Quantum.Synthesis.Ring

Rings

class Ring a

Rings with particular elements

Rings with ½

class HalfRing a

Rings with √2

class RootTwoRing a

Rings with 1/√2

class RootHalfRing a

Rings with i

class ComplexRing a

Rings with ω

class OmegaRing a

Rings with particular automorphisms

Rings with complex conjugation

class Adjoint a

Rings with √2-conjugation

class Adjoint2 a

Normed rings

class NormedRing r

Floor and ceiling

class Floor r

Particular rings

The ring ℤ₂ of integers modulo 2

data Z2

The ring D of dyadic fractions

decompose_dyadic

integer_of_dyadic

The ring ℚ of rational numbers

showsPrec_rational

The ring R[√2]

data RootTwo a

The ring ℤ[√2]

The ring D[√2]

The field ℚ[√2]

The ring R[i]

data Cplx a

The ring ℤ[i] of Gaussian integers

The ring D[i]

The ring ℚ[i] of Gaussian rationals

The ring D[√2, i]

The ring ℚ[√2, i]

The ring ℂ of complex numbers

The ring R[ω]

data Omega a

The ring ℤ[ω]

zroottwo_of_zomega

The ring D[ω]

The field ℚ[ω]

Conversion to dyadic

class ToDyadic a b

Real part

class RealPart a b

Rings of integers

class WholePart a b

Common denominators

class DenomExp a

denomexp_decompose

showsPrec_DenomExp

Conversion to ℚ[ω]

class ToQOmega a

Parity

class Parity a

Auxiliary functions