factor.cpp File Reference

Polynomial factorization (implementation). More...

#include "factor.h"
#include "ex.h"
#include "numeric.h"
#include "operators.h"
#include "inifcns.h"
#include "symbol.h"
#include "relational.h"
#include "power.h"
#include "mul.h"
#include "normal.h"
#include "add.h"
#include <algorithm>
#include <limits>
#include <list>
#include <vector>
#include <stack>
#include <cln/cln.h>

Go to the source code of this file.

Namespaces
	GiNaC

Macros
#define	DCOUT(str)
#define	DCOUTVAR(var)
#define	DCOUT2(str, var)
#define	USE_SAME_DEGREE_FACTOR

Functions
ex	GiNaC::factor (const ex &poly, unsigned options)
	Interface function to the outside world. More...

Detailed Description

Polynomial factorization (implementation).

The interface function factor() at the end of this file is defined in the GiNaC namespace. All other utility functions and classes are defined in an additional anonymous namespace.

Factorization starts by doing a square free factorization and making the coefficients integer. Then, depending on the number of free variables it proceeds either in dedicated univariate or multivariate factorization code.

Univariate factorization does a modular factorization via Berlekamp's algorithm and distinct degree factorization. Hensel lifting is used at the end.

Multivariate factorization uses the univariate factorization (applying a evaluation homomorphism first) and Hensel lifting raises the answer to the multivariate domain. The Hensel lifting code is completely distinct from the code used by the univariate factorization.

Algorithms used can be found in [Wan] An Improved Multivariate Polynomial Factoring Algorithm, P.S.Wang, Mathematics of Computation, Vol. 32, No. 144 (1978) 1215–1231. [GCL] Algorithms for Computer Algebra, K.O.Geddes, S.R.Czapor, G.Labahn, Springer Verlag, 1992. [Mig] Some Useful Bounds, M.Mignotte, In "Computer Algebra, Symbolic and Algebraic Computation" (B.Buchberger et al., eds.), pp. 259-263, Springer-Verlag, New York, 1982.

Definition in file factor.cpp.

Macro Definition Documentation

DCOUT

#define DCOUT

(

str

)

Definition at line 131 of file factor.cpp.

DCOUTVAR

#define DCOUTVAR

(

var

)

Definition at line 132 of file factor.cpp.

DCOUT2

#define DCOUT2	(		str,
			var
	)

Definition at line 133 of file factor.cpp.

USE_SAME_DEGREE_FACTOR

#define USE_SAME_DEGREE_FACTOR

Definition at line 1113 of file factor.cpp.

Variable Documentation

value

const bool value = false

static

Definition at line 231 of file factor.cpp.

Referenced by GiNaC::archive_node::add_bool(), GiNaC::archive_node::add_ex(), GiNaC::archive_node::add_string(), GiNaC::archive_node::add_unsigned(), GiNaC::Li2_(), GiNaC::matrix::set(), and GiNaC::subsvalue().

r

size_t r

private

Definition at line 770 of file factor.cpp.

Referenced by GiNaC::matrix::charpoly(), GiNaC::collect_common_factors(), GiNaC::ex::content(), GiNaC::numeric::csgn(), GiNaC::numeric::denom(), GiNaC::matrix::determinant(), GiNaC::matrix::determinant_minor(), GiNaC::divide(), GiNaC::divide_in_z(), GiNaC::matrix::division_free_elimination(), GiNaC::matrix::echelon_form(), GiNaC::power::eval(), GiNaC::power::expand(), GiNaC::power::expand_add(), GiNaC::power::expand_add_2(), GiNaC::matrix::fraction_free_elimination(), GiNaC::matrix::gauss_elimination(), GiNaC::idx_symmetrization(), GiNaC::matrix::inverse(), GiNaC::iquo(), GiNaC::lsolve(), GiNaC::matrix::markowitz_elimination(), GiNaC::matrix::matrix(), GiNaC::matrix::mul(), GiNaC::matrix::mul_scalar(), GiNaC::numeric::numer(), GiNaC::Order_series(), GiNaC::matrix::pow(), GiNaC::prem(), GiNaC::numeric::print_numeric(), GiNaC::quo(), GiNaC::matrix::rank(), GiNaC::reduced_matrix(), GiNaC::rem(), GiNaC::structure< T, ComparisonPolicy >::return_type_tinfo(), GiNaC::ex::series(), GiNaC::series(), GiNaC::basic::series(), GiNaC::add::series(), GiNaC::fderivative::series(), GiNaC::function::series(), GiNaC::integral::series(), GiNaC::integration_kernel::series(), GiNaC::Eisenstein_kernel::series(), GiNaC::modular_form_kernel::series(), GiNaC::pseries::series(), GiNaC::structure< T, ComparisonPolicy >::series(), GiNaC::mul::series(), GiNaC::power::series(), GiNaC::symbol::series(), GiNaC::refcounted::set_refcount(), GiNaC::simplify_indexed_product(), GiNaC::matrix::solve(), GiNaC::sprem(), GiNaC::sr_gcd(), GiNaC::numeric::step(), GiNaC::sub_matrix(), GiNaC::ex::subs(), GiNaC::matrix::subs(), GiNaC::symbolic_matrix(), GiNaC::matrix::trace(), GiNaC::matrix::transpose(), GiNaC::unit_matrix(), and GiNaC::zeta1_evalf().

