quotient::ModUPol

quotient::ModUPol< C, R > Struct Template Reference

List of all members.

Detailed Description

template<class C, class R = UPolDse<C>>
struct quotient::ModUPol< C, R >

Class providing the arithmetic of univariate polynomials modulo a given polynomial UPQuotient<R>::poly. Elements are represented in the Horner basis associated with poly. All the arithmetic operations are performed in this basis. Only the display of a polynomial needs a change to the monomial basis.

Definition at line 38 of file quotient.h.

Public Types

typedef R::value_type value_type
typedef R::size_type size_type
typedef R::iterator iterator
typedef R::reverse_iterator iterator_r
typedef upol::horner< C > rep_type
typedef ModUPol< C, R > self_t

Public Member Functions

 ModUPol ()
 ModUPol (const R &r)
 ModUPol (const ModUPol< R > &Mod)
template<class S>
void monomial_to_horner (rep_type &h, const S &pol)
template<class S>
void horner_to_monomial (S &h, const rep_type &h)
size_type dim ()
void assign (rep_type &r, const rep_type &a)
void assign (rep_type &r, const R &a)
void assign (rep_type &r, const value_type &a)
void assign (rep_type &r, int a)
void add (rep_type &r, const rep_type &a, const rep_type &b)
 Addition of a and b in r.
void add (rep_type &r, const rep_type &a)
 Inplace addition of a to r.
void sub (rep_type &r, const rep_type &a, const rep_type &b)
 Susbtraction of a and b in r.
void sub (rep_type &r, const rep_type &a)
 Inplace substraction of a to r.
void mul (rep_type &r, const rep_type &a, const rep_type &b)
 Multiply a by b in $$ and put it x.
void mul (rep_type &r, const rep_type &a, const C &b)
void div (rep_type &r, const rep_type &a, const C &b)
void square (rep_type &r, const rep_type &a)
 Square f in $$ and put it x.
void print (std::ostream &os, const rep_type &a)
void read (std::istream &is, rep_type &a)

Public Attributes

R poly

Member Function Documentation

template<class C, class R>
template<class S>
void quotient::ModUPol< C, R >::monomial_to_horner ( rep_type &  x,
const S &  pol 
)

Express the polynomial $x$ from a basis (Monomial or Horner) in the other basis. From the Horner basis to the monomial basis (MtoH=false), the Bezoutian matrix $B_{1,p}$ is used. For the other case (MtoH=true), the matrix $H_{{p}}$ is used.

Definition at line 186 of file quotient.h.

References linalg::rep1d< C >::begin(), degree(), quotient::ModUPol< C, R >::dim(), VECTOR::init(), quotient::ModUPol< C, R >::poly, upol::rep< C >::resize(), and VECTOR::reverse().

Referenced by quotient::ModUPol< C, R >::assign().

template<class C, class R>
template<class S>
void quotient::ModUPol< C, R >::horner_to_monomial ( S &  x,
const rep_type &  pol 
)

Express the polynomial $x$ from a basis (Monomial or Horner) in the other basis. From the Horner basis to the monomial basis (MtoH=false), the Bezoutian matrix $B_{1,p}$ is used. For the other case (MtoH=true), the matrix $H_{{p}}$ is used.

Definition at line 223 of file quotient.h.

References linalg::rep1d< C >::begin(), bezout(), degree(), quotient::ModUPol< C, R >::dim(), upol::rep< C >::end(), VECTOR::init(), quotient::ModUPol< C, R >::poly, and VECTOR::reverse().

Referenced by quotient::ModUPol< C, R >::print().

template<class C, class R>
void quotient::ModUPol< C, R >::add ( rep_type &  r,
const rep_type &  a,
const rep_type &  b 
)

Addition of a and b in r.

Definition at line 85 of file quotient.h.

References add(), quotient::ModUPol< C, R >::dim(), and upol::rep< C >::resize().

Referenced by quotient::ModUPol< C, R >::mul().

template<class C, class R>
void quotient::ModUPol< C, R >::add ( rep_type &  r,
const rep_type &  a 
)

Inplace addition of a to r.

Definition at line 92 of file quotient.h.

References add(), quotient::ModUPol< C, R >::dim(), and upol::rep< C >::resize().

template<class C, class R>
void quotient::ModUPol< C, R >::sub ( rep_type &  r,
const rep_type &  a,
const rep_type &  b 
)

Susbtraction of a and b in r.

Definition at line 99 of file quotient.h.

References quotient::ModUPol< C, R >::dim(), upol::rep< C >::resize(), and sub().

Referenced by quotient::ModUPol< C, R >::mul().

template<class C, class R>
void quotient::ModUPol< C, R >::sub ( rep_type &  r,
const rep_type &  a 
)

Inplace substraction of a to r.

Definition at line 106 of file quotient.h.

References quotient::ModUPol< C, R >::dim(), upol::rep< C >::resize(), and sub().

template<class C, class R>
void quotient::ModUPol< C, R >::mul ( rep_type &  r,
const rep_type &  a,
const rep_type &  b 
)

Multiply a by b in $$ and put it x.

Definition at line 160 of file quotient.h.

References quotient::ModUPol< C, R >::add(), degree(), quotient::ModUPol< C, R >::dim(), VECTOR::div_ext(), quotient::ModUPol< C, R >::square(), and quotient::ModUPol< C, R >::sub().

template<class C, class R>
void quotient::ModUPol< C, R >::square ( rep_type &  r,
const rep_type &  a 
)

Square f in $$ and put it x.

Definition at line 113 of file quotient.h.

References UPOLDAR::checkdegree(), degree(), quotient::ModUPol< C, R >::dim(), VECTOR::init(), UPOLDAR::mul_index(), quotient::ModUPol< C, R >::poly, upol::rep< C >::resize(), and linalg::rep1d< C >::size().

Referenced by quotient::ModUPol< C, R >::mul().

The documentation for this struct was generated from the following file:

SYNAPS DOCUMENTATION
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