Refactor and document operators and periods in sage module (#21)

---------

Co-authored-by: Julian Piribauer <julian.piribauer@gmail.com>
Reviewed-on: #21

tests/test_period_computation.py

@@ -2,94 +2,7 @@ import os
 
 from sage.all import *  # noqa: F401
 
-load(os.path.join(os.path.dirname(__file__), "..", "sage", "period.sage"))
-
-
-def test_apply_operator_univariate():
-    # theta^2 - z applied to log(z) should give -z*log(z), since theta(log z) = 1
-    # and theta^2(log z) = theta(1) = 0.
-    period = Period(no_variables=1, coefficients={(1,): {(0,): 1}}, order=5)
-    op = PFOperator("theta0^2 - z0", no_variables=1)
-
-    result = period.apply_operator(op)
-
-    assert result.coefficients == {(1,): {(1,): -1}}
-
-
-def test_apply_operator_mixes_variables():
-    # z0*theta1 applied to z0*log(z1): theta1 strips log(z1) down to a bare 1
-    # (leaving z0 untouched), then multiplying by z0 gives z0^2.
-    period = Period(no_variables=2, coefficients={(0, 1): {(1, 0): 1}}, order=5)
-    op = PFOperator("z0*theta1", no_variables=2)
-
-    result = period.apply_operator(op)
-
-    assert result.coefficients == {(0, 0): {(2, 0): 1}}
-
-
-def test_apply_operator_truncates_to_order():
-    # Multiplying by z0^2 pushes some terms above the period's order, so they
-    # should be dropped rather than kept with a nonzero coefficient.
-    period = Period(no_variables=1, coefficients={(0,): {(0,): 1, (1,): 1, (2,): 1}}, order=2)
-    op = PFOperator("z0^2", no_variables=1)
-
-    result = period.apply_operator(op)
-
-    assert result.coefficients == {(0,): {(2,): 1}}
-    assert result.order == 2
-
-
-def test_find_annihilating_operators_recovers_theta_squared():
-    # theta0^2 annihilates log(z0): theta0(log z0) = 1, theta0^2(log z0) = theta0(1) = 0.
-    # Among degree-(0, 2) Ansatze this should be the only solution, up to scaling.
-    period = Period(no_variables=1, coefficients={(1,): {(0,): 1}}, order=5)
-
-    ops = period.find_annihilating_operators(z_degree=0, theta_degree=2)
-
-    # A one-dimensional solution space means exactly one basis operator.
-    assert len(ops) == 1
-    assert period.apply_operator(ops[0]).coefficients == {}
-    assert str(ops[0].operator) == "theta0^2"
-
-
-def test_find_annihilating_operators_recovers_geometric_series_operator():
-    # sum_{k=0}^{4} z0^k is annihilated (up to truncation order) by
-    # (1 - z0)*theta0 - z0, i.e. theta0 - z0*theta0 - z0.
-    period = Period(
-        no_variables=1,
-        coefficients={(0,): {(0,): 1, (1,): 1, (2,): 1, (3,): 1, (4,): 1}},
-        order=4,
-    )
-
-    ops = period.find_annihilating_operators(z_degree=1, theta_degree=1)
-
-    assert len(ops) == 1
-    assert period.apply_operator(ops[0]).coefficients == {}
-
-
-def test_find_annihilating_operators_returns_empty_list_when_no_solution_exists():
-    # No degree-0 (constant) operator other than the zero operator can annihilate a
-    # nonzero constant period, so the linear system's only solution is trivial.
-    period = Period(no_variables=1, coefficients={(0,): {(0,): 1}}, order=0)
-
-    ops = period.find_annihilating_operators(z_degree=0, theta_degree=0)
-
-    assert ops == []
-
-
-def test_simplify_factorises_theta_polynomial_per_z_monomial():
-    # theta0^4 - 5*z0*(5*theta0+1)*(5*theta0+2)*(5*theta0+3)*(5*theta0+4), expanded, is the
-    # quintic's Picard-Fuchs operator. simplify() should recover the factorised form: the
-    # z0^0 part (theta0^4) has no theta-factor to pull out, while the z0^1 part factorises
-    # into the four linear pieces.
-    expanded = "theta0^4 - 3125*z0*theta0^4 - 6250*z0*theta0^3 - 4375*z0*theta0^2 - 1250*z0*theta0 - 120*z0"
-    op = PFOperator(expanded, no_variables=1)
-
-    simplified = op.simplify()
-
-    # The underlying (expanded) operator is unchanged - only the display string differs.
-    assert simplified.operator == op.operator
-    assert simplified.operator_string == "-5*(5*theta0 + 4)*(5*theta0 + 3)*(5*theta0 + 2)*(5*theta0 + 1)*z0 + theta0^4"
+load(os.path.join(os.path.dirname(__file__), "..", "sage", "periods.sage"))
 
 
 def test_find_power_series_solution_recovers_quintic_period():
@@ -190,14 +103,3 @@ def test_single_operator_recovers_itself_from_its_holomorphic_period():
     assert ratio != 0
     assert recovered[0].operator == ratio * L.operator
 
-
-def test_change_coordinates_handles_non_monomial_denominator():
-    op = PFOperator("theta0^2 - z0", no_variables=1)
-
-    result = op.change_coordinates("z0/(1-z0)")
-
-    expected = PFOperator(
-        "(1+z0)^3*theta0^2 + z0*(1+z0)^2*theta0 - z0",
-        no_variables=1,
-    )
-    assert result.operator == expected.operator