dedekind::numbers::DiscreteCos< N > Struct Template Reference

The exact discrete COSINE \(\cos_N(k) = \cos(2\pi k/N) = \Re\,\zeta_N^k\) over the Modular<N> angle — the EVEN part of the de Moivre character (= the \(\tfrac12(I+U)\) projection's real value). More...

Public Types
using	Domain = dedekind::morphologies::Modular<N>
using	Codomain = QuadraticReal<2>

Public Member Functions
constexpr QuadraticReal< 2 >	operator() (Domain k) const

Detailed Description

template<unsigned N>
struct dedekind::numbers::DiscreteCos< N >

The exact discrete COSINE \(\cos_N(k) = \cos(2\pi k/N) = \Re\,\zeta_N^k\) over the Modular<N> angle — the EVEN part of the de Moivre character (= the \(\tfrac12(I+U)\) projection's real value).

NOT a new trig table: it is literally Re of character<N>(1) resolved. An IsArrow Modular<N> → ℝ, EXACT where the character resolves (N=8, in ℚ(√2)). With DiscreteSin it gives Euler's formula exactly: \(\zeta_N^k = \cos_N(k) + i\,\sin_N(k)\).

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The documentation for this struct was generated from the following file:

• src/main/modules/dedekind/numbers/complex.cppm