Nestedsums library
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list_of_tgamma Class Reference

The class list_of_tgamma is a container for the class ratio_of_tgamma. More...

#include <list_polygamma.h>

Inheritance diagram for list_of_tgamma:

Public Member Functions

 list_of_tgamma (const GiNaC::ex &l)
 
 list_of_tgamma (const GiNaC::ex &l, const GiNaC::ex &i, const GiNaC::ex &eps, int o)
 
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 eval_explicit () const
 
virtual unsigned get_key (void) const
 
virtual GiNaC::ex hash_data (void) const
 
virtual GiNaC::ex subst_data (void) const
 
GiNaC::ex set_expansion (void) const
 
GiNaC::ex set_index (const GiNaC::ex &new_index) const
 
GiNaC::ex set_expansion_parameter (const GiNaC::ex &new_eps) const
 
GiNaC::ex set_order (int new_order) const
 
GiNaC::ex get_index (void) const
 
unsigned get_depth (void) const
 
GiNaC::ex shift_plus_one (void) const
 
GiNaC::ex shift_minus_one (void) const
 
GiNaC::ex index_eq_one (void) const
 
GiNaC::ex shift_index (const GiNaC::ex &new_index) const
 
GiNaC::ex concat (const GiNaC::ex &l) const
 
int pole_alert (void) const
 
int expansion_alert (void) const
 

Protected Member Functions

GiNaC::ex eval_ncmul (const GiNaC::exvector &v) const override
 
GiNaC::ex derivative (const GiNaC::symbol &s) const override
 
unsigned calchash (void) const override
 

Protected Attributes

GiNaC::ex gamma_sequence
 
GiNaC::ex index
 
GiNaC::ex expansion_parameter
 
int order
 

Friends

class transcendental_sum_type_A
 
class transcendental_sum_type_B
 
class transcendental_sum_type_C
 
class transcendental_sum_type_D
 
GiNaC::ex create_transcendental_sum_type_A_and_set_gammas (const GiNaC::ex &nn, const GiNaC::ex &i, const GiNaC::ex &l, const GiNaC::ex &v, const GiNaC::ex &ss, const GiNaC::ex &eps, int o, int f)
 
GiNaC::ex create_transcendental_sum_type_B_and_set_gammas (const GiNaC::ex &nn, const GiNaC::ex &i, const GiNaC::ex &l, const GiNaC::ex &lr, const GiNaC::ex &v, const GiNaC::ex &vr, const GiNaC::ex &ss, const GiNaC::ex &ssr, const GiNaC::ex &eps, int o, int f)
 
GiNaC::ex create_transcendental_sum_type_C_and_set_gammas (const GiNaC::ex &nn, const GiNaC::ex &i, const GiNaC::ex &l, const GiNaC::ex &v, const GiNaC::ex &ss, const GiNaC::ex &eps, int o, int f)
 
GiNaC::ex create_transcendental_sum_type_D_and_set_gammas (const GiNaC::ex &nn, const GiNaC::ex &i, const GiNaC::ex &l, const GiNaC::ex &lr, const GiNaC::ex &v, const GiNaC::ex &vr, const GiNaC::ex &ss, const GiNaC::ex &ssr, const GiNaC::ex &eps, int o, int f)
 

Detailed Description

The class list_of_tgamma is a container for the class ratio_of_tgamma.

The definition is

\[ \frac{\Gamma(1+d_1\varepsilon)}{\Gamma(1+b_1\varepsilon)} \frac{\Gamma(1+d_2\varepsilon)}{\Gamma(1+b_2\varepsilon)} ... \frac{\Gamma(1+d_k\varepsilon)}{\Gamma(1+b_k\varepsilon)} \]

\[ \frac{\Gamma(i+a_1+b_1\varepsilon)}{\Gamma(i+c_1+d_1\varepsilon)} \frac{\Gamma(i+a_2+b_2\varepsilon)}{\Gamma(i+c_2+d_2\varepsilon)} ... \frac{\Gamma(i+a_k+b_k\varepsilon)}{\Gamma(i+c_k+d_k\varepsilon)} \]

Member Function Documentation

◆ concat()

ex concat ( const GiNaC::ex & l) const

Concats two list_of_tgammas.

◆ eval()

ex eval ( ) const
override

If the index is an integer, the object is evaluated explicitly.

◆ eval_explicit()

ex eval_explicit ( ) const
virtual

Explicit evaluation. The job is delegated to the function nestedsums_helper_expand_lst_tgamma_fct.

◆ eval_ncmul()

ex eval_ncmul ( const GiNaC::exvector & v) const
overrideprotected

If two list_of_tgammas have the same index, they can be merged together.

If the difference between the two indices is an integer, we can merge them according to

\[ \frac{\Gamma(1+d_1\varepsilon)}{\Gamma(1+b_1\varepsilon)} \frac{\Gamma(1+d_2\varepsilon)}{\Gamma(1+b_2\varepsilon)} \frac{\Gamma((i+l)+a_1+b_1 \varepsilon)}{\Gamma((i+l)+c_1+d_1 \varepsilon)} \frac{\Gamma(i+a_2+b_2 \varepsilon)}{\Gamma(i+c_2+d_2 \varepsilon)} \]

\[ = \frac{\Gamma(1+d_1\varepsilon)}{\Gamma(1+b_1\varepsilon)} \frac{\Gamma(1+d_2\varepsilon)}{\Gamma(1+b_2\varepsilon)} \frac{\Gamma(i+(a_1+l)+b_1 \varepsilon)}{\Gamma(i+(c_1+l)+d_1 \varepsilon)} \frac{\Gamma(i+a_2+b_2 \varepsilon)}{\Gamma(i+c_2+d_2 \varepsilon)} \]

where $ l > 0 $. Note that the algorithm returns a product, where both factors have the "smaller" index.

