/Users/mourrain/Devel/mmx/algebramix/include/algebramix/algebraic.hpp File Reference

#include <algebramix/algebraic_extension.hpp>

Go to the source code of this file.

Classes

• struct trivial_extension_helper< FT, C, Extension >
• struct trivial_extension_helper< empty_format, C, Extension >
• class algebraic< C, Extension >
• struct binary_helper< algebraic< C, Extension > >

Namespaces

• namespace mmx

Defines

• #define TMPL_DEF   template<typename C, typename Extension=algebraic_extension<C> >
• #define TMPL   template<typename C, typename Extension>
• #define Polynomial   polynomial<C>
• #define Algebraic   algebraic<C,Extension>
• #define Element   typename Extension::El

Functions

• template<typename C , typename Extension > Extension trivial_extension ()
• template<typename C , typename Extension > Extension trivial_extension (const format< C > &fm)
• STYPE_TO_TYPE (template< typename C, typename Extension >, scalar_type, algebraic< C, Extension >, C)
• template<typename C , typename Extension > format< C > CF (const algebraic< C, Extension > &x)
• template<typename C , typename Extension > Extension field (const algebraic< C, Extension > &x)
• template<typename C , typename Extension > Extension::El value (const algebraic< C, Extension > &x)
• template<typename C , typename Extension > polynomial< C > field_modulus (const algebraic< C, Extension > &x)
• template<typename C , typename Extension > nat hash (const algebraic< C, Extension > &x)
• template<typename C , typename Extension > nat exact_hash (const algebraic< C, Extension > &x)
• template<typename C , typename Extension > nat hard_hash (const algebraic< C, Extension > &x)
• template<typename C , typename Extension > bool exact_eq (const algebraic< C, Extension > &x1, const algebraic< C, Extension > &x2)
• template<typename C , typename Extension > bool exact_neq (const algebraic< C, Extension > &x1, const algebraic< C, Extension > &x2)
• template<typename C , typename Extension > bool hard_eq (const algebraic< C, Extension > &x1, const algebraic< C, Extension > &x2)
• template<typename C , typename Extension > bool hard_neq (const algebraic< C, Extension > &x1, const algebraic< C, Extension > &x2)
• template<typename C , typename Extension > bool is_zero (const algebraic< C, Extension > &x)
• template<typename C , typename Extension > int sign (const algebraic< C, Extension > &x)
• template<typename C , typename Extension > bool operator== (const algebraic< C, Extension > &x1, const algebraic< C, Extension > &x2)
• template<typename C , typename Extension > bool operator!= (const algebraic< C, Extension > &x1, const algebraic< C, Extension > &x2)
• EQUAL_INT_SUGAR (template< typename C, typename Extension >, algebraic< C, Extension >)
• COMPARE_SUGAR (template< typename C, typename Extension >, algebraic< C, Extension >)
• COMPARE_INT_SUGAR (template< typename C, typename Extension >, algebraic< C, Extension >)
• template<typename C , typename Extension > syntactic flatten (const algebraic< C, Extension > &x)
• template<typename C , typename Extension > void upgrade (algebraic< C, Extension > &a1, algebraic< C, Extension > &a2)
• template<typename C , typename Extension > polynomial< C > annihilator (const algebraic< C, Extension > &a)
• template<typename C , typename Extension > algebraic< C, Extension > normalize (const algebraic< C, Extension > &a)
• template<typename C , typename Extension > algebraic< C, Extension > operator+ (const algebraic< C, Extension > &x1b, const algebraic< C, Extension > &x2b)
• template<typename C , typename Extension > algebraic< C, Extension > operator+ (const algebraic< C, Extension > &x1, const C &x2)
• template<typename C , typename Extension > algebraic< C, Extension > operator+ (const C &x1, const algebraic< C, Extension > &x2)
• template<typename C , typename Extension > algebraic< C, Extension > operator- (const algebraic< C, Extension > &x)
• template<typename C , typename Extension > algebraic< C, Extension > operator- (const algebraic< C, Extension > &x1b, const algebraic< C, Extension > &x2b)
• template<typename C , typename Extension > algebraic< C, Extension > operator- (const algebraic< C, Extension > &x1, const C &x2)
• template<typename C , typename Extension > algebraic< C, Extension > operator- (const C &x1, const algebraic< C, Extension > &x2)
• template<typename C , typename Extension > algebraic< C, Extension > square (const algebraic< C, Extension > &x1)
• template<typename C , typename Extension > algebraic< C, Extension > operator* (const algebraic< C, Extension > &x1b, const algebraic< C, Extension > &x2b)
• template<typename C , typename Extension > algebraic< C, Extension > operator* (const algebraic< C, Extension > &x1, const C &x2)
• template<typename C , typename Extension > algebraic< C, Extension > operator* (const C &x1, const algebraic< C, Extension > &x2)
• template<typename C , typename Extension > algebraic< C, Extension > invert (const algebraic< C, Extension > &x1)
• template<typename C , typename Extension > algebraic< C, Extension > operator/ (const C &x1, const algebraic< C, Extension > &x2)
• template<typename C , typename Extension > algebraic< C, Extension > operator/ (const algebraic< C, Extension > &x1, const C &x2)
• template<typename C , typename Extension > algebraic< C, Extension > operator/ (const algebraic< C, Extension > &x1b, const algebraic< C, Extension > &x2b)
• ARITH_SCALAR_INT_SUGAR (template< typename C, typename Extension >, algebraic< C, Extension >)
• template<typename C , typename Extension > algebraic< C, Extension > root (const algebraic< C, Extension > &x, const int &p)
• template<typename C , typename Extension > algebraic< C, Extension > sqrt (const algebraic< C, Extension > &x)

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Define Documentation

#define Algebraic   algebraic<C,Extension>

Definition at line 20 of file algebraic.hpp.