c

size_t c

private

Definition at line 770 of file factor.cpp.

Referenced by GiNaC::abs_print_csrc_float(), GiNaC::abs_print_latex(), GiNaC::symmetry::add(), GiNaC::bernoulli(), GiNaC::matrix::charpoly(), GiNaC::mul::coeff(), GiNaC::ncmul::coeff(), GiNaC::color_d(), GiNaC::color_f(), GiNaC::color_h(), GiNaC::add::combine_ex_with_coeff_to_pair(), GiNaC::mul::combine_ex_with_coeff_to_pair(), GiNaC::mul::combine_overall_coeff(), GiNaC::add::combine_pair_with_coeff_to_pair(), GiNaC::mul::combine_pair_with_coeff_to_pair(), GiNaC::mul::conjugate(), GiNaC::conjugate_print_latex(), GiNaC::ex::content(), GiNaC::crc32(), GiNaC::pseries::derivative(), GiNaC::matrix::determinant(), GiNaC::matrix::determinant_minor(), GiNaC::divide_in_z(), GiNaC::matrix::division_free_elimination(), GiNaC::add::do_print(), GiNaC::basic::do_print(), GiNaC::constant::do_print(), GiNaC::container< C >::do_print(), GiNaC::expairseq::do_print(), GiNaC::fderivative::do_print(), GiNaC::idx::do_print(), GiNaC::varidx::do_print(), GiNaC::spinidx::do_print(), GiNaC::indexed::do_print(), GiNaC::integral::do_print(), GiNaC::integration_kernel::do_print(), GiNaC::basic_log_kernel::do_print(), GiNaC::multiple_polylog_kernel::do_print(), GiNaC::ELi_kernel::do_print(), GiNaC::Ebar_kernel::do_print(), GiNaC::Kronecker_dtau_kernel::do_print(), GiNaC::Kronecker_dz_kernel::do_print(), GiNaC::Eisenstein_kernel::do_print(), GiNaC::Eisenstein_h_kernel::do_print(), GiNaC::modular_form_kernel::do_print(), GiNaC::user_defined_kernel::do_print(), GiNaC::matrix::do_print(), GiNaC::mul::do_print(), GiNaC::ncmul::do_print(), GiNaC::numeric::do_print(), GiNaC::pseries::do_print(), GiNaC::relational::do_print(), GiNaC::symbol::do_print(), GiNaC::symmetry::do_print(), GiNaC::wildcard::do_print(), GiNaC::ncmul::do_print_csrc(), GiNaC::add::do_print_csrc(), GiNaC::fderivative::do_print_csrc(), GiNaC::idx::do_print_csrc(), GiNaC::mul::do_print_csrc(), GiNaC::numeric::do_print_csrc(), GiNaC::power::do_print_csrc(), GiNaC::numeric::do_print_csrc_cl_N(), GiNaC::power::do_print_csrc_cl_N(), GiNaC::clifford::do_print_dflt(), GiNaC::power::do_print_dflt(), GiNaC::fderivative::do_print_latex(), GiNaC::add::do_print_latex(), GiNaC::clifford::do_print_latex(), GiNaC::constant::do_print_latex(), GiNaC::idx::do_print_latex(), GiNaC::spinidx::do_print_latex(), GiNaC::indexed::do_print_latex(), GiNaC::integral::do_print_latex(), GiNaC::matrix::do_print_latex(), GiNaC::mul::do_print_latex(), GiNaC::numeric::do_print_latex(), GiNaC::power::do_print_latex(), GiNaC::pseries::do_print_latex(), GiNaC::symbol::do_print_latex(), GiNaC::container< C >::do_print_python(), GiNaC::power::do_print_python(), GiNaC::pseries::do_print_python(), GiNaC::add::do_print_python_repr(), GiNaC::basic::do_print_python_repr(), GiNaC::constant::do_print_python_repr(), GiNaC::container< C >::do_print_python_repr(), GiNaC::matrix::do_print_python_repr(), GiNaC::mul::do_print_python_repr(), GiNaC::numeric::do_print_python_repr(), GiNaC::power::do_print_python_repr(), GiNaC::pseries::do_print_python_repr(), GiNaC::relational::do_print_python_repr(), GiNaC::symbol::do_print_python_repr(), GiNaC::wildcard::do_print_python_repr(), GiNaC::basic::do_print_tree(), GiNaC::clifford::do_print_tree(), GiNaC::constant::do_print_tree(), GiNaC::container< C >::do_print_tree(), GiNaC::fderivative::do_print_tree(), GiNaC::idx::do_print_tree(), GiNaC::varidx::do_print_tree(), GiNaC::spinidx::do_print_tree(), GiNaC::indexed::do_print_tree(), GiNaC::numeric::do_print_tree(), GiNaC::pseries::do_print_tree(), GiNaC::symbol::do_print_tree(), GiNaC::symmetry::do_print_tree(), GiNaC::wildcard::do_print_tree(), GiNaC::matrix::echelon_form(), GiNaC::EllipticE_print_latex(), GiNaC::EllipticK_print_latex(), GiNaC::mul::eval(), GiNaC::power::eval(), GiNaC::power::expand_add(), GiNaC::power::expand_add_2(), GiNaC::factorial_print_dflt_latex(), GiNaC::matrix::fraction_free_elimination(), GiNaC::matrix::gauss_elimination(), GiNaC::H_print_latex(), GiNaC::power::imag_part(), GiNaC::imag_part_print_latex(), GiNaC::add::integer_content(), GiNaC::matrix::inverse(), GiNaC::lcmcoeff(), GiNaC::Li_print_latex(), GiNaC::lsolve(), GiNaC::matrix::markowitz_elimination(), GiNaC::matrix::matrix(), GiNaC::matrix::mul(), GiNaC::matrix::mul_scalar(), GiNaC::print_functor::operator()(), GiNaC::print_ptrfun_handler< T, C >::operator()(), GiNaC::print_memfun_handler< T, C >::operator()(), GiNaC::error_and_integral_is_less::operator()(), GiNaC::matrix::pivot(), GiNaC::pseries::power_const(), GiNaC::ex::primpart(), GiNaC::basic::print(), GiNaC::ex::print(), GiNaC::fderivative::print(), GiNaC::function::print(), GiNaC::structure< T, ComparisonPolicy >::print(), GiNaC::expair::print(), GiNaC::add::print_add(), GiNaC::basic::print_dispatch(), GiNaC::matrix::print_elements(), GiNaC::idx::print_index(), GiNaC::indexed::print_indexed(), GiNaC::print_integer_csrc(), GiNaC::numeric::print_numeric(), GiNaC::print_operator(), GiNaC::mul::print_overall_coeff(), GiNaC::power::print_power(), GiNaC::print_real_cl_N(), GiNaC::print_real_csrc(), GiNaC::print_real_number(), GiNaC::pseries::print_series(), GiNaC::print_sym_pow(), GiNaC::indexed::printindices(), GiNaC::container< C >::printseq(), GiNaC::numeric::read_archive(), GiNaC::power::real_part(), GiNaC::real_part_print_latex(), GiNaC::reduced_matrix(), GiNaC::S_print_latex(), GiNaC::set_print_context(), GiNaC::matrix::solve(), GiNaC::sr_gcd(), GiNaC::sub_matrix(), GiNaC::clifford::subs(), GiNaC::matrix::subs(), GiNaC::symbolic_matrix(), GiNaC::matrix::transpose(), GiNaC::ex::unit(), GiNaC::unit_matrix(), GiNaC::ex::unitcontprim(), GiNaC::zeta1_print_latex(), and GiNaC::zeta2_print_latex().

m

mvec m

private

Definition at line 771 of file factor.cpp.

