Nestedsums library
Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
root_of_unity Class Reference

#include <root_of_unity.h>

Inheritance diagram for root_of_unity:

Public Member Functions

 root_of_unity (unsigned l, unsigned k)
 
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
 

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

unsigned l
 
unsigned k
 

Detailed Description

A root of unity is defined by

\[ r_k^l = \exp \left( \frac{2 \pi i l}{k} \right) \]

Member Function Documentation

◆ eval()

ex eval ( ) const
override

The following simplifications are done:

  • If $l = 0$ return 1.
  • If $l > k$, the root of unity is reduced to $r_k^{l'}$, where $ l' = l \; \mbox{mod} \; k$.
  • If $\mbox{gcd}(l,k) \neq 1$ the gcd is divided out.

◆ eval_ncmul()

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

Multiplication is done according to

\[ r_{k_1}^{l_1} r_{k_2}^{l_2} = \exp \left( 2 \pi i \frac{k_2 l_1 + k_1 l_2}{k_1 k_2} \right) \]

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