Referenced by binary_helper< algebraic< C, Extension > >::assemble(), mmx::invert(), mmx::normalize(), mmx::operator*(), mmx::operator+(), mmx::operator-(), mmx::operator/(), binary_helper< algebraic< C, Extension > >::read(), mmx::root(), mmx::square(), and mmx::upgrade().

#define Element   typename Extension::El

Definition at line 21 of file algebraic.hpp.

Referenced by binary_helper< algebraic< C, Extension > >::read(), and mmx::upgrade().

#define Polynomial   polynomial<C>

Examples:

modular_polynomial_test.cpp, polynomial_int_test.cpp, polynomial_integer_test.cpp, polynomial_modular_test.cpp, polynomial_polynomial_test.cpp, polynomial_test.cpp, and quotient_test.cpp.

Definition at line 19 of file algebraic.hpp.

Referenced by implementation< polynomial_subresultant_base, V, polynomial_gcd_ring_dicho_inc< BV > >::_half_gcd(), implementation< polynomial_evaluate, V, polynomial_dicho< BV > >::_multi_rem(), implementation< polynomial_evaluate, V, polynomial_naive >::annulator(), implementation< polynomial_evaluate, V, polynomial_dicho< BV > >::annulator(), implementation< polynomial_subresultant_base, V, polynomial_gcd_ring_ducos_inc< BV > >::defected_prem(), implementation< polynomial_subresultant_base, V, polynomial_gcd_ring_naive_inc< W > >::defected_prem(), root_modular_naive::degree_one_factorization(), implementation< polynomial_evaluate, V, polynomial_dicho< BV > >::evaluate(), implementation< polynomial_gcd, V, polynomial_ring_naive< W > >::gcd(), implementation< polynomial_gcd, V, polynomial_naive >::gcd(), implementation< polynomial_subresultant_base, V, polynomial_gcd_ring_dicho_inc< BV > >::half_subresultant(), implementation< polynomial_subresultant_base, V, polynomial_gcd_ring_dicho_inc< BV > >::half_subresultant_rec(), implementation< polynomial_evaluate, V, polynomial_naive >::interpolate(), implementation< polynomial_evaluate, V, polynomial_dicho< BV > >::interpolate(), implementation< polynomial_gcd, V, polynomial_ring_naive< W > >::invert_mod(), implementation< polynomial_gcd, V, polynomial_naive >::invert_mod(), implementation< polynomial_gcd, V, polynomial_ring_naive< W > >::lcm(), implementation< polynomial_gcd, V, polynomial_naive >::lcm(), root_modular_naive::linear_factorization(), root_modular_naive::linear_splitting(), implementation< polynomial_evaluate, V, polynomial_naive >::multi_rem(), mmx::normalize(), implementation< polynomial_gcd, V, polynomial_ring_naive< W > >::pade(), implementation< polynomial_gcd, V, polynomial_naive >::pade(), root_modular_naive::pow_mod(), mmx::root(), root_modular_naive::roots(), implementation< polynomial_subresultant_base, V, polynomial_ring_naive< W > >::subresultant(), implementation< polynomial_subresultant_base, V, polynomial_gcd_ring_dicho_inc< BV > >::subresultant_compose(), implementation< polynomial_subresultant_base, V, polynomial_gcd_ring_ducos_inc< BV > >::subresultant_sequence(), implementation< polynomial_subresultant_base, V, polynomial_gcd_ring_naive_inc< W > >::subresultant_sequence(), implementation< polynomial_subresultant_base, V, polynomial_ring_naive< W > >::subresultant_sequence(), implementation< polynomial_subresultant_base, V, polynomial_naive >::subresultant_sequence(), implementation< polynomial_evaluate, V, polynomial_naive >::tevaluate(), implementation< polynomial_evaluate, V, polynomial_dicho< BV > >::tevaluate(), and implementation< polynomial_evaluate, V, polynomial_dicho< BV > >::tinterpolate().

#define TMPL   template<typename C, typename Extension>

Examples:

p_adic_test.cpp, polynomial_int_test.cpp, polynomial_integer_test.cpp, polynomial_modular_test.cpp, polynomial_polynomial_test.cpp, and polynomial_test.cpp.

Definition at line 18 of file algebraic.hpp.

#define TMPL_DEF   template<typename C, typename Extension=algebraic_extension<C> >

Definition at line 17 of file algebraic.hpp.