Nestedsums library
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The class transcendental_sum_type_B may contain
#include <transcendental_B.h>
Public Member Functions | |
transcendental_sum_type_B (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) | |
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 |
GiNaC::ex | set_expansion (void) const |
GiNaC::ex | distribute_over_subsum (void) const |
GiNaC::ex | distribute_over_letter (void) const |
GiNaC::ex | distribute_over_subsum_rev (void) const |
GiNaC::ex | distribute_over_letter_rev (void) const |
GiNaC::ex | shift_plus_one (void) const |
GiNaC::ex | shift_plus_one_rev (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 |
The class transcendental_sum_type_B may contain
The definition is
Here,
Note that the upper summation limit is
ex distribute_over_letter | ( | void | ) | const |
letter is allowed to contain a sum of products (e.g. an expression in expanded form). Each term can contain scalars and basic_letters.
This routine converts the transcendental_sum_type_B to a canonical form, so that afterwards letter only contains a basic_letter.
ex distribute_over_letter_rev | ( | void | ) | const |
letter_rev is allowed to contain a sum of products (e.g. an expression in expanded form). Each term can contain scalars and basic_letters.
This routine converts the transcendental_sum_type_B to a canonical form, so that afterwards letter_rev only contains a basic_letter.
ex distribute_over_subsum | ( | void | ) | const |
subsum is allowed to contain a sum of products (e.g. an expression in expanded form). Each term can contain scalars, basic_letters, list_of_tgammas, Zsums or Ssums.
This routine converts the transcendental_sum_type_B to a canonical form, so that afterwards subsum only contains a Zsum.
The algorithm is based on the following steps:
ex distribute_over_subsum_rev | ( | void | ) | const |
subsum_rev is allowed to contain a sum of products (e.g. an expression in expanded form). Each term can contain scalars, basic_letters, list_of_tgammas, Zsums or Ssums.
This routine converts the transcendental_sum_type_B to a canonical form, so that afterwards subsum_rev only contains a Zsum.
The algorithm is based on the following steps:
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override |
Simplifications, which are always performed are:
If flag_expand_status == expand_status::expansion_required, the evaluation routine performs a set of consistency checks:
If one of the tests fails, the object is put into a zombie state.
If flag_expand_status == expand_status::check_for_poles, it assures that the Gamma functions in the numerator do not give rise to poles. The functions shift_plus_one() and shift_plus_one_rev() are used.
If flag_expand_status == expand_status::expand_gamma_functions, the Gamma functions are expanded into Euler Zagier sums. This is done by setting the expansion_required flag in the ratio_of_tgamma class.
If flag_expand_status == expand_status::do_partial_fractioning, the sum is of the form
For
For
For
For
For
If flag_expand_status == expand_status::do_outermost_sum, the sum is of the form
If the depth of
Otherwise we have the recursion
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virtual |
Explicit evaluation
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overrideprotected |
No automatic simplifications
ex set_expansion | ( | void | ) | const |
Sets the flag flag_expand_status to expand_status::expansion_required. The object is then automatically expanded up to the order specified in the member variable order.
ex shift_plus_one | ( | void | ) | const |
This routine performs the substitution index -> index - 1. The formula used is
This routine is called from eval/expansion_required, and eval/check_for_poles.
ex shift_plus_one_rev | ( | void | ) | const |
This routine takes out the term at index = n - 1. The formula used is
This routine is called from eval/expansion_required, and eval/check_for_poles.