integration_kernel.h

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/*
 *  GiNaC Copyright (C) 1999-2023 Johannes Gutenberg University Mainz, Germany
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */
 
#ifndef GINAC_INTEGRATION_KERNEL_H
#define GINAC_INTEGRATION_KERNEL_H
 
#include "basic.h"
#include "archive.h"
#include "numeric.h"
#include "lst.h"
 
#include <cln/complex.h>
#include <vector>
 
namespace GiNaC {
 
ex ifactor(const numeric & n);
bool is_discriminant_of_quadratic_number_field(const numeric & n);
numeric kronecker_symbol(const numeric & a, const numeric & n);
numeric primitive_dirichlet_character(const numeric & n, const numeric & a);
numeric dirichlet_character(const numeric & n, const numeric & a, const numeric & N);
numeric generalised_Bernoulli_number(const numeric & k, const numeric & b);
ex Bernoulli_polynomial(const numeric & k, const ex & x);
 
class integration_kernel : public basic
{
    GINAC_DECLARE_REGISTERED_CLASS(integration_kernel, basic)
 
    // ctors
public:
 
    // functions overriding virtual functions from base classes
public:
    ex series(const relational & r, int order, unsigned options = 0) const override;
 
protected:
 
    // new virtual functions which can be overridden by derived classes
public:
    virtual bool has_trailing_zero(void) const;
    virtual bool is_numeric(void) const;
    virtual ex Laurent_series(const ex & x, int order) const;
    virtual ex  get_numerical_value(const ex & lambda, int N_trunc = 0) const;
 
protected:
    virtual bool uses_Laurent_series() const;
    virtual cln::cl_N series_coeff_impl(int i) const;
 
    // non-virtual functions 
public:
    size_t get_cache_size(void) const;
    void set_cache_step(int cache_steps) const;
    ex get_series_coeff(int i) const;
    cln::cl_N series_coeff(int i) const;
 
protected:
    ex  get_numerical_value_impl(const ex & lambda, const ex & pre, int shift, int N_trunc) const;
    void do_print(const print_context & c, unsigned level) const;
 
        // friends :
 
    // member variables :
 
protected:
    // cache is increased by steps of cache_step_size
    mutable int cache_step_size;
    // cache already computed series coefficients
    mutable std::vector<cln::cl_N> series_vec;
 
};
 
GINAC_DECLARE_UNARCHIVER(integration_kernel);
 
class basic_log_kernel : public integration_kernel
{
    GINAC_DECLARE_REGISTERED_CLASS(basic_log_kernel, integration_kernel)
 
    // ctors
public:
 
    // functions overriding virtual functions from base classes
public:
 
protected:
    cln::cl_N series_coeff_impl(int i) const override;
 
    // new virtual functions which can be overridden by derived classes
public:
 
protected:
 
    // non-virtual functions 
public:
 
protected:
    void do_print(const print_context & c, unsigned level) const;
 
    // friends :
 
    // member variables :
 
protected:
 
};
 
GINAC_DECLARE_UNARCHIVER(basic_log_kernel);
 
class multiple_polylog_kernel : public integration_kernel
{
    GINAC_DECLARE_REGISTERED_CLASS(multiple_polylog_kernel, integration_kernel)
 
    // ctors
public:
    multiple_polylog_kernel(const ex & z);
 
    // functions overriding virtual functions from base classes
public:
    size_t nops() const override;
    ex op(size_t i) const override;
    ex & let_op(size_t i) override;
 
    bool is_numeric(void) const override;
 
protected:
    cln::cl_N series_coeff_impl(int i) const override;
 
    // new virtual functions which can be overridden by derived classes
public:
 
protected:
 
    // non-virtual functions 
public:
 
protected:
    void do_print(const print_context & c, unsigned level) const;
 
        // friends :
 
    // member variables :
 
protected:
    ex z;
 
};
 
GINAC_DECLARE_UNARCHIVER(multiple_polylog_kernel);
 
class ELi_kernel : public integration_kernel
{
    GINAC_DECLARE_REGISTERED_CLASS(ELi_kernel, integration_kernel)
 
    // ctors
public:
    ELi_kernel(const ex & n, const ex & m, const ex & x, const ex & y);
 
    // functions overriding virtual functions from base classes
public:
    size_t nops() const override;
    ex op(size_t i) const override;
    ex & let_op(size_t i) override;
 
    bool is_numeric(void) const override;
    ex get_numerical_value(const ex & qbar, int N_trunc = 0) const override;
 
protected:
    cln::cl_N series_coeff_impl(int i) const override;
 
