Finding operators and simplifying them

tests/test_period_computation.py

@@ -46,3 +46,56 @@ def test_apply_operator_rejects_variable_count_mismatch():
 
     with pytest.raises(ValueError):
         period.apply_operator(op)
+
+
+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"