include/realroot/sparse_monomials.hpp File Reference

#include <list>
#include <vector>
#include <algorithm>
#include <realroot/binomials.hpp>
#include <realroot/Seq.hpp>
#include <realroot/monomial.hpp>
#include <realroot/monomial_ordering.hpp>

Go to the source code of this file.

Classes

• struct monomial_seq< C, O, MONOM, rep >
• struct use< operators_of, sparse::monomial_seq< C, O, MONOM, poly.rep() > >

Namespaces

• namespace mmx
• namespace mmx::sparse

  namespace for representation of polynomials as sequence of monomials

  
  

• namespace mmx::let

  Namespace for explicit type conversion.

  
  

Defines

• #define TMPL   template<class C, class O, class MONOM, class REP>
• #define TMPLX   template<class C, class O, class MONOM, class REP, class X>
• #define Polynomial   monomial_seq<C,O,MONOM,REP>
• #define CLASS   monomial_seq
• #define sparse_monomials   sparse::monomial_seq
• #define SparsePolynomial   sparse:: monomial_seq<C,O,MONOM,REP>

Functions

• template<class C , class O , class MONOM , class poly. rep> void add (monomial_seq< C, O, MONOM, poly.rep() > &result, const monomial_seq< C, O, MONOM, poly.rep() > &p1, const monomial_seq< C, O, MONOM, poly.rep() > &p2)
• template<class C , class O , class MONOM , class poly. rep> void add (monomial_seq< C, O, MONOM, poly.rep() > &p1, const monomial_seq< C, O, MONOM, poly.rep() > &p2)

  Inplace addition.
  

• template<class C , class O , class MONOM , class poly. rep, class I , class J , class M > I add (monomial_seq< C, O, MONOM, poly.rep() > &p1, I b1, J e1, const M &m2)
• template<class C , class O , class MONOM , class poly. rep> void add (monomial_seq< C, O, MONOM, poly.rep() > &p, const typename monomial_seq< C, O, MONOM, poly.rep() >::monom_t &m)
• template<class C , class O , class MONOM , class poly. rep> void add (monomial_seq< C, O, MONOM, poly.rep() > &p, const C &c)
• template<class C , class O , class MONOM , class poly. rep, class X > void add (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &q, const X &c)
• template<class C , class O , class MONOM , class poly. rep> void add (monomial_seq< C, O, MONOM, poly.rep() > &r, const C &c, const monomial_seq< C, O, MONOM, poly.rep() > &q)
• template<class C , class O , class MONOM , class poly. rep> void sub (monomial_seq< C, O, MONOM, poly.rep() > &result, const monomial_seq< C, O, MONOM, poly.rep() > &p1, const monomial_seq< C, O, MONOM, poly.rep() > &p2)
• template<class C , class O , class MONOM , class poly. rep> void sub (monomial_seq< C, O, MONOM, poly.rep() > &p, const monomial_seq< C, O, MONOM, poly.rep() > &q)
• template<class C , class O , class MONOM , class poly. rep, class X > void sub (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &q, const X &c)
• template<class C , class O , class MONOM , class poly. rep, class X > void sub (monomial_seq< C, O, MONOM, poly.rep() > &r, const X &c, const monomial_seq< C, O, MONOM, poly.rep() > &q)
• template<class C , class O , class MONOM , class poly. rep> void mul (monomial_seq< C, O, MONOM, poly.rep() > &r, const C &c)

  Multiplication of a polynomial by a monomial or a scalar.
  

• template<class C , class O , class MONOM , class poly. rep> void mul (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &p, const C &c)
• template<class C , class O , class MONOM , class poly. rep, class X > void mul (monomial_seq< C, O, MONOM, poly.rep() > &r, const X &c, const monomial_seq< C, O, MONOM, poly.rep() > &p)
• template<class C , class O , class MONOM , class poly. rep, class M > void mul_ext (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &a, const M &m)

  Multiplication of a polynomial by a monomial or a scalar.
  

• template<class C , class O , class MONOM , class poly. rep> void mul (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &a, const typename monomial_seq< C, O, MONOM, poly.rep() >::monom_t &m)

  Multiplication of a polynomial by a monomial or a scalar.
  