Referenced by GiNaC::mul::algebraic_subs_mul(), GiNaC::charpoly(), GiNaC::Eisenstein_h_kernel::coefficient_an(), GiNaC::cols(), GiNaC::convert_H_to_Li(), GiNaC::determinant(), GiNaC::power::eval(), GiNaC::tensdelta::eval_indexed(), GiNaC::tensmetric::eval_indexed(), GiNaC::evalf(), GiNaC::add::evalm(), GiNaC::mul::evalm(), GiNaC::expand(), GiNaC::power::expand(), GiNaC::power::expand_mul(), GiNaC::fibonacci(), GiNaC::H_deriv(), GiNaC::H_eval(), GiNaC::H_evalf(), GiNaC::H_print_latex(), GiNaC::H_series(), GiNaC::inverse(), GiNaC::lgamma_series(), GiNaC::Li_deriv(), GiNaC::Li_eval(), GiNaC::Li_evalf(), GiNaC::Li_print_latex(), GiNaC::Li_series(), GiNaC::nops(), GiNaC::Order_eval(), GiNaC::psi1_series(), GiNaC::psi2_eval(), GiNaC::psi2_series(), GiNaC::rank(), GiNaC::reduced_matrix(), GiNaC::reposition_dummy_indices(), GiNaC::resultant(), GiNaC::rows(), GiNaC::S_eval(), GiNaC::smod(), GiNaC::sub_matrix(), GiNaC::subs(), GiNaC::basic::subs(), GiNaC::clifford::subs(), GiNaC::container< C >::subs(), GiNaC::idx::subs(), GiNaC::numeric::subs(), GiNaC::power::subs(), GiNaC::pseries::subs(), GiNaC::relational::subs(), GiNaC::structure< T, ComparisonPolicy >::subs(), GiNaC::symbol::subs(), GiNaC::ex::subs(), GiNaC::basic::subs_one_level(), GiNaC::container< C >::subschildren(), GiNaC::tgamma_series(), GiNaC::trace(), GiNaC::transpose(), GiNaC::zeta1_deriv(), GiNaC::zeta1_eval(), GiNaC::zeta1_print_latex(), GiNaC::zeta2_deriv(), GiNaC::zeta2_eval(), and GiNaC::zeta2_print_latex().

lr

umodpoly lr[2]

private

Definition at line 1459 of file factor.cpp.

Referenced by GiNaC::subs(), and GiNaC::ex::subs().

cache

vector<vector<umodpoly> > cache

private

Definition at line 1460 of file factor.cpp.

factors

upvec factors

private

Definition at line 1461 of file factor.cpp.

Referenced by GiNaC::ncmul::count_factors(), GiNaC::ncmul::eval(), GiNaC::mul::expand(), GiNaC::mul::mul(), GiNaC::sqrfree(), and GiNaC::sqrfree_yun().

one

umodpoly one

private

Definition at line 1462 of file factor.cpp.

Referenced by GiNaC::integration_kernel::get_numerical_value_impl(), and GiNaC::iterated_integral_evalf_impl().

n

size_t n

private

Definition at line 1463 of file factor.cpp.

