Implementation of some special functions related to elliptic curves. More...

#include "inifcns.h"
#include "add.h"
#include "constant.h"
#include "lst.h"
#include "mul.h"
#include "numeric.h"
#include "operators.h"
#include "power.h"
#include "pseries.h"
#include "relational.h"
#include "symbol.h"
#include "utils.h"
#include "wildcard.h"
#include "integration_kernel.h"
#include "utils_multi_iterator.h"
#include <cln/cln.h>
#include <sstream>
#include <stdexcept>
#include <vector>
#include <cmath>

Namespaces
namespace	GiNaC

Functions
static ex	GiNaC::EllipticK_evalf (const ex &k)

static ex	GiNaC::EllipticK_eval (const ex &k)

static ex	GiNaC::EllipticK_deriv (const ex &k, unsigned deriv_param)

static ex	GiNaC::EllipticK_series (const ex &k, const relational &rel, int order, unsigned options)

static void	GiNaC::EllipticK_print_latex (const ex &k, const print_context &c)

	GiNaC::REGISTER_FUNCTION (EllipticK, evalf_func(EllipticK_evalf). eval_func(EllipticK_eval). derivative_func(EllipticK_deriv). series_func(EllipticK_series). print_func< print_latex >(EllipticK_print_latex). do_not_evalf_params())

static ex	GiNaC::EllipticE_evalf (const ex &k)

static ex	GiNaC::EllipticE_eval (const ex &k)

static ex	GiNaC::EllipticE_deriv (const ex &k, unsigned deriv_param)

static ex	GiNaC::EllipticE_series (const ex &k, const relational &rel, int order, unsigned options)

static void	GiNaC::EllipticE_print_latex (const ex &k, const print_context &c)

	GiNaC::REGISTER_FUNCTION (EllipticE, evalf_func(EllipticE_evalf). eval_func(EllipticE_eval). derivative_func(EllipticE_deriv). series_func(EllipticE_series). print_func< print_latex >(EllipticE_print_latex). do_not_evalf_params())

static ex	GiNaC::iterated_integral_evalf_impl (const ex &kernel_lst, const ex &lambda, const ex &N_trunc)

static ex	GiNaC::iterated_integral2_evalf (const ex &kernel_lst, const ex &lambda)

static ex	GiNaC::iterated_integral3_evalf (const ex &kernel_lst, const ex &lambda, const ex &N_trunc)

static ex	GiNaC::iterated_integral2_eval (const ex &kernel_lst, const ex &lambda)

static ex	GiNaC::iterated_integral3_eval (const ex &kernel_lst, const ex &lambda, const ex &N_trunc)

Detailed Description

Implementation of some special functions related to elliptic curves.

The functions are: complete elliptic integral of the first kind EllipticK(k) complete elliptic integral of the second kind EllipticE(k) iterated integral iterated_integral(a,y) or iterated_integral(a,y,N_trunc)

Some remarks:

All formulae used can be looked up in the following publication: [WW] Numerical evaluation of iterated integrals related to elliptic Feynman integrals, M.Walden, S.Weinzierl, arXiv:2010.05271
When these routines and methods are used for scientific work that leads to publication in a scientific journal, please refer to this program as : M.Walden, S.Weinzierl, "Numerical evaluation of iterated integrals related to elliptic Feynman integrals", arXiv:2010.05271
As these routines build on the core part of GiNaC, it is also polite to acknowledge C. Bauer, A. Frink, R. Kreckel, "Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language", J. Symbolic Computations 33, 1 (2002), cs.sc/0004015

Definition in file inifcns_elliptic.cpp.

Namespaces

Functions

Detailed Description