A multiple polylog sum is a special case of a Zsum. More...

#include <multiple_polylog.h>

Inheritance diagram for multiple_polylog:

Public Member Functions
	multiple_polylog (const GiNaC::ex &llc)

void	archive (GiNaC::archive_node &node) const override

void	read_archive (const GiNaC::archive_node &node, GiNaC::lst &sym_lst) override

void	print (const GiNaC::print_context &c, unsigned level=0) const override

GiNaC::ex	eval () const override

virtual GiNaC::ex	eval_approx () const

Public Member Functions inherited from Zsum
	Zsum (const GiNaC::ex &nc)

	Zsum (const GiNaC::ex &nc, const GiNaC::ex &llc)

void	archive (GiNaC::archive_node &node) const override

void	read_archive (const GiNaC::archive_node &node, GiNaC::lst &sym_lst) override

unsigned	return_type (void) const override

void	print (const GiNaC::print_context &c, unsigned level=0) const override

unsigned	precedence (void) const override

GiNaC::ex	eval () const override

GiNaC::ex	subs (const GiNaC::exmap &m, unsigned options=0) const override

virtual GiNaC::ex	convert_to_Ssum_exvector (const GiNaC::exvector &Z0, const GiNaC::exvector &Z1) const

virtual GiNaC::ex	shuffle_exvector (const GiNaC::exvector &Z0, const GiNaC::exvector &Z1, const GiNaC::exvector &Z2) const

virtual GiNaC::ex	set_index (const GiNaC::ex &i) const

virtual GiNaC::ex	shift_plus_one (void) const

virtual GiNaC::ex	shift_minus_one (void) const

virtual GiNaC::ex	adjust_upper_limit_downwards (const GiNaC::ex &i) const

virtual GiNaC::ex	adjust_upper_limit_upwards (const GiNaC::ex &i) const

virtual GiNaC::ex	adjust_upper_limit_plus_one (void) const

virtual GiNaC::ex	index_eq_one (void) const

virtual GiNaC::ex	get_head (int k) const

virtual GiNaC::ex	get_tail (int k) const

virtual GiNaC::ex	antipode (void) const

virtual GiNaC::ex	expand_members (int level=0) const

virtual GiNaC::ex	eval_explicit () const

virtual GiNaC::ex	get_first_letter (void) const

virtual GiNaC::ex	remove_first_letter (void) const

virtual GiNaC::ex	remove_first_letter (const GiNaC::ex &nc) const

virtual GiNaC::ex	prepend_letter (const GiNaC::ex &lc) const

virtual GiNaC::ex	prepend_letter (const GiNaC::ex &nc, const GiNaC::ex &lc) const

virtual GiNaC::ex	append_letter (const GiNaC::ex &lc) const

virtual GiNaC::ex	append_letter_list (const GiNaC::ex &lc) const

GiNaC::ex	get_index (void) const

GiNaC::ex	get_letter_list (void) const

unsigned	get_depth (void) const

GiNaC::ex	get_weight (void) const

Additional Inherited Members
Protected Member Functions inherited from Zsum
GiNaC::ex	eval_ncmul (const GiNaC::exvector &v) const override

GiNaC::ex	derivative (const GiNaC::symbol &s) const override

unsigned	calchash (void) const override

virtual GiNaC::ex	cast_to_Ssum (void) const

virtual GiNaC::ex	multiply_letter_with_last_letter (const GiNaC::ex &lc) const

virtual GiNaC::ex	multiply_letter_with_first_letter (const GiNaC::ex &lc) const

virtual GiNaC::ex	concat_two_sums (const GiNaC::ex &Z1, const GiNaC::ex &Z2) const

Protected Attributes inherited from Zsum
GiNaC::ex	n

GiNaC::ex	letter_list

Detailed Description

A multiple polylog sum is a special case of a Zsum.

Multiple polylogs are in the notation of Goncharov defined by

$\mbox{Li}_{m_k,...,m_1}(x_k,...,x_1) = Z(\infty;m_1,...,m_k;x_1,...,x_k)$

There are two "print" formats available. The default option prints multiple polylogarithms with reversed order of the arguments, as in the definition above. This notation is for example used by Goncharov.

If the flag "print_format::no_reversed_order" in the variable "_print_format" is set, multiple polylogarithms are printed without reversing the order of the arguments, e.g.

$Z(\infty;m_1,...,m_k;x_1,...,x_k) = \mbox{Li}_{m_1,...,m_k}(x_1,...,x_k)$