Sector decomposition
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integrand Class Reference

#include <integrand.h>

Public Member Functions

 integrand ()
 
 integrand (const std::vector< size_t > &index, const std::vector< exponent > &nu, const std::vector< GiNaC::ex > &poly_list, const std::vector< exponent > &c)
 
 integrand (const std::vector< exponent > &nu, const std::vector< GiNaC::ex > &poly_list, const std::vector< exponent > &c)
 
 integrand (size_t n, const std::vector< GiNaC::ex > &poly_list, const std::vector< exponent > &c)
 
 integrand (const std::vector< size_t > &index, const std::vector< exponent > &nu, const std::vector< GiNaC::ex > &poly_list, const std::vector< exponent > &c, GiNaC::ex extra_factor)
 
 integrand (const std::vector< size_t > &index, const std::vector< exponent > &nu, GiNaC::ex extra_factor)
 
 integrand (const std::vector< exponent > &nu, const std::vector< GiNaC::ex > &poly_list, const std::vector< exponent > &c, GiNaC::ex extra_factor)
 
 integrand (size_t n, const std::vector< GiNaC::ex > &poly_list, const std::vector< exponent > &c, GiNaC::ex extra_factor)
 
GiNaC::ex get_integrand (const integration_data &global_data) const
 
GiNaC::ex get_weight_factor (const integration_data &global_data) const
 
GiNaC::ex get_polynomials (const integration_data &global_data) const
 
GiNaC::ex get_polynomials_without_exponent (const integration_data &global_data) const
 
GiNaC::ex get_extra_factor () const
 
bool check_homogeneous_polynomial (size_t k, const integration_data &global_data) const
 
int get_homogeneous_degree (size_t k, const integration_data &global_data) const
 
int get_degree (GiNaC::ex poly, const integration_data &global_data) const
 
void make_homogeneous (size_t k, const integration_data &global_data)
 
void make_homogeneous (const integration_data &global_data)
 
void restrict_to_primary_sector (size_t k, const integration_data &global_data)
 
void restrict_to_primary_sector_cube (const multi_index_counter &index_set, const integration_data &global_data)
 
bool check_zero (size_t k, const multi_index_ordered &index_set, const integration_data &global_data) const
 
bool check_zero (const multi_index_ordered &index_set, const integration_data &global_data) const
 
int get_ldegree (size_t k, const multi_index_ordered &index_set, const integration_data &global_data) const
 
int get_ldegree (const multi_index_ordered &index_set, const integration_data &global_data) const
 
GiNaC::ex get_polyhedra_polynomial (const integration_data &global_data) const
 
bool find_min_max (std::vector< size_t > &k_min_max_set, const integration_data &global_data)
 
bool get_S_strategy_B (std::vector< size_t > &index_set, const integration_data &global_data)
 
bool get_S_strategy_C (std::vector< size_t > &index_set, const integration_data &global_data)
 
void create_subsector (size_t k, const std::vector< size_t > &index_set, const integration_data &global_data)
 
void create_subsector (size_t k, const multi_index_ordered &index_set, const integration_data &global_data)
 
int get_subtraction_vector (std::vector< size_t > &subtr_vec, std::vector< size_t > &index_set) const
 
GiNaC::ex taylor_term (GiNaC::ex polynomials, const multi_index_counter_indv &counter, const std::vector< size_t > &index_set, const integration_data &global_data) const
 
void integrated_taylor_term (const multi_index_counter_indv &counter, const std::vector< size_t > &index_set, const integration_data &global_data)
 

Public Attributes

std::vector< size_t > index
 a vector, serving as an index for integration_data::list_feynman_parameter
 
std::vector< exponent > weight
 a vector holding the exponents of the single factors $x_i$
 
std::vector< GiNaC::ex > polynomial_list
 a vector holding the $r$ polynomials
 
std::vector< exponent > poly_exponent
 a vector holding the exponents of the polynomials
 
GiNaC::ex extra_factor
 an extra prefactor
 

Friends

std::ostream & operator<< (std::ostream &os, const integrand &arg)
 

Detailed Description

The class integrand defines an integrand of the form

\[ C \left( \prod\limits_{i=1}^k x_i^{\nu_0+\nu_1 \varepsilon } \right) \left[ \prod\limits_{j=1}^r \left( P_j(x) \right)^{c_0+ c_1 \varepsilon} \right]. \]

The data members are:

Constructor & Destructor Documentation

◆ integrand() [1/8]

integrand ( )

Constructor.

