Certify a familiar identity with real and complex balls¶
Continuously checked
This is the exact source run by make test-examples and the ordinary Python test gate.
Domains: root
Source: examples/02_ball_arithmetic.py
# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Certify a familiar identity with real and complex balls."""
from fractions import Fraction
from noether import ComplexBallField, RealBallField
def main() -> None:
reals = RealBallField(192)
one_third = reals(Fraction(1, 3))
assert (3 * one_third).overlaps(reals.one())
complexes = ComplexBallField(192)
imaginary_unit = complexes(0, 1)
assert (imaginary_unit**2).overlaps(complexes(-1))
assert (1 + imaginary_unit).overlaps(complexes(1, 1))
print(f"1/3 = {one_third}; i^2 = {imaginary_unit**2}")
if __name__ == "__main__":
main()