Calculate trace and norm in a concrete quadratic finite field¶
Continuously checked
This is the exact source run by make test-examples and the ordinary Python test gate.
Domains: numthy
Source: examples/08_finite_field_extensions.py
# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Calculate trace and norm in a concrete quadratic finite field."""
from noether.numthy import FiniteField
def main() -> None:
field = FiniteField.extension(5, 2)
generator = field.generator()
assert generator**2 + field(4) * generator + field(2) == field.zero()
assert generator.trace() == field(1)
assert generator.norm() == field(2)
print(f"{field}: Tr(a)={generator.trace()}, Nm(a)={generator.norm()}")
if __name__ == "__main__":
main()