|
GiNaC 1.8.7
|
This file implements several functions that work on univariate and multivariate polynomials and rational functions. More...
#include "normal.h"#include "basic.h"#include "ex.h"#include "add.h"#include "constant.h"#include "expairseq.h"#include "fail.h"#include "inifcns.h"#include "lst.h"#include "mul.h"#include "numeric.h"#include "power.h"#include "relational.h"#include "operators.h"#include "matrix.h"#include "pseries.h"#include "symbol.h"#include "utils.h"#include "polynomial/chinrem_gcd.h"#include <algorithm>#include <map>Go to the source code of this file.
Classes | |
| struct | GiNaC::sym_desc |
| This structure holds information about the highest and lowest degrees in which a symbol appears in two multivariate polynomials "a" and "b". More... | |
| class | GiNaC::gcdheu_failed |
| Exception thrown by heur_gcd() to signal failure. More... | |
| struct | GiNaC::normal_map_function |
| Function object to be applied by basic::normal(). More... | |
Namespaces | |
| namespace | GiNaC |
Macros | |
| #define | FAST_COMPARE 1 |
| #define | USE_REMEMBER 0 |
| #define | USE_TRIAL_DIVISION 0 |
| #define | STATISTICS 0 |
Typedefs | |
| typedef std::vector< sym_desc > | GiNaC::sym_desc_vec |
Functions | |
| static bool | GiNaC::get_first_symbol (const ex &e, ex &x) |
| Return pointer to first symbol found in expression. More... | |
| static void | GiNaC::add_symbol (const ex &s, sym_desc_vec &v) |
| static void | GiNaC::collect_symbols (const ex &e, sym_desc_vec &v) |
| static void | GiNaC::get_symbol_stats (const ex &a, const ex &b, sym_desc_vec &v) |
| Collect statistical information about symbols in polynomials. More... | |
| static numeric | GiNaC::lcmcoeff (const ex &e, const numeric &l) |
| static numeric | GiNaC::lcm_of_coefficients_denominators (const ex &e) |
| Compute LCM of denominators of coefficients of a polynomial. More... | |
| static ex | GiNaC::multiply_lcm (const ex &e, const numeric &lcm) |
| Bring polynomial from Q[X] to Z[X] by multiplying in the previously determined LCM of the coefficient's denominators. More... | |
| ex | GiNaC::quo (const ex &a, const ex &b, const ex &x, bool check_args) |
| Quotient q(x) of polynomials a(x) and b(x) in Q[x]. More... | |
| ex | GiNaC::rem (const ex &a, const ex &b, const ex &x, bool check_args) |
| Remainder r(x) of polynomials a(x) and b(x) in Q[x]. More... | |
| ex | GiNaC::decomp_rational (const ex &a, const ex &x) |
| Decompose rational function a(x)=N(x)/D(x) into P(x)+n(x)/D(x) with degree(n, x) < degree(D, x). More... | |
| ex | GiNaC::prem (const ex &a, const ex &b, const ex &x, bool check_args) |
| Pseudo-remainder of polynomials a(x) and b(x) in Q[x]. More... | |
| ex | GiNaC::sprem (const ex &a, const ex &b, const ex &x, bool check_args) |
| Sparse pseudo-remainder of polynomials a(x) and b(x) in Q[x]. More... | |
| bool | GiNaC::divide (const ex &a, const ex &b, ex &q, bool check_args) |
| Exact polynomial division of a(X) by b(X) in Q[X]. More... | |
| static bool | GiNaC::divide_in_z (const ex &a, const ex &b, ex &q, sym_desc_vec::const_iterator var) |
| Exact polynomial division of a(X) by b(X) in Z[X]. More... | |
| static ex | GiNaC::sr_gcd (const ex &a, const ex &b, sym_desc_vec::const_iterator var) |
| Compute GCD of multivariate polynomials using the subresultant PRS algorithm. More... | |
| static ex | GiNaC::interpolate (const ex &gamma, const numeric &xi, const ex &x, int degree_hint=1) |
| xi-adic polynomial interpolation More... | |
| static bool | GiNaC::heur_gcd_z (ex &res, const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const_iterator var) |
| Compute GCD of multivariate polynomials using the heuristic GCD algorithm. More... | |
| static bool | GiNaC::heur_gcd (ex &res, const ex &a, const ex &b, ex *ca, ex *cb, sym_desc_vec::const_iterator var) |
| Compute GCD of multivariate polynomials using the heuristic GCD algorithm. More... | |
| static ex | GiNaC::gcd_pf_pow (const ex &a, const ex &b, ex *ca, ex *cb) |
| static ex | GiNaC::gcd_pf_mul (const ex &a, const ex &b, ex *ca, ex *cb) |
| ex | GiNaC::gcd (const ex &a, const ex &b, ex *ca, ex *cb, bool check_args, unsigned options) |
| Compute GCD (Greatest Common Divisor) of multivariate polynomials a(X) and b(X) in Z[X]. More... | |
| static ex | GiNaC::gcd_pf_pow_pow (const ex &a, const ex &b, ex *ca, ex *cb) |
| ex | GiNaC::lcm (const ex &a, const ex &b, bool check_args) |
| Compute LCM (Least Common Multiple) of multivariate polynomials in Z[X]. More... | |
| static epvector | GiNaC::sqrfree_yun (const ex &a, const symbol &x) |
| Compute square-free factorization of multivariate polynomial a(x) using Yun's algorithm. More... | |
| ex | GiNaC::sqrfree (const ex &a, const lst &l) |
| Compute a square-free factorization of a multivariate polynomial in Q[X]. More... | |
| ex | GiNaC::sqrfree_parfrac (const ex &a, const symbol &x) |
| Compute square-free partial fraction decomposition of rational function a(x). More... | |
| static ex | GiNaC::replace_with_symbol (const ex &e, exmap &repl, exmap &rev_lookup, lst &modifier) |
| Create a symbol for replacing the expression "e" (or return a previously assigned symbol). More... | |
| static ex | GiNaC::replace_with_symbol (const ex &e, exmap &repl) |
| Create a symbol for replacing the expression "e" (or return a previously assigned symbol). More... | |
| static ex | GiNaC::frac_cancel (const ex &n, const ex &d) |
| Fraction cancellation. More... | |
| static ex | GiNaC::find_common_factor (const ex &e, ex &factor, exmap &repl) |
| Remove the common factor in the terms of a sum 'e' by calculating the GCD, and multiply it into the expression 'factor' (which needs to be initialized to 1, unless you're accumulating factors). More... | |
| ex | GiNaC::collect_common_factors (const ex &e) |
| Collect common factors in sums. More... | |
| ex | GiNaC::resultant (const ex &e1, const ex &e2, const ex &s) |
| Resultant of two expressions e1,e2 with respect to symbol s. More... | |
This file implements several functions that work on univariate and multivariate polynomials and rational functions.
These functions include polynomial quotient and remainder, GCD and LCM computation, square-free factorization and rational function normalization.
Definition in file normal.cpp.
| #define FAST_COMPARE 1 |
Definition at line 54 of file normal.cpp.
| #define USE_REMEMBER 0 |
Definition at line 57 of file normal.cpp.
| #define USE_TRIAL_DIVISION 0 |
Definition at line 62 of file normal.cpp.
| #define STATISTICS 0 |
Definition at line 65 of file normal.cpp.