CompositionAlgebra
CompositionAlgebra<
T,R> =object
Defined in: evidence.ts:82
Composition algebra evidence for T over the scalar field R — an algebra
equipped with a multiplicative quadratic norm: N(a · b) = N(a) · N(b).
By Hurwitz’s theorem the only such algebras over ℝ are ℝ, ℂ, ℍ and 𝕆. The octonions are non-associative, so they satisfy this but not DivisionRing’s associativity assumption.
Type Parameters
Section titled “Type Parameters”T
The carrier set of the algebra.
R
The scalar field the norm maps into.
Properties
Section titled “Properties”
readonlyone:T
Defined in: evidence.ts:84
readonlyzero:T
Defined in: evidence.ts:83
Methods
Section titled “Methods”add(
a,b):T
Defined in: evidence.ts:85
Parameters
Section titled “Parameters”T
T
Returns
Section titled “Returns”T
conjugate()
Section titled “conjugate()”conjugate(
a):T
Defined in: evidence.ts:89
Parameters
Section titled “Parameters”T
Returns
Section titled “Returns”T
mul(
a,b):T
Defined in: evidence.ts:88
Parameters
Section titled “Parameters”T
T
Returns
Section titled “Returns”T
neg(
a):T
Defined in: evidence.ts:87
Parameters
Section titled “Parameters”T
Returns
Section titled “Returns”T
norm()
Section titled “norm()”norm(
a):R
Defined in: evidence.ts:90
Parameters
Section titled “Parameters”T
Returns
Section titled “Returns”R
scale()
Section titled “scale()”scale(
a,scalar):T
Defined in: evidence.ts:91
Parameters
Section titled “Parameters”T
scalar
Section titled “scalar”R
Returns
Section titled “Returns”T
sub(
a,b):T
Defined in: evidence.ts:86
Parameters
Section titled “Parameters”T
T
Returns
Section titled “Returns”T