include/algebramix/series.hpp File Reference

#include <algebramix/series_naive.hpp>

Go to the source code of this file.

Classes

class series< C, V >
class recursive_series_rep< C, V >
class recursive_container_series_rep< C, V >
class series_iterator_rep< C, V >
class zero_series_rep
class scalar_series_rep< C, V >
class polynomial_series_rep< C, V >
class iterator_series_rep< C, V >
class fast_series_rep< C, V >
class slow_series_rep< C, V >
struct fast_helper< series< C, V > >
class cast_series_rep< C, V, K, W >
struct as_helper< series< T, TV >, series< F, FV > >
class map_series_rep< C, V, S, SV, Fun >
class gcd_series_rep< C, V >
class lcm_series_rep< C, V >
class lshiftz_series_rep< C, V >
class restrict_series_rep< C, V >
class piecewise_series_rep< C, V >
class derive_series_rep< C, V >
class xderive_series_rep< C, V >
class integrate_series_rep< C, V >
class shift_series_rep< C, V >
class q_difference_series_rep< C, V >
class dilate_series_rep< C, V >
class deflate_series_rep< C, V >
class change_precision_series_rep< C, V >

Namespaces

namespace mmx

Defines

#define Series_variant(C) series_variant_helper<C>::SV
#define TMPL template<typename C, typename V>
#define TMPLK template<typename C, typename V, typename K>
#define Format format<C>
#define Series series<C,V>
#define Series_rep series_rep<C,V>
#define Recursive_series_rep recursive_series_rep<C,V>
#define Polynomial polynomial<C, typename series_polynomial_helper<C,V>::PV>
#define PolynomialV polynomial<C,V>
#define Truncated_series Polynomial
#define Completed_series Series
#define Truncated_polynomial Polynomial
#define Completed_polynomial Series
#define Quotient quotient<PolynomialV,PolynomialV>