Referenced by GiNaC::class_info< OPT >::tree_node::add_child(), GiNaC::archive::add_node(), GiNaC::basic::archive(), GiNaC::clifford::archive(), GiNaC::color::archive(), GiNaC::constant::archive(), GiNaC::container< C >::archive(), GiNaC::expairseq::archive(), GiNaC::fderivative::archive(), GiNaC::function::archive(), GiNaC::idx::archive(), GiNaC::varidx::archive(), GiNaC::spinidx::archive(), GiNaC::indexed::archive(), GiNaC::integral::archive(), GiNaC::matrix::archive(), GiNaC::numeric::archive(), GiNaC::power::archive(), GiNaC::pseries::archive(), GiNaC::relational::archive(), GiNaC::symbol::archive(), GiNaC::symmetry::archive(), GiNaC::minkmetric::archive(), GiNaC::tensepsilon::archive(), GiNaC::wildcard::archive(), GiNaC::archive::archive(), GiNaC::bernoulli(), GiNaC::binomial(), GiNaC::basic::coeff(), GiNaC::ex::coeff(), GiNaC::add::coeff(), GiNaC::mul::coeff(), GiNaC::ncmul::coeff(), GiNaC::numeric::coeff(), GiNaC::power::coeff(), GiNaC::pseries::coeff(), GiNaC::structure< T, ComparisonPolicy >::coeff(), GiNaC::coeff(), GiNaC::Eisenstein_h_kernel::coefficient_an(), GiNaC::basic::collect(), GiNaC::const_postorder_iterator::const_postorder_iterator(), GiNaC::const_preorder_iterator::const_preorder_iterator(), GiNaC::composition_generator::coolmulti::coolmulti(), GiNaC::matrix::determinant_minor(), GiNaC::dirichlet_character(), GiNaC::matrix::division_free_elimination(), GiNaC::doublefactorial(), GiNaC::class_info< OPT >::dump_tree(), GiNaC::matrix::echelon_form(), GiNaC::power::eval(), GiNaC::mul::expand(), GiNaC::power::expand_add(), GiNaC::power::expand_mul(), GiNaC::factorial(), GiNaC::fibonacci(), GiNaC::frac_cancel(), GiNaC::matrix::fraction_free_elimination(), GiNaC::function_options::function_options(), GiNaC::matrix::gauss_elimination(), GiNaC::gcd(), GiNaC::golden_ratio_hash(), GiNaC::H_eval(), GiNaC::ifactor(), GiNaC::power::imag_part(), GiNaC::is_discriminant_of_quadratic_number_field(), GiNaC::kronecker_symbol(), GiNaC::integration_kernel::Laurent_series(), GiNaC::log2(), GiNaC::log_series(), GiNaC::basic::map(), GiNaC::matrix::markowitz_elimination(), GiNaC::multinomial_coefficient(), GiNaC::add::normal(), GiNaC::mul::normal(), GiNaC::pseries::normal(), GiNaC::const_iterator::operator+(), GiNaC::const_iterator::operator+=(), GiNaC::const_iterator::operator-(), GiNaC::const_iterator::operator-=(), GiNaC::operator<<(), GiNaC::operator>>(), GiNaC::const_iterator::operator[](), GiNaC::primitive_dirichlet_character(), GiNaC::psi2_deriv(), GiNaC::psi2_eval(), GiNaC::psi2_evalf(), GiNaC::psi2_series(), GiNaC::clifford::read_archive(), GiNaC::color::read_archive(), GiNaC::container< C >::read_archive(), GiNaC::constant::read_archive(), GiNaC::expairseq::read_archive(), GiNaC::fderivative::read_archive(), GiNaC::function::read_archive(), GiNaC::idx::read_archive(), GiNaC::varidx::read_archive(), GiNaC::spinidx::read_archive(), GiNaC::indexed::read_archive(), GiNaC::integral::read_archive(), GiNaC::matrix::read_archive(), GiNaC::numeric::read_archive(), GiNaC::power::read_archive(), GiNaC::pseries::read_archive(), GiNaC::relational::read_archive(), GiNaC::symbol::read_archive(), GiNaC::symmetry::read_archive(), GiNaC::minkmetric::read_archive(), GiNaC::tensepsilon::read_archive(), GiNaC::wildcard::read_archive(), GiNaC::power::real_part(), GiNaC::container_storage< C >::reserve(), GiNaC::rotate_left(), GiNaC::S_deriv(), GiNaC::S_eval(), GiNaC::S_evalf(), GiNaC::S_print_latex(), GiNaC::S_series(), GiNaC::basic::series(), GiNaC::symbol::set_name(), GiNaC::function_options::set_name(), GiNaC::symbol::set_TeX_name(), GiNaC::matrix::solve(), GiNaC::function_options::test_and_set_nparams(), GiNaC::tgamma_eval(), GiNaC::ex::traverse_postorder(), GiNaC::ex::traverse_preorder(), GiNaC::symmetry::validate(), GiNaC::write_real_float(), GiNaC::zetaderiv_deriv(), and GiNaC::zetaderiv_eval().

len

size_t len

private

Definition at line 1464 of file factor.cpp.

Referenced by GiNaC::crc32().

last

size_t last

private

Definition at line 1465 of file factor.cpp.

Referenced by GiNaC::antisymmetrize(), GiNaC::canonicalize(), GiNaC::cyclic_permutation(), GiNaC::mul::eval(), GiNaC::power::expand_add_2(), GiNaC::mul::expandchildren(), GiNaC::find_free_and_dummy(), GiNaC::permutation_sign(), GiNaC::shaker_sort(), GiNaC::symm(), GiNaC::symmetrize(), and GiNaC::symmetrize_cyclic().

k

vector<int> k

private

Definition at line 1466 of file factor.cpp.

