include/algebramix/algebraic_number.hpp File Reference

#include <algebramix/algebraic.hpp>
#include <numerix/ball_complex.hpp>

Go to the source code of this file.

Classes

• class algebraic_number_extension< C, Ball >
• struct binary_helper< algebraic_number_extension< C, Ball > >

Namespaces

• namespace mmx

Defines

• #define TMPL_DEF   template<typename C, typename Ball>
• #define TMPL   template<typename C, typename Ball>
• #define Extension   algebraic_extension<C>
• #define Field   algebraic_number_extension<C,Ball>
• #define Polynomial   polynomial<C>
• #define Element   typename algebraic_number_extension<C,Ball>::El

Typedefs

• typedef
  algebraic_number_extension
  < rational, ball< floating<> > > algebraic_real_extension
• typedef
  algebraic_number_extension
  < rational, ball< complex
  < floating<> > > > algebraic_complex_extension
• typedef algebraic< rational,
  algebraic_real_extension > algebraic_real
• typedef algebraic< rational,
  algebraic_complex_extension > algebraic_number

Functions

• template<typename C , typename Ball > bool shrink (const polynomial< C > &p, Ball &x)
• template<typename C , typename Ball > polynomial< C > annihilator (const algebraic_number_extension< C, Ball > &ext, const typename algebraic_number_extension< C, Ball >::El &p)
• UNARY_RETURN_TYPE (STMPL, Re_op, algebraic_number, algebraic_real)
• UNARY_RETURN_TYPE (STMPL, abs_op, algebraic_number, algebraic_real)
• BINARY_RETURN_TYPE (STMPL, gaussian_op, algebraic_real, algebraic_real, algebraic_number)
• template<typename C , typename Ball > nat hash (const algebraic_number_extension< C, Ball > &x)
• template<typename C , typename Ball > nat exact_hash (const algebraic_number_extension< C, Ball > &x)
• template<typename C , typename Ball > nat hard_hash (const algebraic_number_extension< C, Ball > &x)
• template<typename C , typename Ball > bool operator== (const algebraic_number_extension< C, Ball > &x, const algebraic_number_extension< C, Ball > &y)
• template<typename C , typename Ball > bool operator!= (const algebraic_number_extension< C, Ball > &x, const algebraic_number_extension< C, Ball > &y)
• template<typename C , typename Ball > bool exact_eq (const algebraic_number_extension< C, Ball > &x, const algebraic_number_extension< C, Ball > &y)
• template<typename C , typename Ball > bool exact_neq (const algebraic_number_extension< C, Ball > &x, const algebraic_number_extension< C, Ball > &y)
• template<typename C , typename Ball > bool hard_eq (const algebraic_number_extension< C, Ball > &x, const algebraic_number_extension< C, Ball > &y)
• template<typename C , typename Ball > bool hard_neq (const algebraic_number_extension< C, Ball > &x, const algebraic_number_extension< C, Ball > &y)
• template<typename C , typename Ball > syntactic flatten (const algebraic_number_extension< C, Ball > &x)
• template<typename C , typename V , typename K > K eval (const polynomial< C, V > &p, const K &x)
• template<typename C , typename Ball > bool improve_zero (const polynomial< C > &p, Ball &z)
• template<typename C , typename Ball > void shrink_check (const polynomial< C > &p, Ball &x)
• template<typename C , typename Ball > void increase_precision (const algebraic_number_extension< C, Ball > &ext)
• template<typename C , typename Ball > Ball eval (const algebraic_number_extension< C, Ball > &ext, const typename algebraic_number_extension< C, Ball >::El &p1)
• template<typename C , typename Ball > Ball eval (const algebraic_number_extension< C, Ball > &ext1, const algebraic_number_extension< C, Ball > &ext2, const vector< C > &v)
• template<typename C , typename Ball > Ball as_ball (const algebraic< C, algebraic_number_extension< C, Ball > > &a)
• template<typename C , typename Ball > Center_type (Ball) as_floating(const algebraic<C