Functions

template<typename C , typename V > syntactic flatten (const series< C, V > &f, const syntactic &z)
template<typename C , typename V > series< C, V > lshiftz (const series< C, V > &f, const int &shift=1)
template<typename C , typename V > series< C, V > rshiftz (const series< C, V > &f, const int &shift=1)
template<typename C , typename V = typename matrix_variant_helper< C >::MV> class matrix_rep REP_STRUCT_1 (C)
INDIRECT_IMPL_2 (series, series_rep, typename C, C, typename V, V) DEFINE_UNARY_FORMAT_2(series) STYPE_TO_TYPE(template< typename C
template<typename C , typename V > format< C > CF (const series< C, V > &f)
template<typename C , typename V > void set_variable_name (const series< C, V > &, const generic &x)
template<typename C , typename V > void set_output_order (const series< C, V > &, const nat &n)
template<typename C , typename V > void set_cancel_order (const series< C, V > &, const nat &n)
template<typename C , typename V > void set_formula_output (const series< C, V > &, const bool &b)
template<typename C , typename V > series< C, V > recursive (const series< C, V > &f)
template<typename C , typename V > generic var (const series< C, V > &f)
template<typename C , typename V > void increase_order (const series< C, V > &f, nat l)
template<typename C , typename V > polynomial< C, typename
series_polynomial_helper< C, V >
::PV > truncate (const series< C, V > &f, nat n)
template<typename C , typename V > polynomial< C, typename
series_polynomial_helper< C, V >
::PV > range (const series< C, V > &f, nat start, nat end)
template<typename C , typename V > iterator< C > iterate (const series< C, V > &f)
HARD_TO_EXACT_IDENTITY_SUGAR (template< typename C, typename V >, series< C, V >) template< typename Op
V nat unary_hash (const series< C, V > &s)
template<typename C , typename V > nat hash (const series< C, V > &s)
template<typename Op , typename C , typename V > bool binary_test (const series< C, V > &f1, const series< C, V > &f2)
template<typename C , typename V > bool operator== (const series< C, V > &f1, const series< C, V > &f2)
template<typename C , typename V > bool operator!= (const series< C, V > &f1, const series< C, V > &f2)
template<typename C , typename V > bool is_exact_zero (const series< C, V > &f)
template<typename C , typename V > syntactic flatten (const series< C, V > &f)
template<typename C , typename V > int val (const series< C, V > &f)
template<typename C , typename V > int sign (const series< C, V > &f)
template<typename C , typename V > int compare (const series< C, V > &f1, const series< C, V > &f2)
EQUAL_INT_SUGAR (template< typename C, typename V >, series< C, V >) COMPARE_SUGAR(template< typename C
series< C, V > COMPARE_INT_SUGAR (template< typename C, typename V >, series< C, V >) EQUAL_SCALAR_SUGAR(template< typename C
series< C, V > C COMPARE_SCALAR_SUGAR (template< typename C, typename V >, series< C, V >, C) EQUAL_SCALAR_SUGAR_BIS(template< typename C
series< C, V > C C COMPARE_SCALAR_SUGAR_BIS (template< typename C, typename V >, series< C, V >, C) template< typename C
template<typename T , typename F , typename TV , typename FV > void set_as (series< T, TV > &r, const series< F, FV > &f)
template<typename C , typename V , typename T > void set_as (series< C, V > &r, const T &x)
template<typename Op , typename C , typename V , typename X > series< C, V > binary_scalar_series (const series< C, V > &f, const X &x)
template<typename Op , typename C , typename V , typename X , typename Y > series< C, V > ternary_scalar_series (const series< C, V > &f, const X &x, const Y &y)
template<typename Op , typename C , typename V , typename S , typename SV > series< C, V > unary_map_as (const series< S, SV > &f)
template<typename S1 , typename D , typename Fun > series< D > map (const Fun &fun, const series< S1 > &f, const format< D > &fm)
template<typename Op , typename C > series< C > nullary_recursive_series (const C &c=Op::template op< C >())
template<typename Op , typename C , typename V > series< C, V > unary_recursive_series (const series< C, V > &f)
template<typename Op , typename C , typename V > series< C, V > unary_recursive_series (const series< C, V > &f, const C &c)
template<typename Op , typename C , typename V > series< C, V > binary_recursive_series (const series< C, V > &f, const series< C, V > &g)
template<typename Op , typename C , typename V , typename X > series< C, V > binary_scalar_recursive_series (const series< C, V > &f, const X &x)
template<typename Op , typename C , typename V , typename X > series< C, V > binary_scalar_recursive_series (const series< C, V > &f, const X &x, const C &init)
template<typename Op , typename C , typename V , typename L > series< C, V > unary_polynomial_recursive_series (const polynomial< L > &P)
template<typename Op , typename C , typename V , typename L > series< C, V > unary_polynomial_recursive_series (const polynomial< L > &P, const C &init)
template<typename Op , typename C , typename V > series< C, V > unary_series (const series< C, V > &f)
template<typename Op , typename C , typename V > series< C, V > binary_series (const series< C, V > &f, const series< C, V > &g)
template<typename C , typename V > series< C, V > operator+ (const series< C, V > &f, const series< C, V > &g)
template<typename C , typename V > series< C, V > operator+ (const C &c, const series< C, V > &f)
template<typename C , typename V > series< C, V > operator+ (const series< C, V > &f, const C &c)
template<typename C , typename V > series< C, V > operator- (const series< C, V > &f)
template<typename C , typename V > series< C, V > operator- (const series< C, V > &f, const series< C, V > &g)
template<typename C , typename V > series< C, V > operator- (const C &c, const series< C, V > &f)
template<typename C , typename V > series< C, V > operator- (const series< C, V > &f, const C &c)
template<typename C , typename V > series< C, V > operator* (const series< C, V > &f, const C &c)
template<typename C , typename V > series< C, V > operator* (const C &c, const series< C, V > &f)
template<typename C , typename V > series< C, V > gcd (const series< C, V > &f, const series< C, V > &g)
template<typename C , typename V > series< C, V > lcm (const series< C, V > &f, const series< C, V > &g)
template<typename C , typename V > series< C, V > restrict (const series< C, V > &f, nat start, nat end)
template<typename C , typename V > series< C, V > piecewise (const series< C, V > &f, const series< C, V > &g, nat pos)
template<typename C , typename V > series< C, V > derive (const series< C, V > &f)
template<typename C , typename V , typename T > series< C, V > derive_coeffs (const series< C, V > &f, const T &v)
template<typename C , typename V > series< C, V > xderive (const series< C, V > &f)
template<typename C , typename V > series< C, V > integrate (const series< C, V > &f)
template<typename C , typename V > series< C, V > integrate_init (const series< C, V > &f, const C &c)
template<typename C , typename V , typename T > series< C, V > integrate_coeffs (const series< C, V > &f, const T &v)
template<typename C , typename V > series< C, V > shift (const series< C, V > &f, const C &q, nat order)
template<typename C , typename V > series< C, V > series_shift_default (const series< C, V > &s, const C &sh)
template<typename C , typename V > series< C, V > q_difference (const series< C, V > &f, const C &q)
template<typename C , typename V > series< C, V > dilate (const series< C, V > &f, nat p)
template<typename C , typename V > series< C, V > deflate (const series< C, V > &f, nat p)
template<typename C , typename V > series< C, V > operator* (const series< C, V > &f, const series< C, V > &g)
template<typename C , typename V > series< C, V > truncate_mul (const series< C, V > &f, const series< C, V > &g, nat nf, nat ng)
template<typename C , typename V > series< C, V > operator/ (const series< C, V > &f, const C &c)
template<typename C , typename V > series< C, V > operator/ (const series< C, V > &f, const series< C, V > &g)
template<typename C , typename V > series< C, V > operator/ (const C &c, const series< C, V > &f)
template<typename C , typename V > series< C, V > invert (const series< C, V > &f)
template<typename C , typename V > series< C, V > quo (const series< C, V > &f, const C &c)
template<typename C , typename V > series< C, V > quo (const series< C, V > &f, const series< C, V > &g)
template<typename C , typename V > series< C, V > rem (const series< C, V > &f, const C &c)
template<typename C , typename V > series< C, V > rem (const series< C, V > &f, const series< C, V > &g)
template<typename C , typename V > bool divides (const series< C, V > &f, const series< C, V > &g)
ARITH_SCALAR_INT_SUGAR (template< typename C, typename V >, series< C, V >)
template<typename C , typename V > series< C, V > separable_root (const series< C, V > &f, nat n)
template<typename C , typename V > series< C, V > separable_root_init (const series< C, V > &f, nat n, const C &init)
template<typename C , typename V , typename L > series< C, V > polynomial_regular_root (const polynomial< L > &P)
template<typename C , typename V , typename L > series< C, V > polynomial_regular_root_init (const polynomial< L > &P, const C &init)
template<typename C , typename V > series< C, V > pth_root (const series< C, V > &f)
template<typename C , typename V > series< C, V > compose (const series< C, V > &f, const series< C, V > &g)
template<typename C , typename V > series< C, V > reverse (const series< C, V > &f)
template<typename C , typename V > series< C, V > change_precision (const series< C, V > &f, nat p)
template<typename C , typename V > nat precision (const series< C, V > &f)
template<typename C , typename V > series< C, V > sharpen (const series< C, V > &f)
template<typename C , typename V , typename K > series< C, V > blur (const series< C, V > &f, const K &x)
BINARY_RETURN_TYPE (template< typename C, typename V >, truncate_op, series< C, V >, nat, polynomial< C, typename series_polynomial_helper< C, V >::PV >)
UNARY_RETURN_TYPE (template< typename C, typename V >, complete_op, series< C, V >, series< C, V >)
template<typename C , typename V > series< C, V > complete (const series< C, V > &f)
BINARY_RETURN_TYPE (template< typename C, typename V >, truncate_op, polynomial< C, V >, nat, polynomial< C, V >)
UNARY_RETURN_TYPE (template< typename C, typename V >, complete_op, polynomial< C, V >, series< C >)
template<typename C , typename V > polynomial< C, V > truncate (const polynomial< C, V > &p, nat sigma)
template<typename C , typename V > series< C > complete (const polynomial< C, V > &p)
UNARY_RETURN_TYPE (template< typename C, typename V >, complete_op, quotient< polynomial< C, V >, polynomial< C, V > >, series< C >)
template<typename C , typename V > series< C > complete (const quotient< polynomial< C, V >, polynomial< C, V > > &f)