    // new virtual functions which can be overridden by derived classes
public:
 
protected:
 
    // non-virtual functions 
public:
 
protected:
    void do_print(const print_context & c, unsigned level) const;
 
        // friends :
 
    // member variables :
 
protected:
    ex n;
    ex m;
    ex x;
    ex y;
 
};
 
GINAC_DECLARE_UNARCHIVER(ELi_kernel);
 
class Ebar_kernel : public integration_kernel
{
    GINAC_DECLARE_REGISTERED_CLASS(Ebar_kernel, integration_kernel)
 
    // ctors
public:
    Ebar_kernel(const ex & n, const ex & m, const ex & x, const ex & y);
 
    // functions overriding virtual functions from base classes
public:
    size_t nops() const override;
    ex op(size_t i) const override;
    ex & let_op(size_t i) override;
 
    bool is_numeric(void) const override;
    ex get_numerical_value(const ex & qbar, int N_trunc = 0) const override;
 
protected:
    cln::cl_N series_coeff_impl(int i) const override;
 
    // new virtual functions which can be overridden by derived classes
public:
 
protected:
 
    // non-virtual functions 
public:
 
protected:
    void do_print(const print_context & c, unsigned level) const;
 
        // friends :
 
    // member variables :
 
protected:
    ex n;
    ex m;
    ex x;
    ex y;
 
};
 
GINAC_DECLARE_UNARCHIVER(Ebar_kernel);
 
class Kronecker_dtau_kernel : public integration_kernel
{
    GINAC_DECLARE_REGISTERED_CLASS(Kronecker_dtau_kernel, integration_kernel)
 
    // ctors
public:
    Kronecker_dtau_kernel(const ex & n, const ex & z, const ex & K = numeric(1), const ex & C_norm = numeric(1));
 
    // functions overriding virtual functions from base classes
public:
    size_t nops() const override;
    ex op(size_t i) const override;
    ex & let_op(size_t i) override;
 
    bool is_numeric(void) const override;
    ex get_numerical_value(const ex & qbar, int N_trunc = 0) const override;
 
protected:
    cln::cl_N series_coeff_impl(int i) const override;
 
    // new virtual functions which can be overridden by derived classes
public:
 
protected:
 
    // non-virtual functions 
public:
 
protected:
    void do_print(const print_context & c, unsigned level) const;
 
        // friends :
 
    // member variables :
 
protected:
    ex n;
    ex z;
    ex K;
    ex C_norm;
};
 
GINAC_DECLARE_UNARCHIVER(Kronecker_dtau_kernel);
 
 
class Kronecker_dz_kernel : public integration_kernel
{
    GINAC_DECLARE_REGISTERED_CLASS(Kronecker_dz_kernel, integration_kernel)
 
    // ctors
public:
    Kronecker_dz_kernel(const ex & n, const ex & z_j, const ex & tau, const ex & K = numeric(1), const ex & C_norm = numeric(1));
 
    // functions overriding virtual functions from base classes
public:
    size_t nops() const override;
    ex op(size_t i) const override;
    ex & let_op(size_t i) override;
 
    bool is_numeric(void) const override;
    ex get_numerical_value(const ex & z, int N_trunc = 0) const override;
 
protected:
    cln::cl_N series_coeff_impl(int i) const override;
 
    // new virtual functions which can be overridden by derived classes
public:
 
protected:
 
    // non-virtual functions 
public:
 
protected:
    void do_print(const print_context & c, unsigned level) const;
 
        // friends :
 
    // member variables :
 
protected:
    ex n;
    ex z_j;
    ex tau;
    ex K;
    ex C_norm;
 
};
 
GINAC_DECLARE_UNARCHIVER(Kronecker_dz_kernel);
 
 
class Eisenstein_kernel : public integration_kernel
{
    GINAC_DECLARE_REGISTERED_CLASS(Eisenstein_kernel, integration_kernel)
 
    // ctors
public:
    Eisenstein_kernel(const ex & k, const ex & N, const ex & a, const ex & b, const ex & K, const ex & C_norm = numeric(1));
 
    // functions overriding virtual functions from base classes
public:
    ex series(const relational & r, int order, unsigned options = 0) const override;
 
    size_t nops() const override;
    ex op(size_t i) const override;
    ex & let_op(size_t i) override;
 
    bool is_numeric(void) const override;
    ex Laurent_series(const ex & x, int order) const override;
    ex get_numerical_value(const ex & qbar, int N_trunc = 0) const override;
 
protected:
    bool uses_Laurent_series() const override;
 
