ENH: desmos [3d]: Support complex exponents; with i and/or a complex() function
Test equations for geogebra:
equation -- what I think it looks like
xi^2 -- Integer coordinate grid
e^xπi -- Unit circle with another little circle also about the origin (0,0)
e^(πi^x) -- crash / not responding: a(x)=e^(πi^(x))
though it seems to work with x in Z+
e**(x*pi*I)
e^(x π i^π) -- somewhat scale-invariant interposed spirals around a single point attractor. (Zoom in/out)
Only SageMath preprocesses Python to replace XOR (^) with exp() or **, so:
f(x) = x^2
g(x) = x**2 # Python
h(x) = exp(x, 2)
x**2 # SymPy Gamma, Beta
x**math.pi # Python: 3.141592653589793
x**pi # SymPy: π
x**1j # Python
x**I # SymPy
x**(1+I) # BUG/ENH: Plot complex expressions with SymPy
import sympy as sy
display(sy.E, sy.I, sy.pi)
from sympy import E, pi, I
x,y = sy.symbols('x,y', real=True); display(x,y)
eq01 = sy.Eq(y, E**(x*pi*I)); display(eq01)
eq02 = sy.Rel(y, E**(x*pi*I), '=='); display(eq02)
func01 = sy.Function('f')(E**(x*pi*I)); display(func01)
func02 = sy.Function('f')(eq02.rhs); display(func02)
assert eq01 == eq01
assert func01 == func02
import unittest
test = unittest.TestCase()
test.assertEqual(eq01, eq02)
test.assertEqual(func01, func02)
Sympy Gamma:
https://gamma.sympy.org/Sympy Beta is SymPy Gamma compiled to WASM: https://github.com/eagleoflqj/sympy_beta
What methods for visualizing complex coordinate(s) are helpful?
You can map the complex coordinate into e.g. the z-axis; or is complex phase - as is necessary to model [qubit] wave functions psi - just another high-dimensional dimension to also visualize?