree_factor (Rational))>> Vector (Squarefree_factor (Integer))>> Vector (Squarefree_factor (Modular (Integer)))>> Vector (Squarefree_factor (Ffe (Modular (Integer))))>> Vector (Squarefree_factor (Polynomial (Integer)))>> Vector (Squarefree_factor (Polynomial (Rational)))>> Vector (Squarefree_factor (Polynomial (Modular (Integer))))>> Vector (Squarefree_factor (Polynomial (Polynomial (Integer))))>> Vector (Squarefree_factor (Polynomial (Polynomial (Rational))))>> Vector (Squarefree_factor (Polynomial (Ffe (Modular (Integer)))))>> Vector (Squarefree_factor (Polynomial (Polynomial (Modular (Integer)))))>> Vector (Squarefree_factor (Polynomial (Polynomial (Ffe (Modular (Integer))))))>> <\input> <|input> x == polynomial (0 :\ Rational, 1 :\ Rational); <\unfolded-io> <|unfolded-io> squarefree_factorization (-(x-1)^10 * (x-2)^2) <|unfolded-io> *> <\input> <|input> x == polynomial (0 :\ Integer, 1 :\ Integer); <\unfolded-io> <|unfolded-io> squarefree_factorization ((x-1)^10 * (x-2)^2 mod modulus 5) <|unfolded-io> *> <\unfolded-io> <|unfolded-io> separable_factorization ((x-1)^10 * (x-2)^2 mod modulus 5) <|unfolded-io> *+4|)>> <\unfolded-io> <|unfolded-io> squarefree_factorization (100064500091 * 9 * (x^10-1)^3 * (x-2)^2) <|unfolded-io> **-1|)>> <\unfolded-io> <|unfolded-io> squarefree_factorization% (100064500091 * (x^10-1)^3 * (x-2)^2) <|unfolded-io> *-1|)>> <\input> <|input> y == polynomial (polynomial (0 :\ Rational), polynomial (1 :\ Rational)); <\unfolded-io> <|unfolded-io> f == (y - x - 1)^2 * (y^2 - x^10 - 2 * x +1) <|unfolded-io> +*y++x+2|)>*y++2*x+4*x+2*x-2|)>*y-x-2*x-x-2*x-3*x+1> <\unfolded-io> <|unfolded-io> squarefree_factorization f <|unfolded-io> -x-2*x+1|)>*> <\input> <|input> y == polynomial (polynomial (0 :\ Integer), polynomial (1 :\ Integer)); <\unfolded-io> <|unfolded-io> f == (y - x - 1)^2 * (y^2 - x^10 - 2 * x +1) <|unfolded-io> +*y++x+2|)>*y++2*x+4*x+2*x-2|)>*y-x-2*x-x-2*x-3*x+1> <\unfolded-io> <|unfolded-io> squarefree_factorization f <|unfolded-io> -x-2*x+1|)>*> <\unfolded-io> <|unfolded-io> squarefree_factorization (f mod modulus 2) <|unfolded-io> ++x|)>*y+x+x+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> <\input> <|input> a == ffe (x, q); <\input> <|input> set_variable_name (a, 'a); <\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> squarefree_factorization ((x-one)^10 * (x^2+x+one)^2) <|unfolded-io> +x+1|)>*> <\input> <|input> y == polynomial (polynomial zero, polynomial one); <\unfolded-io> <|unfolded-io> f == (y - x - one) * (y^2 - x^10 - x - x + one) <|unfolded-io> +*y++1|)>*y+x+x+x+1> <\unfolded-io> <|unfolded-io> squarefree_factorization f <|unfolded-io> *+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.> >