    // new virtual functions which can be overridden by derived classes
public:
 
protected:
 
    // non-virtual functions 
public:
    ex q_expansion_modular_form(const ex & q, int order) const;
 
protected:
    void do_print(const print_context & c, unsigned level) const;
 
        // friends :
 
    // member variables :
 
protected:
    ex k;
    ex N;
    ex a;
    ex b;
    ex K;
    ex C_norm;
 
};
 
GINAC_DECLARE_UNARCHIVER(Eisenstein_kernel);
 
 
class Eisenstein_h_kernel : public integration_kernel
{
    GINAC_DECLARE_REGISTERED_CLASS(Eisenstein_h_kernel, integration_kernel)
 
    // ctors
public:
    Eisenstein_h_kernel(const ex & k, const ex & N, const ex & r, const ex & s, const ex & C_norm = numeric(1));
 
    // functions overriding virtual functions from base classes
public:
    ex series(const relational & r, int order, unsigned options = 0) const override;
 
    size_t nops() const override;
    ex op(size_t i) const override;
    ex & let_op(size_t i) override;
 
    bool is_numeric(void) const override;
    ex Laurent_series(const ex & x, int order) const override;
    ex get_numerical_value(const ex & qbar, int N_trunc = 0) const override;
 
protected:
    bool uses_Laurent_series() const override;
 
    // new virtual functions which can be overridden by derived classes
public:
 
protected:
 
    // non-virtual functions 
public:
    ex coefficient_a0(const numeric & k, const numeric & r, const numeric & s, const numeric & N) const;
    ex coefficient_an(const numeric & n, const numeric & k, const numeric & r, const numeric & s, const numeric & N) const;
    ex q_expansion_modular_form(const ex & q, int order) const;
 
protected:
    void do_print(const print_context & c, unsigned level) const;
 
        // friends :
 
    // member variables :
 
protected:
    ex k;
    ex N;
    ex r;
    ex s;
    ex C_norm;
 
};
 
GINAC_DECLARE_UNARCHIVER(Eisenstein_h_kernel);
 
 
class modular_form_kernel : public integration_kernel
{
    GINAC_DECLARE_REGISTERED_CLASS(modular_form_kernel, integration_kernel)
 
    // ctors
public:
    modular_form_kernel(const ex & k, const ex & P, const ex & C_norm = numeric(1));
 
    // functions overriding virtual functions from base classes
public:
    ex series(const relational & r, int order, unsigned options = 0) const override;
 
    size_t nops() const override;
    ex op(size_t i) const override;
    ex & let_op(size_t i) override;
 
    bool is_numeric(void) const override;
    ex Laurent_series(const ex & qbar, int order) const override;
    ex get_numerical_value(const ex & qbar, int N_trunc = 0) const override;
 
protected:
    bool uses_Laurent_series() const override;
 
    // new virtual functions which can be overridden by derived classes
public:
 
protected:
 
    // non-virtual functions 
public:
    ex q_expansion_modular_form(const ex & q, int order) const;
 
protected:
    void do_print(const print_context & c, unsigned level) const;
 
        // friends :
 
    // member variables :
 
protected:
    ex k;
    ex P;
    ex C_norm;
 
};
 
GINAC_DECLARE_UNARCHIVER(modular_form_kernel);
 
 
class user_defined_kernel : public integration_kernel
{
    GINAC_DECLARE_REGISTERED_CLASS(user_defined_kernel, integration_kernel)
 
    // ctors
public:
    user_defined_kernel(const ex & f, const ex & x);
 
    // functions overriding virtual functions from base classes
public:
    size_t nops() const override;
    ex op(size_t i) const override;
    ex & let_op(size_t i) override;
 
    bool is_numeric(void) const override;
    ex Laurent_series(const ex & x, int order) const override;
 
protected:
    bool uses_Laurent_series() const override;
 
    // new virtual functions which can be overridden by derived classes
public:
 
protected:
 
    // non-virtual functions 
public:
 
protected:
    void do_print(const print_context & c, unsigned level) const;
 
        // friends :
 
    // member variables :
 
protected:
    ex f;
    ex x;
 
};
 
GINAC_DECLARE_UNARCHIVER(user_defined_kernel);
 
} // namespace GiNaC
 
#endif // ndef GINAC_INTEGRATION_KERNEL_H