• template<class C , class O , class MONOM , class poly. rep> void mul (monomial_seq< C, O, MONOM, poly.rep() > &r, const typename monomial_seq< C, O, MONOM, poly.rep() >::monom_t &m)

  Multiplication of a polynomial by a monomial or a scalar.
  

• template<class C , class O , class MONOM , class poly. rep, class M > void mul_ext_e (monomial_seq< C, O, MONOM, poly.rep() > &result, const monomial_seq< C, O, MONOM, poly.rep() > &a, const M &m)
• template<class C , class O , class MONOM , class poly. rep> void mul (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &a, const monomial_seq< C, O, MONOM, poly.rep() > &b)

  Multiplication of two polynomials.
  

• template<class C , class O , class MONOM , class poly. rep, class X > void mul (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &a, const monomial_seq< C, O, MONOM, poly.rep() > &b, const X &o)

  Specialisation for list.
  

• template<class C , class O , class MONOM , class poly. rep> void mul (monomial_seq< C, O, MONOM, poly.rep() > &r, typename monomial_seq< C, O, MONOM, poly.rep() >::const_iterator b, typename monomial_seq< C, O, MONOM, poly.rep() >::const_iterator e, const monomial_seq< C, O, MONOM, poly.rep() > &p)
• template<class C , class O , class MONOM , class poly. rep> void mul (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &p)
• template<class C , class O , class MONOM , class poly. rep> void div (monomial_seq< C, O, MONOM, poly.rep() > &q, const monomial_seq< C, O, MONOM, poly.rep() > &a, const monomial_seq< C, O, MONOM, poly.rep() > &b)
• template<class C , class O , class MONOM , class poly. rep> void div (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &b)
• template<class C , class O , class MONOM , class poly. rep> void div (monomial_seq< C, O, MONOM, poly.rep() > &f, const typename monomial_seq< C, O, MONOM, poly.rep() >::Scalar &c)
• template<class C , class O , class MONOM , class poly. rep> void div (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &p, const C &c)
• template<class C , class O , class MONOM , class poly. rep> void rem (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &a, const monomial_seq< C, O, MONOM, poly.rep() > &b)
• template<class C , class O , class MONOM , class poly. rep, class U > void coefficients (Seq< U > &r, const monomial_seq< C, O, MONOM, poly.rep() > &f, int v)
• template<class C , class O , class MONOM , class poly. rep> void coefficients (Seq< C > &r, const monomial_seq< C, O, MONOM, poly.rep() > &f)
• template<class R > int lvar (const R &p)

  Index of the leading variable (of maximal index) of a polynomial.
  

• template<class R > unsigned nbvar (const R &p)

  Number of variables of a polynomial.
  

• template<class R > int degree (const R &p)

  Degree of a polynomial.
  

• template<class R > int degree (const R &p, int i)

  Degree of a polynomial with respect to the i th variable..
  

• template<class R > R::coeff_t & leadingcoeff (R &a)
• template<class R > R::coeff_t leadingcoeff (const R &a)
• template<class POL > POL::coeff_t coeffof (const POL &p, const typename POL::monom_t &mono)
• template<class POL > POL::const_iterator last_term (const POL &p)
• template<class R > void div_rem (R &q, R &a, const R &b0)

  Divide a in place by b, concidering all the monomials.
  

• template<class C , class O , class MONOM , class poly. rep> void diff (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &p, int i)

  Derivative of p with respect to i th variable put in r.
  

• template<class C , class O , class MONOM , class poly. rep> void shift (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &p, const typename monomial_seq< C, O, MONOM, poly.rep() >::monom_t &m)

  Multiply p by a monomial m and put the result in r.
  

• template<class C , class O , class MONOM , class poly. rep> void copy (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &a)

  Copy of a in r.
  

