Certify symmetries, realizations, and completions of integral lines¶
Continuously checked
This is the exact source run by make test-examples and the ordinary Python test gate.
Domains: linalg
Source: examples/29_integral_line_configurations.py
# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Certify symmetries, realizations, and completions of integral lines."""
from noether.linalg import IntegralLineConfiguration
def main() -> None:
axes = IntegralLineConfiguration(2, [[1, 0], [0, 1]])
symmetries = axes.automorphism_group()
symmetries.verify()
assert symmetries.order == 8
a2_lines = IntegralLineConfiguration(2, [[1, 0], [0, 1], [1, -1]])
realization = a2_lines.realize_minimum(max_iterations=20)
realization.verify()
assert realization.status == "realized"
assert realization.realization is not None
completion = axes.complete_minimum(max_iterations=20)
completion.verify()
assert completion.status == "completed"
assert completion.realization is not None
print(
"integral lines:",
f"axis symmetry order={symmetries.order}",
f"A2 Gram matrix={realization.realization.gram_matrix}",
f"axis completion={completion.realization.configuration.vectors}",
)
if __name__ == "__main__":
main()