The kernel corresponding to the Eisenstein series $h_{k,N,r,s}(\tau)$ . More...

#include <integration_kernel.h>

Inheritance diagram for GiNaC::Eisenstein_h_kernel:

Public Member Functions
	Eisenstein_h_kernel (const ex &k, const ex &N, const ex &r, const ex &s, const ex &C_norm=numeric(1))

ex	series (const relational &r, int order, unsigned options=0) const override
	The series method for this class returns the qbar-expansion of the modular form, without an additional factor of C_norm/qbar. More...

size_t	nops () const override
	Number of operands/members. More...

ex	op (size_t i) const override
	Return operand/member at position i. More...

ex &	let_op (size_t i) override
	Return modifiable operand/member at position i. More...

bool	is_numeric (void) const override
	This routine returns true, if the integration kernel can be evaluated numerically. More...

ex	Laurent_series (const ex &x, int order) const override
	Returns the Laurent series, starting possibly with the pole term. More...

ex	get_numerical_value (const ex &qbar, int N_trunc=0) const override
	Returns the value of the modular form. More...

ex	coefficient_a0 (const numeric &k, const numeric &r, const numeric &s, const numeric &N) const
	The constant coefficient in the Fourier expansion. More...

ex	coefficient_an (const numeric &n, const numeric &k, const numeric &r, const numeric &s, const numeric &N) const
	The higher coefficients in the Fourier expansion. More...

ex	q_expansion_modular_form (const ex &q, int order) const

Public Member Functions inherited from GiNaC::integration_kernel
ex	series (const relational &r, int order, unsigned options=0) const override
	Default implementation of ex::series(). More...

virtual bool	has_trailing_zero (void) const
	This routine returns true, if the integration kernel has a trailing zero. More...

virtual bool	is_numeric (void) const
	This routine returns true, if the integration kernel can be evaluated numerically. More...

virtual ex	Laurent_series (const ex &x, int order) const
	Returns the Laurent series, starting possibly with the pole term. More...

virtual ex	get_numerical_value (const ex &lambda, int N_trunc=0) const
	Evaluates the integrand at lambda. More...

size_t	get_cache_size (void) const
	Returns the current size of the cache. More...

void	set_cache_step (int cache_steps) const
	Sets the step size by which the cache is increased. More...

ex	get_series_coeff (int i) const
	Wrapper around series_coeff(i), converts cl_N to numeric. More...

cln::cl_N	series_coeff (int i) const
	Subclasses have either to implement series_coeff_impl or the two methods Laurent_series and uses_Laurent_series. More...

Public Member Functions inherited from GiNaC::basic
virtual	~basic ()
	basic destructor, virtual because class ex will delete objects of derived classes via a basic*. More...

	basic (const basic &other)

const basic &	operator= (const basic &other)
	basic assignment operator: the other object might be of a derived class. More...

virtual basic *	duplicate () const
	Create a clone of this object on the heap. More...

virtual ex	eval () const
	Perform automatic non-interruptive term rewriting rules. More...

virtual ex	evalf () const
	Evaluate object numerically. More...

virtual ex	evalm () const
	Evaluate sums, products and integer powers of matrices. More...

virtual ex	eval_integ () const
	Evaluate integrals, if result is known. More...

virtual ex	eval_indexed (const basic &i) const
	Perform automatic symbolic evaluations on indexed expression that contains this object as the base expression. More...

virtual void	print (const print_context &c, unsigned level=0) const
	Output to stream. More...

virtual void	dbgprint () const
	Little wrapper around print to be called within a debugger. More...

virtual void	dbgprinttree () const
	Little wrapper around printtree to be called within a debugger. More...

virtual unsigned	precedence () const
	Return relative operator precedence (for parenthezing output). More...

virtual bool	info (unsigned inf) const
	Information about the object. More...

virtual size_t	nops () const
	Number of operands/members. More...

virtual ex	op (size_t i) const
	Return operand/member at position i. More...

virtual ex	operator[] (const ex &index) const

virtual ex	operator[] (size_t i) const

virtual ex &	let_op (size_t i)
	Return modifiable operand/member at position i. More...

virtual ex &	operator[] (const ex &index)

virtual ex &	operator[] (size_t i)

virtual bool	has (const ex &other, unsigned options=0) const
	Test for occurrence of a pattern. More...

virtual bool	match (const ex &pattern, exmap &repls) const
	Check whether the expression matches a given pattern. More...

virtual ex	subs (const exmap &m, unsigned options=0) const
	Substitute a set of objects by arbitrary expressions. More...

virtual ex	map (map_function &f) const
	Construct new expression by applying the specified function to all sub-expressions (one level only, not recursively). More...

virtual void	accept (GiNaC::visitor &v) const

virtual bool	is_polynomial (const ex &var) const
	Check whether this is a polynomial in the given variables. More...

virtual int	degree (const ex &s) const
	Return degree of highest power in object s. More...

virtual int	ldegree (const ex &s) const
	Return degree of lowest power in object s. More...

virtual ex	coeff (const ex &s, int n=1) const
	Return coefficient of degree n in object s. More...