Referenced by GiNaC::bernoulli(), GiNaC::Bernoulli_polynomial(), GiNaC::binomial(), GiNaC::scalar_products::debugprint(), GiNaC::divide_in_z(), GiNaC::EllipticE_deriv(), GiNaC::EllipticE_eval(), GiNaC::EllipticE_evalf(), GiNaC::EllipticE_print_latex(), GiNaC::EllipticE_series(), GiNaC::EllipticK_deriv(), GiNaC::EllipticK_eval(), GiNaC::EllipticK_evalf(), GiNaC::EllipticK_print_latex(), GiNaC::EllipticK_series(), GiNaC::ncmul::expand(), GiNaC::power::expand_add(), GiNaC::find_common_factor(), GiNaC::generalised_Bernoulli_number(), GiNaC::multi_iterator_permutation< T >::get_sign(), GiNaC::log2(), GiNaC::matrix::markowitz_elimination(), GiNaC::basic_partition_generator::mpartition2::mpartition2(), GiNaC::basic_partition_generator::mpartition2::next_partition(), GiNaC::composition_generator::coolmulti::next_permutation(), GiNaC::multi_iterator_ordered< T >::operator++(), GiNaC::multi_iterator_ordered_eq< T >::operator++(), GiNaC::multi_iterator_ordered_eq_indv< T >::operator++(), GiNaC::multi_iterator_counter< T >::operator++(), GiNaC::multi_iterator_counter_indv< T >::operator++(), GiNaC::multi_iterator_permutation< T >::operator++(), GiNaC::multi_iterator_shuffle< T >::operator++(), GiNaC::matrix::pivot(), GiNaC::reposition_dummy_indices(), GiNaC::resultant(), GiNaC::ELi_kernel::series_coeff_impl(), GiNaC::Ebar_kernel::series_coeff_impl(), GiNaC::simplify_indexed(), and GiNaC::sqrfree_parfrac().

poly

upoly poly

Definition at line 1474 of file factor.cpp.

Referenced by GiNaC::matrix::charpoly(), and GiNaC::factor().

x

ex x

Definition at line 1641 of file factor.cpp.

