Complex

Usage

import from Complex R

Parameter	Type	Description
R	ArithmeticType	Type to be extended

Description

Complex R implements the algebraic extension of R generated by a root of $X^2+1 = 0$. The coefficient type R must satisfy 2 additional mathematical properties for the arithmetic of Complex R to be correct, namely:

• $X^2 + 1$ is irreducible over R.
• The element $\alpha$ such that $\alpha^2 + 1 = 0$ must commute with all the elements of R (which is obviously satisfied when the multiplication of R is commutative).

Exports

ArithmeticType
CopyableType
LinearCombinationType R
coerce:	R $\to$ %	Natural embedding
complex:	(R, R) $\to$ %	create a complex
conjugate:	% $\to$ %	conjugation
conjugate!:	% $\to$ %	in-place conjugation
copy!:	(%, R, R) $\to$ %	in-place copy
imag:	% $\to$ R	imaginary part
real:	% $\to$ R	real part

if R has FloatType then

/:

(%, %) $\to$ %

Division

if R has InputType then

InputType

if R has OutputType then

OutputType

if R has SerializableType then

SerializableType