virtual ex	expand (unsigned options=0) const
	Expand expression, i.e. More...

virtual ex	collect (const ex &s, bool distributed=false) const
	Sort expanded expression in terms of powers of some object(s). More...

virtual ex	series (const relational &r, int order, unsigned options=0) const
	Default implementation of ex::series(). More...

virtual ex	normal (exmap &repl, exmap &rev_lookup, lst &modifier) const
	Default implementation of ex::normal(). More...

virtual ex	to_rational (exmap &repl) const
	Default implementation of ex::to_rational(). More...

virtual ex	to_polynomial (exmap &repl) const

virtual numeric	integer_content () const

virtual ex	smod (const numeric &xi) const
	Apply symmetric modular homomorphism to an expanded multivariate polynomial. More...

virtual numeric	max_coefficient () const
	Implementation ex::max_coefficient(). More...

virtual exvector	get_free_indices () const
	Return a vector containing the free indices of an expression. More...

virtual ex	add_indexed (const ex &self, const ex &other) const
	Add two indexed expressions. More...

virtual ex	scalar_mul_indexed (const ex &self, const numeric &other) const
	Multiply an indexed expression with a scalar. More...

virtual bool	contract_with (exvector::iterator self, exvector::iterator other, exvector &v) const
	Try to contract two indexed expressions that appear in the same product. More...

virtual unsigned	return_type () const

virtual return_type_t	return_type_tinfo () const

virtual ex	conjugate () const

virtual ex	real_part () const

virtual ex	imag_part () const

template<class T >
void	print_dispatch (const print_context &c, unsigned level) const
	Like print(), but dispatch to the specified class. More...

void	print_dispatch (const registered_class_info &ri, const print_context &c, unsigned level) const
	Like print(), but dispatch to the specified class. More...

virtual void	archive (archive_node &n) const
	Save (serialize) the object into archive node. More...

virtual void	read_archive (const archive_node &n, lst &syms)
	Load (deserialize) the object from an archive node. More...

ex	subs_one_level (const exmap &m, unsigned options) const
	Helper function for subs(). More...

ex	diff (const symbol &s, unsigned nth=1) const
	Default interface of nth derivative ex::diff(s, n). More...

int	compare (const basic &other) const
	Compare objects syntactically to establish canonical ordering. More...

bool	is_equal (const basic &other) const
	Test for syntactic equality. More...

const basic &	hold () const
	Stop further evaluation. More...

unsigned	gethash () const

const basic &	setflag (unsigned f) const
	Set some status_flags. More...

const basic &	clearflag (unsigned f) const
	Clear some status_flags. More...

Public Member Functions inherited from GiNaC::refcounted
	refcounted () noexcept

unsigned int	add_reference () noexcept

unsigned int	remove_reference () noexcept

unsigned int	get_refcount () const noexcept

void	set_refcount (unsigned int r) noexcept

Protected Member Functions
bool	uses_Laurent_series () const override
	Returns true, if the coefficients are computed from the Laurent series (in which case the method Laurent_series needs to be implemented). More...

void	do_print (const print_context &c, unsigned level) const

Protected Member Functions inherited from GiNaC::integration_kernel
virtual bool	uses_Laurent_series () const
	Returns true, if the coefficients are computed from the Laurent series (in which case the method Laurent_series needs to be implemented). More...

virtual cln::cl_N	series_coeff_impl (int i) const
	For $\omega = d\lambda$ only the coefficient of $\lambda^0$ is non-zero. More...

ex	get_numerical_value_impl (const ex &lambda, const ex &pre, int shift, int N_trunc) const
	The actual implementation for computing a numerical value for the integrand. More...

void	do_print (const print_context &c, unsigned level) const

Protected Member Functions inherited from GiNaC::basic
	basic ()

virtual ex	eval_ncmul (const exvector &v) const

virtual bool	match_same_type (const basic &other) const
	Returns true if the attributes of two objects are similar enough for a match. More...

virtual ex	derivative (const symbol &s) const
	Default implementation of ex::diff(). More...

virtual int	compare_same_type (const basic &other) const
	Returns order relation between two objects of same type. More...

virtual bool	is_equal_same_type (const basic &other) const
	Returns true if two objects of same type are equal. More...

virtual unsigned	calchash () const
	Compute the hash value of an object and if it makes sense to store it in the objects status_flags, do so. More...

void	ensure_if_modifiable () const
	Ensure the object may be modified without hurting others, throws if this is not the case. More...

void	do_print (const print_context &c, unsigned level) const
	Default output to stream. More...

void	do_print_tree (const print_tree &c, unsigned level) const
	Tree output to stream. More...

void	do_print_python_repr (const print_python_repr &c, unsigned level) const
	Python parsable output to stream. More...

Protected Attributes
ex	k

ex	N

ex	r

ex	s

ex	C_norm

Protected Attributes inherited from GiNaC::integration_kernel
int	cache_step_size

std::vector< cln::cl_N >	series_vec

Protected Attributes inherited from GiNaC::basic
unsigned	flags
	of type status_flags More...

unsigned	hashvalue
	hash value More...