• template<class C , class O , class MONOM , class poly. rep> monomial_seq< C, O, MONOM,
  poly.rep() >::coeff_t eval (const monomial_seq< C, O, MONOM, poly.rep() > &p, const typename monomial_seq< C, O, MONOM, poly.rep() >::coeff_t &x, const typename monomial_seq< C, O, MONOM, poly.rep() >::coeff_t &y)

  Evaluate the polynomial p for x0=x, x1=y, and the other xi=1.
  

• template<class C , class O , class MONOM , class poly. rep, class R , class VCT > void eval_at (R &r, const monomial_seq< C, O, MONOM, poly.rep() > &p, const VCT &x)
• template<class R , class C , class O , class MONOM , class poly. rep, class X > void eval (R &r, const monomial_seq< C, O, MONOM, poly.rep() > &p, const X &x)

  Evaluate the polynomial p for x0=x, x1=y, and the other xi=1. **/.
  

• template<class C , class O , class MONOM , class poly. rep> void homogenize (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &p, const monomial_seq< C, O, MONOM, poly.rep() > &v)
• template<class C , class O , class MONOM , class poly. rep> void homogenize (monomial_seq< C, O, MONOM, poly.rep() > &r, const monomial_seq< C, O, MONOM, poly.rep() > &p, int n, const monomial_seq< C, O, MONOM, poly.rep() > &v)
• template<class MP > MP convert (const MP &P, typename MP::coeff_t x, typename MP::coeff_t y, int ind)
• template<class OS , class C , class O , class MONOM , class poly. rep, class VARIABLES > OS & print (OS &os, const monomial_seq< C, O, MONOM, poly.rep() > &P, const VARIABLES &V)
• template<class OS , class C , class O , class MONOM , class poly. rep, class VARIABLES > OS & print_as_double (OS &os, const monomial_seq< C, O, MONOM, poly.rep() > &P, const VARIABLES &V)
• template<class OS , class C , class O , class MONOM , class poly. rep> OS & print (OS &os, const monomial_seq< C, O, MONOM, poly.rep() > &P)
• template<class OS , class C , class O , class MONOM , class poly. rep> OS & print_verbatim (OS &os, const monomial_seq< C, O, MONOM, poly.rep() > &P)
• template<class POL , class C > POL shift (typename POL::const_iterator monom, const C &a, int i)
• template<class POL , class C > POL scale (const POL &p, C a, int v)
• template<class T , class MP , class V > T eval (const MP &p, const V &v)
• template<class R , class MP , class V > void eval (R &r, const MP &p, const V &v, unsigned n)
• template<class MP , class X > MP subs (unsigned var, const X &val, const MP &P)
• template<class MP > MP subs (const MP &P, int var, typename MP::coeff_t val)
• template<class MP > MP subs (const MP &P, char *x, typename MP::coeff_t val)
• template<class T > void print (const T &x)
• template<class MP > MP swap (const MP &P, int var_i, int var_j)
• template<class MP > MP swap (const MP &P, char *x_i, char *x_j)
• template<class C , class O , class MONOM , class poly. rep> C content (const monomial_seq< C, O, MONOM, poly.rep() > &P)
• template<class C , class O , class MONOM , class poly. rep> void assign (sparse::monomial_seq< C, O, MONOM, poly.rep() > &p, const C &c)
• template<class U , class V , class O , class UMONOM , class UREP , class VMONOM , class VREP > void assign (sparse::monomial_seq< U, O, UMONOM, UREP > &p, const sparse::monomial_seq< V, O, VMONOM, VREP > &q)

---

Define Documentation

#define CLASS   monomial_seq

Definition at line 13 of file sparse_monomials.hpp.

#define Polynomial   monomial_seq<C,O,MONOM,REP>

Definition at line 12 of file sparse_monomials.hpp.

#define sparse_monomials   sparse::monomial_seq

Definition at line 14 of file sparse_monomials.hpp.

#define SparsePolynomial   sparse:: monomial_seq<C,O,MONOM,REP>

Definition at line 1038 of file sparse_monomials.hpp.

#define TMPL   template<class C, class O, class MONOM, class REP>

Definition at line 10 of file sparse_monomials.hpp.

#define TMPLX   template<class C, class O, class MONOM, class REP, class X>

Definition at line 11 of file sparse_monomials.hpp.