◆ integrand() [2/8]

integrand ( const std::vector< size_t > &  arg_index,
const std::vector< exponent > &  nu,
const std::vector< GiNaC::ex > &  poly_list,
const std::vector< exponent > &  c 
)

Constructor.

index is initialised with arg_index, weight is initialised with nu, polynomial_list is initialised with poly_list, poly_exponent is initialised with c.

extra_factor is initialised with 1.

◆ integrand() [3/8]

integrand ( const std::vector< exponent > &  nu,
const std::vector< GiNaC::ex > &  poly_list,
const std::vector< exponent > &  c 
)

Constructor.

weight is initialised with nu, polynomial_list is initialised with poly_list, poly_exponent is initialised with c.

extra_factor is initialised with 1, index is initialised with (0,1,2,...)

◆ integrand() [4/8]

integrand ( size_t  n,
const std::vector< GiNaC::ex > &  poly_list,
const std::vector< exponent > &  c 
)

Constructor.

polynomial_list is initialised with poly_list, poly_exponent is initialised with c.

extra_factor is initialised with 1, index is initialised with (0,1,2,...,n-1), weight is initialised with n copies of exponent(0,0).

◆ integrand() [5/8]

integrand ( const std::vector< size_t > &  arg_index,
const std::vector< exponent > &  nu,
const std::vector< GiNaC::ex > &  poly_list,
const std::vector< exponent > &  c,
GiNaC::ex  arg_extra_factor 
)

Constructor.

index is initialised with arg_index, weight is initialised with nu, polynomial_list is initialised with poly_list, poly_exponent is initialised with c. extra_factor is initialised with arg_extra_factor.

◆ integrand() [6/8]

integrand ( const std::vector< size_t > &  arg_index,
const std::vector< exponent > &  nu,
GiNaC::ex  arg_extra_factor 
)

Constructor.

index is initialised with arg_index, weight is initialised with nu, extra_factor is initialised with arg_extra_factor.

polynomial_list and poly_exponent are empty.

◆ integrand() [7/8]

integrand ( const std::vector< exponent > &  nu,
const std::vector< GiNaC::ex > &  poly_list,
const std::vector< exponent > &  c,
GiNaC::ex  arg_extra_factor 
)

Constructor.

weight is initialised with nu, polynomial_list is initialised with poly_list, poly_exponent is initialised with c.

extra_factor is initialised with arg_extra_factor. index is initialised with (0,1,2,...)

◆ integrand() [8/8]

integrand ( size_t  n,
const std::vector< GiNaC::ex > &  poly_list,
const std::vector< exponent > &  c,
GiNaC::ex  arg_extra_factor 
)

Constructor.

polynomial_list is initialised with poly_list, poly_exponent is initialised with c.

extra_factor is initialised with arg_extra_factor. index is initialised with (0,1,2,...,n-1), weight is initialised with n copies of exponent(0,0).

Member Function Documentation

◆ check_homogeneous_polynomial()

bool check_homogeneous_polynomial ( size_t  k,
const integration_data &  global_data 
) const

Returns true if the $k$'s polynomial is homogeneous.

◆ check_zero() [1/2]

bool check_zero ( const multi_index_ordered &  index_set,
const integration_data &  global_data 
) const

Returns true if at least one of the polynomials vanishes, when the elements of index_set are set to zero.

◆ check_zero() [2/2]

bool check_zero ( size_t  k,
const multi_index_ordered &  index_set,
const integration_data &  global_data 
) const

Checks if the $k$'s polynomial vanishes if the elements of index_set are set to zero.

◆ create_subsector() [1/2]

void create_subsector ( size_t  k,
const multi_index_ordered &  index_set,
const integration_data &  global_data 
)

Creates the $k$'th subsector by remapping the variables given by index_set.

◆ create_subsector() [2/2]

void create_subsector ( size_t  k,
const std::vector< size_t > &  index_set,
const integration_data &  global_data 
)

Creates the $k$'th subsector by remapping the variables given by index_set.