• Ball
  algebraic_number_extension< C,
  Ball >::El square (const algebraic_number_extension< C, Ball > &ext, const typename algebraic_number_extension< C, Ball >::El &p1)
• template<typename C , typename Ball > algebraic_number_extension< C,
  Ball >::El mul (const algebraic_number_extension< C, Ball > &ext, const typename algebraic_number_extension< C, Ball >::El &p1, const typename algebraic_number_extension< C, Ball >::El &p2)
• template<typename C , typename Ball > algebraic_number_extension< C,
  Ball >::El invert (const algebraic_number_extension< C, Ball > &ext, const typename algebraic_number_extension< C, Ball >::El &p1)
• template<typename C , typename Ball > algebraic_number_extension< C,
  Ball >::El div (const algebraic_number_extension< C, Ball > &ext, const C &c1, const typename algebraic_number_extension< C, Ball >::El &p2)
• template<typename C , typename Ball > algebraic_number_extension< C,
  Ball >::El div (const algebraic_number_extension< C, Ball > &ext, const typename algebraic_number_extension< C, Ball >::El &p1, const typename algebraic_number_extension< C, Ball >::El &p2)
• template<typename C , typename Ball > bool is_zero (const algebraic_number_extension< C, Ball > &ext, const typename algebraic_number_extension< C, Ball >::El &p1)
• template<typename C , typename Ball > int sign (const algebraic_number_extension< C, Ball > &ext, const typename algebraic_number_extension< C, Ball >::El &p1)
• template<typename C , typename Ball > algebraic_number_extension< C,
  Ball > join (const algebraic_number_extension< C, Ball > &ext1, const algebraic_number_extension< C, Ball > &ext2, typename algebraic_number_extension< C, Ball >::El &z1, typename algebraic_number_extension< C, Ball >::El &z2)
• template<typename C , typename Ball > algebraic_number_extension< C,
  Ball > upgrade (const algebraic_number_extension< C, Ball > &ext1, const algebraic_number_extension< C, Ball > &ext2, typename algebraic_number_extension< C, Ball >::El &p1, typename algebraic_number_extension< C, Ball >::El &p2)
• template<typename C , typename Ball > algebraic_number_extension< C,
  Ball > normalize (const algebraic_number_extension< C, Ball > &ext, const typename algebraic_number_extension< C, Ball >::El &p)
• template<typename C , typename Ball > algebraic_number_extension< C,
  Ball > ramify (const algebraic_number_extension< C, Ball > &ext, nat p)
• void set_imaginary (algebraic_number &z)
• algebraic_number times_i (const algebraic_number &z)
• algebraic_number over_i (const algebraic_number &z)
• algebraic_number gaussian (const algebraic_real &x, const algebraic_real &y)
• template<typename C , typename Ball > algebraic_number_extension< C,
  Ball > conj (const algebraic_number_extension< C, Ball > &ext)
• algebraic_number conj (const algebraic_number &z)
• algebraic_real Re (const algebraic_number &z)
• algebraic_real Im (const algebraic_number &z)
• algebraic_real abs (const algebraic_number &z)

---

Define Documentation

#define Element   typename algebraic_number_extension<C,Ball>::El

Definition at line 23 of file algebraic_number.hpp.

#define Extension   algebraic_extension<C>

Definition at line 20 of file algebraic_number.hpp.

#define Field   algebraic_number_extension<C,Ball>

Definition at line 21 of file algebraic_number.hpp.

Referenced by binary_helper< algebraic_number_extension< C, Ball > >::assemble(), mmx::conj(), mmx::increase_precision(), mmx::join(), mmx::normalize(), mmx::ramify(), and mmx::upgrade().

#define Polynomial   polynomial<C>

Definition at line 22 of file algebraic_number.hpp.

#define TMPL   template<typename C, typename Ball>

Definition at line 19 of file algebraic_number.hpp.

#define TMPL_DEF   template<typename C, typename Ball>

Definition at line 18 of file algebraic_number.hpp.