◆ expansion_alert()

int expansion_alert ( void ) const

Returns $> 0$ if $a_j$ or $c_j$ are not integers, and 0 otherwise.

◆ get_depth()

unsigned get_depth ( void ) const
inline

Returns the depth.

◆ get_index()

GiNaC::ex get_index ( void ) const
inline

Returns the upper summation limit.

◆ get_key()

unsigned get_key ( void ) const
virtual

Returns the hash key to be used in connection with the class hash_entry.

◆ hash_data()

ex hash_data ( void ) const
virtual

Returns an expression which allows a comparison up to equivalence with an entry in a hash map.

In this case the comparison is exact and the method returns *this.

◆ index_eq_one()

ex index_eq_one ( void ) const

Returns

\[ \frac{\Gamma(1+d_1\varepsilon)}{\Gamma(1+b_1\varepsilon)} ... \frac{\Gamma(1+d_k\varepsilon)}{\Gamma(1+b_k\varepsilon)} \frac{\Gamma(a_1+1+b_1 \varepsilon)}{\Gamma(c_1+1+d_1 \varepsilon)} ... \frac{\Gamma(a_k+1+b_k \varepsilon)}{\Gamma(c_k+1+d_k \varepsilon)} \]

◆ pole_alert()

int pole_alert ( void ) const

Returns $> 0$ if $a_j \le 0 $, and 0 otherwise.

◆ set_expansion()

ex set_expansion ( void ) const

Sets the flag expansion_required for ratio_of_tgamma. The object is then automatically expanded up to the order specified in the member variable order.

This function should be called after all possible poles have been taken care of, e.g. all $a_1$ in the numerator are non-negative.

The result is in expanded form.

◆ set_expansion_parameter()

ex set_expansion_parameter ( const GiNaC::ex & new_eps) const

Sets the member variable expansion_parameter to new_eps.

◆ set_index()

ex set_index ( const GiNaC::ex & new_index) const

Sets the member variable index to new_index.

◆ set_order()

ex set_order ( int new_order) const

Sets the member variable order to new_order.

◆ shift_index()

ex shift_index ( const GiNaC::ex & new_index) const

Returns a list_of_tgamma with

\[ \Gamma(i + a + o + b \varepsilon ) \]

with $ o = j-i$, where $i$ is the new index and $j$ is the old index.

◆ shift_minus_one()

ex shift_minus_one ( void ) const

Returns

\[ \frac{\Gamma(1+d_1\varepsilon)}{\Gamma(1+b_1\varepsilon)} ... \frac{\Gamma(1+d_k\varepsilon)}{\Gamma(1+b_k\varepsilon)} \frac{\Gamma(i+a_1-1+b_1 \varepsilon)}{\Gamma(i+c_1-1+d_1 \varepsilon)} ... \frac{\Gamma(i+a_k-1+b_k \varepsilon)}{\Gamma(i+c_k-1+d_k \varepsilon)} \]

The order parameter is not changed.

◆ shift_plus_one()

ex shift_plus_one ( void ) const

Returns

\[ \frac{\Gamma(1+d_1\varepsilon)}{\Gamma(1+b_1\varepsilon)} ... \frac{\Gamma(1+d_k\varepsilon)}{\Gamma(1+b_k\varepsilon)} \frac{\Gamma(i+a_1+1+b_1 \varepsilon)}{\Gamma(i+c_1+1+d_1 \varepsilon)} ... \frac{\Gamma(i+a_k+1+b_k \varepsilon)}{\Gamma(i+c_k+1+d_k \varepsilon)} \]

The order parameter is not changed.

◆ subst_data()

ex subst_data ( void ) const
virtual

Returns the data which has to be substitued if the comparison with a hash entry is only up to equivalence.

In this case, the comparison is exact, and no data needs to be substituted.

Friends And Related Symbol Documentation

◆ create_transcendental_sum_type_A_and_set_gammas

GiNaC::ex create_transcendental_sum_type_A_and_set_gammas ( const GiNaC::ex & nn,
const GiNaC::ex & i,
const GiNaC::ex & l,
const GiNaC::ex & v,
const GiNaC::ex & ss,
const GiNaC::ex & eps,
int o,
int f )
friend

Named ctor on the heap.

◆ create_transcendental_sum_type_B_and_set_gammas

GiNaC::ex create_transcendental_sum_type_B_and_set_gammas ( const GiNaC::ex & nn,
const GiNaC::ex & i,
const GiNaC::ex & l,
const GiNaC::ex & lr,
const GiNaC::ex & v,
const GiNaC::ex & vr,
const GiNaC::ex & ss,
const GiNaC::ex & ssr,
const GiNaC::ex & eps,
int o,
int f )
friend

Named ctor on the heap.

◆ create_transcendental_sum_type_C_and_set_gammas

GiNaC::ex create_transcendental_sum_type_C_and_set_gammas ( const GiNaC::ex & nn,
const GiNaC::ex & i,
const GiNaC::ex & l,
const GiNaC::ex & v,
const GiNaC::ex & ss,
const GiNaC::ex & eps,
int o,
int f )
friend

Named ctor on the heap.

◆ create_transcendental_sum_type_D_and_set_gammas

GiNaC::ex create_transcendental_sum_type_D_and_set_gammas ( const GiNaC::ex & nn,
const GiNaC::ex & i,
const GiNaC::ex & l,
const GiNaC::ex & lr,
const GiNaC::ex & v,
const GiNaC::ex & vr,
const GiNaC::ex & ss,
const GiNaC::ex & ssr,
const GiNaC::ex & eps,
int o,
int f )
friend

Named ctor on the heap.

The documentation for this class was generated from the following files:
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