# ideas by u/DaVinci103
# MIT License, Copyright (c) 2024 Marvin Borner

:import std/Combinator .
:import std/Pair .
:import std/Number N
:import std/Math/Rational Q
:import std/Math/Real R

i (+0.0+1.0i)

# converts a balanced ternary number to a complex number
number→complex [[(R.number→real 1 0) : ((+0.0r) 0)]] ⧗ Number → Complex

:test (number→complex (+5)) ((+5.0+0.0i))

# returns real part of a complex number
real [[1 0 [[1]]]] ⧗ Complex → Real

:test (real (+5.0+2.0i)) ((+5.0r))

# returns imaginary part of a complex number
imag [[1 0 [[0]]]] ⧗ Complex → Real

:test (imag (+5.0+2.0i)) ((+2.0r))

# adds two complex numbers
add φ &[[&[[(Q.add 3 1) : (Q.add 2 0)]]]] ⧗ Complex → Complex → Complex

…+… add

# subtracts two complex numbers
sub φ &[[&[[(Q.sub 3 1) : (Q.sub 2 0)]]]] ⧗ Complex → Complex → Complex

…-… sub

# multiplies two complex numbers
mul φ &[[&[[p : q]]]] ⧗ Complex → Complex → Complex
	p Q.sub (Q.mul 3 1) (Q.mul 2 0)
	q Q.add (Q.mul 3 0) (Q.mul 2 1)

…⋅… mul

# divides two complex numbers
div φ &[[&[[p : q]]]] ⧗ Complex → Complex → Complex
	p Q.div (Q.add (Q.mul 3 1) (Q.mul 2 0)) (Q.add (Q.mul 1 1) (Q.mul 0 0))
	q Q.div (Q.sub (Q.mul 2 1) (Q.mul 3 0)) (Q.add (Q.mul 1 1) (Q.mul 0 0))

…/… div

# negates a complex number
negate b &[[(Q.negate 1) : (Q.negate 0)]] ⧗ Complex → Complex

-‣ negate

# inverts a complex number
invert b &[[p : q]] ⧗ Complex → Complex
	p Q.div 1 (Q.add (Q.mul 1 1) (Q.mul 0 0))
	q Q.div 0 (Q.add (Q.mul 1 1) (Q.mul 0 0))

~‣ invert

# ---

:import std/List L

# power function: complex^number
pow-n [L.nth-iterate (mul 0) (+1.0+0.0i)] ⧗ Complex → Number → Complex

exp [[L.nth-iterate &[[[[op]]]] start 0 [[[[1]]]] 0]] ⧗ Complex → Complex
	start [0 (+1.0+0.0i) (+1.0+0.0i) (+1.0+0.0i) (+1)]
	op [[[2 1 0 (4 + (1 / 0)) N.++3]] pow fac]
		pow 6 ⋅ 4
		fac 3 ⋅ (number→complex 1)

ln [[[p : q] (1 0)]] ⧗ Complex → Complex
	p R.ln (&[[R.hypot [2] [1]]] 0) 1
	q &[[\R.atan2 [2] [1]]] 0 1

# complex power function: complex^complex
pow [[exp (0 ⋅ (ln 1))]] ⧗ Complex → Complex → Complex

…**… pow