Referenced by GiNaC::abs(), GiNaC::acos(), GiNaC::acos_conjugate(), GiNaC::acos_deriv(), GiNaC::acos_eval(), GiNaC::acos_evalf(), GiNaC::acosh(), GiNaC::acosh_conjugate(), GiNaC::acosh_deriv(), GiNaC::acosh_eval(), GiNaC::acosh_evalf(), GiNaC::adaptivesimpson(), GiNaC::asin(), GiNaC::asin_conjugate(), GiNaC::asin_deriv(), GiNaC::asin_eval(), GiNaC::asin_evalf(), GiNaC::asinh(), GiNaC::asinh_conjugate(), GiNaC::asinh_deriv(), GiNaC::asinh_eval(), GiNaC::asinh_evalf(), GiNaC::atan(), GiNaC::atan2_deriv(), GiNaC::atan2_eval(), GiNaC::atan2_evalf(), GiNaC::atan_conjugate(), GiNaC::atan_deriv(), GiNaC::atan_eval(), GiNaC::atan_evalf(), GiNaC::atanh(), GiNaC::atanh_conjugate(), GiNaC::atanh_deriv(), GiNaC::atanh_eval(), GiNaC::atanh_evalf(), GiNaC::beta_deriv(), GiNaC::beta_eval(), GiNaC::beta_evalf(), GiNaC::binomial_conjugate(), GiNaC::binomial_eval(), GiNaC::binomial_evalf(), GiNaC::binomial_real_part(), GiNaC::binomial_sym(), GiNaC::lanczos_coeffs::calc_lanczos_A(), GiNaC::basic::collect(), GiNaC::container< C >::conjugate(), GiNaC::matrix::conjugate(), GiNaC::mul::conjugate(), GiNaC::ex::content(), GiNaC::convert_H_to_Li(), GiNaC::cos(), GiNaC::cos_conjugate(), GiNaC::cos_deriv(), GiNaC::cos_eval(), GiNaC::cos_evalf(), GiNaC::cos_imag_part(), GiNaC::cos_real_part(), GiNaC::cosh(), GiNaC::cosh_conjugate(), GiNaC::cosh_deriv(), GiNaC::cosh_eval(), GiNaC::cosh_evalf(), GiNaC::cosh_imag_part(), GiNaC::cosh_real_part(), GiNaC::csgn(), GiNaC::decomp_rational(), GiNaC::denom(), GiNaC::divide(), GiNaC::divide_in_z(), GiNaC::eta_conjugate(), GiNaC::eta_eval(), GiNaC::eta_evalf(), GiNaC::eta_imag_part(), GiNaC::eta_series(), GiNaC::tensepsilon::eval_indexed(), GiNaC::exp(), GiNaC::exp_conjugate(), GiNaC::exp_deriv(), GiNaC::exp_eval(), GiNaC::exp_evalf(), GiNaC::exp_imag_part(), GiNaC::exp_power(), GiNaC::exp_real_part(), GiNaC::factorial_conjugate(), GiNaC::factorial_eval(), GiNaC::factorial_evalf(), GiNaC::factorial_print_dflt_latex(), GiNaC::factorial_real_part(), GiNaC::find_common_factor(), GiNaC::frac_cancel(), GiNaC::fsolve(), GiNaC::G(), GiNaC::G2_eval(), GiNaC::G2_evalf(), GiNaC::G3_eval(), GiNaC::G3_evalf(), GiNaC::gcd(), GiNaC::get_first_symbol(), GiNaC::guess_precision(), GiNaC::H_deriv(), GiNaC::H_eval(), GiNaC::H_evalf(), GiNaC::H_print_latex(), GiNaC::H_series(), GiNaC::make_flat_inserter::handle_factor(), GiNaC::hasindex(), GiNaC::haswild(), GiNaC::heur_gcd_z(), GiNaC::imag(), GiNaC::interpolate(), GiNaC::inverse(), GiNaC::is_cinteger(), GiNaC::is_crational(), GiNaC::is_even(), GiNaC::is_integer(), GiNaC::is_negative(), GiNaC::is_nonneg_integer(), GiNaC::is_odd(), GiNaC::is_pos_integer(), GiNaC::is_positive(), GiNaC::is_prime(), GiNaC::is_rational(), GiNaC::is_real(), GiNaC::is_the_function(), GiNaC::is_the_function< G_SERIAL >(), GiNaC::is_the_function< iterated_integral_SERIAL >(), GiNaC::is_the_function< psi_SERIAL >(), GiNaC::is_the_function< zeta_SERIAL >(), GiNaC::is_zero(), GiNaC::isqrt(), GiNaC::lgamma(), GiNaC::lgamma_conjugate(), GiNaC::lgamma_deriv(), GiNaC::lgamma_eval(), GiNaC::lgamma_evalf(), GiNaC::Li2(), GiNaC::Li2_conjugate(), GiNaC::Li2_deriv(), GiNaC::Li2_eval(), GiNaC::Li2_evalf(), GiNaC::Li2_projection(), GiNaC::Li2_series(), GiNaC::Li3_eval(), GiNaC::Li_deriv(), GiNaC::Li_eval(), GiNaC::Li_evalf(), GiNaC::Li_print_latex(), GiNaC::Li_series(), GiNaC::log(), GiNaC::log_conjugate(), GiNaC::log_deriv(), GiNaC::log_eval(), GiNaC::log_evalf(), GiNaC::log_imag_part(), GiNaC::log_real_part(), GiNaC::make_real_float(), GiNaC::matrix::matrix(), GiNaC::numer(), GiNaC::sym_desc::operator<(), GiNaC::Order_conjugate(), GiNaC::Order_eval(), GiNaC::Order_imag_part(), GiNaC::Order_real_part(), GiNaC::Order_series(), GiNaC::pow(), GiNaC::prem(), GiNaC::ex::primpart(), GiNaC::print_integer_csrc(), GiNaC::print_real_cl_N(), GiNaC::print_real_csrc(), GiNaC::print_real_number(), GiNaC::print_sym_pow(), GiNaC::psi1_deriv(), GiNaC::psi1_eval(), GiNaC::psi1_evalf(), GiNaC::psi2_deriv(), GiNaC::psi2_eval(), GiNaC::psi2_evalf(), GiNaC::quo(), GiNaC::read_real_float(), GiNaC::real(), GiNaC::rem(), GiNaC::S_deriv(), GiNaC::S_eval(), GiNaC::S_evalf(), GiNaC::S_print_latex(), GiNaC::S_series(), GiNaC::sin(), GiNaC::sin_conjugate(), GiNaC::sin_deriv(), GiNaC::sin_eval(), GiNaC::sin_evalf(), GiNaC::sin_imag_part(), GiNaC::sin_real_part(), GiNaC::sinh(), GiNaC::sinh_conjugate(), GiNaC::sinh_deriv(), GiNaC::sinh_eval(), GiNaC::sinh_evalf(), GiNaC::sinh_imag_part(), GiNaC::sinh_real_part(), GiNaC::sprem(), GiNaC::sqrfree(), GiNaC::sqrfree_parfrac(), GiNaC::sqrfree_yun(), GiNaC::sqrt(), GiNaC::sr_gcd(), GiNaC::step(), GiNaC::tan(), GiNaC::tan_conjugate(), GiNaC::tan_deriv(), GiNaC::tan_eval(), GiNaC::tan_evalf(), GiNaC::tan_imag_part(), GiNaC::tan_real_part(), GiNaC::tan_series(), GiNaC::tanh(), GiNaC::tanh_conjugate(), GiNaC::tanh_deriv(), GiNaC::tanh_eval(), GiNaC::tanh_evalf(), GiNaC::tanh_imag_part(), GiNaC::tanh_real_part(), GiNaC::tanh_series(), GiNaC::tgamma(), GiNaC::tgamma_conjugate(), GiNaC::tgamma_deriv(), GiNaC::tgamma_eval(), GiNaC::tgamma_evalf(), GiNaC::to_double(), GiNaC::to_int(), GiNaC::to_long(), GiNaC::ex::unit(), GiNaC::unit_matrix(), GiNaC::ex::unitcontprim(), GiNaC::zeta(), GiNaC::zeta1_evalf(), GiNaC::zeta2_evalf(), GiNaC::zetaderiv_deriv(), and GiNaC::zetaderiv_eval().

