Certify a complete presentation of the mod-two cohomology of C2¶
Continuously checked
This is the exact source run by make test-examples and the ordinary Python test gate.
Domains: groups
Source: examples/34_finite_group_cohomology.py
# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Certify a complete presentation of the mod-two cohomology of C2."""
from noether.groups import Permutation, PermutationGroup
def main() -> None:
transposition = Permutation.from_images([1, 0])
cyclic_two = PermutationGroup.from_generators(2, [transposition])
truncation = cyclic_two.modular_cohomology(2, 2)
truncation.verify()
assert [truncation.dimension(degree) for degree in range(3)] == [1, 1, 1]
complete = truncation.algebra_truncation().certify_symonds_universal_bound()
complete.verify()
assert complete.completion_strategy == "symonds_universal_bound"
print(
f"H^0..2(C2; F2) dimensions="
f"{[truncation.dimension(degree) for degree in range(3)]}; "
f"completion={complete.completion_strategy}"
)
if __name__ == "__main__":
main()