import math

from cosmosmesh_privacy_preserving_federated.catopt_bridge import (
    CatOptBridge,
    LocalProblem,
    SharedVariable,
    DualVariable,
)


def test_basic_roundtrip_encoding():
    # Build a tiny LocalProblem and signals
    lp = LocalProblem(
        problem_id="lp-task-01",
        objective="minimize_energy",
        variables=["x1", "x2"],
        constraints=["x1>=0", "x2>=0", "x1+x2<=10"],
        version=1,
    )

    sv1 = SharedVariable(name="sigma", value=0.5, version=1)
    dv1 = DualVariable(name="lambda", value=1.25, version=1)

    round_msg = CatOptBridge.build_round_trip(lp, [sv1], [dv1])

    # Basic invariants about the payload
    assert round_msg["kind"] == "RoundTrip"
    payload = round_msg["payload"]
    assert payload["object"]["id"] == lp.problem_id
    assert any(m.get("name") == sv1.name for m in payload["morphisms"])
    assert any(m.get("name") == dv1.name for m in payload["morphisms"])