◆ find_min_max()

bool find_min_max ( std::vector< size_t > &  k_min_max_set,
const integration_data &  global_data 
)

Implementation of Zeillinger's strategy.

◆ get_degree()

int get_degree ( GiNaC::ex  poly,
const integration_data &  global_data 
) const

Returns the degree of poly.

◆ get_extra_factor()

GiNaC::ex get_extra_factor ( ) const

Returns the prefactor.

◆ get_homogeneous_degree()

int get_homogeneous_degree ( size_t  k,
const integration_data &  global_data 
) const

Returns the homogeneous degree, if the $k$'s polynomial is homogeneous.

Returns $-1$ if it is not a homogeneous polynomial.

◆ get_integrand()

GiNaC::ex get_integrand ( const integration_data &  global_data) const

Returns the explicit form of the integrand.

◆ get_ldegree() [1/2]

int get_ldegree ( const multi_index_ordered &  index_set,
const integration_data &  global_data 
) const

Returns the ldegree of the product of all polynomials in the elements of index_set.

◆ get_ldegree() [2/2]

int get_ldegree ( size_t  k,
const multi_index_ordered &  index_set,
const integration_data &  global_data 
) const

Returns the ldegree of the $k$'s polynomial in the elements of index_set.

◆ get_polyhedra_polynomial()

GiNaC::ex get_polyhedra_polynomial ( const integration_data &  global_data) const

Returns a polynomial, where only terms corresponding to corners of a polyhedra have been kept.

◆ get_polynomials()

GiNaC::ex get_polynomials ( const integration_data &  global_data) const

Returns the explicit form of the polynomials.

◆ get_polynomials_without_exponent()

GiNaC::ex get_polynomials_without_exponent ( const integration_data &  global_data) const

Returns the explicit form of the polynomials without the exponent.

The polynomial is returned in expanded form.

◆ get_S_strategy_B()

bool get_S_strategy_B ( std::vector< size_t > &  index_set,
const integration_data &  global_data 
)

Determines a subset of Feynman parameters accoriding to Spivakovsky's strategy.

◆ get_S_strategy_C()

bool get_S_strategy_C ( std::vector< size_t > &  index_set,
const integration_data &  global_data 
)

Determines a subset of Feynman parameters accoriding to strategy C.

◆ get_subtraction_vector()

int get_subtraction_vector ( std::vector< size_t > &  subtr_vec,
std::vector< size_t > &  index_set 
) const

The routine fills a vector, indicating how many subtractions are needed for each variable. The indices for the corresponding variables are stored in index_set. If no subtractions are needed, the corresponding entry is not included. The return value is the number of variables, in which subtractions are needed.

◆ get_weight_factor()

GiNaC::ex get_weight_factor ( const integration_data &  global_data) const

Returns the explicit form of the weight factor.

◆ integrated_taylor_term()

void integrated_taylor_term ( const multi_index_counter_indv &  counter,
const std::vector< size_t > &  index_set,
const integration_data &  global_data 
)

Returns one term in the Taylor expansion, integrated over the singular variables.

◆ make_homogeneous() [1/2]

void make_homogeneous ( const integration_data &  global_data)

Transforms all polynomials into homogeneous polynomials.

◆ make_homogeneous() [2/2]

void make_homogeneous ( size_t  k,
const integration_data &  global_data 
)

Transforms the $k$'s polynomial into a homogeneous polynomial.

◆ restrict_to_primary_sector()

void restrict_to_primary_sector ( size_t  k,
const integration_data &  global_data 
)

Restricts to the $k$'s primary sector.

◆ restrict_to_primary_sector_cube()

void restrict_to_primary_sector_cube ( const multi_index_counter &  index_set,
const integration_data &  global_data 
)

Restricts to one primary sector for the integration over the standard hyper-cube.

◆ taylor_term()

GiNaC::ex taylor_term ( GiNaC::ex  expr,
const multi_index_counter_indv &  counter,
const std::vector< size_t > &  index_set,
const integration_data &  global_data 
) const

Returns one term in the Taylor expansion.

Friends And Related Function Documentation

◆ operator<<

std::ostream & operator<< ( std::ostream &  os,
const integrand &  arg 
)
friend

Output. Prints out the data of the class integrand without reference to a class integration_data.

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