evalpoint

int evalpoint

Definition at line 1642 of file factor.cpp.

R

cl_modint_ring R

Definition at line 1822 of file factor.cpp.

syms

exset syms

Definition at line 2434 of file factor.cpp.

Referenced by GiNaC::lsolve().

options

unsigned options

Definition at line 2480 of file factor.cpp.

Referenced by GiNaC::abs_expand(), GiNaC::mul::algebraic_subs_mul(), GiNaC::atan_series(), GiNaC::atanh_series(), GiNaC::beta_series(), GiNaC::csgn_series(), GiNaC::determinant(), GiNaC::exp_expand(), GiNaC::expand(), GiNaC::basic::expand(), GiNaC::ex::expand(), GiNaC::add::expand(), GiNaC::function::expand(), GiNaC::indexed::expand(), GiNaC::integral::expand(), GiNaC::mul::expand(), GiNaC::ncmul::expand(), GiNaC::power::expand(), GiNaC::pseries::expand(), GiNaC::structure< T, ComparisonPolicy >::expand(), GiNaC::power::expand_add(), GiNaC::power::expand_add_2(), GiNaC::power::expand_mul(), GiNaC::mul::expandchildren(), GiNaC::ncmul::expandchildren(), GiNaC::factor(), GiNaC::gcd(), GiNaC::basic::has(), GiNaC::mul::has(), GiNaC::power::has(), GiNaC::structure< T, ComparisonPolicy >::has(), GiNaC::ex::has(), GiNaC::has(), GiNaC::lgamma_series(), GiNaC::Li2_series(), GiNaC::log_expand(), GiNaC::log_series(), GiNaC::lsolve(), GiNaC::expand_map_function::operator()(), GiNaC::function_options::print_func(), GiNaC::registered_class_options::print_func(), GiNaC::psi1_series(), GiNaC::psi2_series(), GiNaC::S_series(), GiNaC::ex::series(), GiNaC::series(), GiNaC::add::series(), GiNaC::fderivative::series(), GiNaC::function::series(), GiNaC::integral::series(), GiNaC::pseries::series(), GiNaC::structure< T, ComparisonPolicy >::series(), GiNaC::mul::series(), GiNaC::power::series(), GiNaC::set_print_context(), GiNaC::set_print_func(), GiNaC::set_print_options(), GiNaC::simplify_indexed(), GiNaC::step_series(), GiNaC::subs(), GiNaC::basic::subs(), GiNaC::clifford::subs(), GiNaC::container< C >::subs(), GiNaC::idx::subs(), GiNaC::matrix::subs(), GiNaC::numeric::subs(), GiNaC::power::subs(), GiNaC::pseries::subs(), GiNaC::relational::subs(), GiNaC::structure< T, ComparisonPolicy >::subs(), GiNaC::symbol::subs(), GiNaC::ex::subs(), GiNaC::basic::subs_one_level(), GiNaC::container< C >::subschildren(), GiNaC::tan_series(), GiNaC::tanh_series(), and GiNaC::tgamma_series().