> <\body> <\session|mathemagix|default> <\input> <|input> use "factorix" <\unfolded-io> <|unfolded-io> help irreducible_factorization <|unfolded-io> <\text> Vector (Irreducible_factor (Rational))>> Vector (Irreducible_factor (Integer))>> Vector (Irreducible_factor (Modular (Integer)))>> Vector (Irreducible_factor (Ffe (Modular (Integer))))>> Vector (Irreducible_factor (Polynomial (Integer)))>> Vector (Irreducible_factor (Polynomial (Rational)))>> Vector (Irreducible_factor (Polynomial (Modular (Integer))))>> Vector (Irreducible_factor (Polynomial (Polynomial (Integer))))>> Vector (Irreducible_factor (Polynomial (Polynomial (Rational))))>> Vector (Irreducible_factor (Polynomial (Series (Rational))))>> Vector (Irreducible_factor (Polynomial (Polynomial (Modular (Integer)))))>> Vector (Irreducible_factor (Polynomial (Ffe (Modular (Integer)))))>> Vector (Irreducible_factor (Polynomial (Series (Modular (Integer)))))>> Vector (Irreducible_factor (Polynomial (Polynomial (Ffe (Modular (Integer))))))>> Vector (Irreducible_factor (Polynomial (Series (Ffe (Modular (Integer))))))>> <\unfolded-io> <|unfolded-io> irreducible? 35164639 <|unfolded-io> <\unfolded-io> <|unfolded-io> irreducible_factorization 100! <|unfolded-io> *41*43*47*29*31*23*17*19*13*11*7*5*3*2> <\unfolded-io> <|unfolded-io> x == polynomial (0, 1) <|unfolded-io> <\unfolded-io> <|unfolded-io> irreducible_factorization (15*(x-1)^10 * (x-2)^2) <|unfolded-io> *> <\unfolded-io> <|unfolded-io> irreducible_factorization (-(x-1)^10 * (x-2)^2) <|unfolded-io> *> <\unfolded-io> <|unfolded-io> irreducible_factorization ((x-1)^10 * (x-2)^2 mod modulus 5) <|unfolded-io> *> <\unfolded-io> <|unfolded-io> irreducible_factorization (1000640091 * 9 * (x^10-1)^3 * (x-2)^2) <|unfolded-io> *3***-x+x-x+1|)>*+x+x+x+1|)>> <\unfolded-io> <|unfolded-io> irreducible_factorization ((x^10-1)^3 * (x-2)^2 mod modulus 11) <|unfolded-io> *********> <\input> <|input> y == polynomial (polynomial (0 :\ Rational), polynomial (1 :\ Rational)); <\unfolded-io> <|unfolded-io> irreducible_factorization ((y - x - 1) * (y^2 - x^10 - 2 * x +1)) <|unfolded-io> *-x-2*x+1|)>> <\input> <|input> p == modulus 3; <\input> <|input> x == polynomial (0, 1) mod p; <\unfolded-io> <|unfolded-io> q == irreducible_polynomial (x, 3) <|unfolded-io> +2*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> irreducible_factorization (x^27-x) <|unfolded-io> +2|)>*x**+2*a+2|)>*+2*a|)>*|)>*+a+1|)>**+a|)>**+a+1|)>*+2*a+1|)>*+a+2|)>**+1|)>**+2*a+2|)>****+a|)>*+2*a|)>*+2*a+1|)>*+1|)>*|)>*+2|)>*+a+2|)>> <\input> <|input> y == polynomial (polynomial zero, polynomial one); <\unfolded-io> <|unfolded-io> f == (y - x - a)^2 * (y^7 - x^6 - x + one) <|unfolded-io> +*y++2*a*x+a|)>*y++2*x+1|)>*y++2*a*x+2*x+*x+a|)>*y+2*x+a*x+2*a*x+2*x+*x++2*a|)>*x+a> <\unfolded-io> <|unfolded-io> irreducible_factorization f <|unfolded-io> +2*x+2*x+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.> >