Variables

Define Documentation

#define Completed_polynomial Series

Definition at line 30 of file series.hpp.

#define Completed_series Series

Definition at line 28 of file series.hpp.

#define Format format<C>

Definition at line 21 of file series.hpp.

#define Polynomial polynomial<C, typename series_polynomial_helper<C,V>::PV>

Definition at line 25 of file series.hpp.

#define PolynomialV polynomial<C,V>

Definition at line 26 of file series.hpp.

#define Quotient quotient<PolynomialV,PolynomialV>

Definition at line 1281 of file series.hpp.

#define Recursive_series_rep recursive_series_rep<C,V>

Definition at line 24 of file series.hpp.

Referenced by recursive_container_series_rep< C, V >::recursive_container_series_rep(), and recursive_container_series_rep< C, V >::~recursive_container_series_rep().

#define Series series<C,V>

Definition at line 22 of file series.hpp.

#define Series_rep series_rep<C,V>

Definition at line 23 of file series.hpp.

#define Series_variant ( C ) series_variant_helper<C>::SV

Definition at line 18 of file series.hpp.

Referenced by div_series_rep< M, V >::initialize(), rdiv_sc_series_rep< M, V, X >::initialize(), mmx::map(), and mmx::nullary_recursive_series().

#define TMPL template<typename C, typename V>

Definition at line 19 of file series.hpp.

#define TMPLK template<typename C, typename V, typename K>

Definition at line 20 of file series.hpp.

#define Truncated_polynomial Polynomial

Definition at line 29 of file series.hpp.

#define Truncated_series Polynomial

Definition at line 27 of file series.hpp.