refactor(api): consistent naming for spherical + hyper-ideal helpers (A1–A3)

Standardize the low-level free-function API on <verb>_<geom>_<rest>,
matching the already-consistent setup_<geom>_maps. Old names kept as
[[deprecated]] inline aliases for one release; all internal call sites
migrated.

Renames:
  assign_vertex_dof_indices      -> assign_spherical_vertex_dof_indices
  assign_all_spherical_dof_indices -> assign_spherical_all_dof_indices
  assign_all_dof_indices         -> assign_hyper_ideal_all_dof_indices
  compute_lambda0_from_mesh      -> compute_spherical_lambda0_from_mesh
  gradient_check                 -> gradient_check_hyper_ideal

A4/A5 (public CGAL API) intentionally deferred pending the license/
provenance decision (see CGAL submission audit G0/G1).

Verified: 277/277 CGAL tests pass, no deprecation warnings.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

code/tests/cgal/test_hyper_ideal_functional.cpp

@@ -41,10 +41,10 @@ static std::vector<double> make_x_all_variable(
     ConformalMesh& mesh, HyperIdealMaps& maps,
     double b_val, double a_val)
 {
-    int n = assign_all_dof_indices(mesh, maps);
+    int n = assign_hyper_ideal_all_dof_indices(mesh, maps);
     std::vector<double> x(static_cast<std::size_t>(n));
 
-    // Vertices first, then edges (matching assign_all_dof_indices order)
+    // Vertices first, then edges (matching assign_hyper_ideal_all_dof_indices order)
     for (auto v : mesh.vertices())
         x[static_cast<std::size_t>(maps.v_idx[v])] = b_val;
     for (auto e : mesh.edges())
@@ -62,7 +62,7 @@ TEST(HyperIdealFunctional, HessianSymmetryCheck)
     // Hessian is now implemented (numerical FD).  Verify it is symmetric.
     auto mesh = make_triangle();
     auto maps = setup_hyper_ideal_maps(mesh);
-    int n = assign_all_dof_indices(mesh, maps);
+    int n = assign_hyper_ideal_all_dof_indices(mesh, maps);
 
     std::vector<double> x(static_cast<std::size_t>(n), 0.5);
     auto H = hyper_ideal_hessian_sym(mesh, x, maps);
@@ -86,7 +86,7 @@ TEST(HyperIdealFunctional, GradientCheck_AllHyperIdealTriangle)
     auto maps = setup_hyper_ideal_maps(mesh);
     auto x    = make_x_all_variable(mesh, maps, /*b=*/1.0, /*a=*/0.5);
 
-    EXPECT_TRUE(gradient_check(mesh, x, maps))
+    EXPECT_TRUE(gradient_check_hyper_ideal(mesh, x, maps))
         << "Finite-difference gradient check failed on all-hyper-ideal triangle";
 }
 
@@ -103,7 +103,7 @@ TEST(HyperIdealFunctional, GradientCheck_ExtendedDomain)
     auto maps = setup_hyper_ideal_maps(mesh);
     auto x    = make_x_all_variable(mesh, maps, /*b=*/2.0, /*a=*/1.5);
 
-    EXPECT_TRUE(gradient_check(mesh, x, maps))
+    EXPECT_TRUE(gradient_check_hyper_ideal(mesh, x, maps))
         << "Finite-difference gradient check failed in extended domain";
 }
 
@@ -120,7 +120,7 @@ TEST(HyperIdealFunctional, GradientCheck_TetrahedronAllVariable)
     auto maps = setup_hyper_ideal_maps(mesh);
     auto x    = make_x_all_variable(mesh, maps, /*b=*/1.0, /*a=*/0.5);
 
-    EXPECT_TRUE(gradient_check(mesh, x, maps))
+    EXPECT_TRUE(gradient_check_hyper_ideal(mesh, x, maps))
         << "Finite-difference gradient check failed on all-variable tetrahedron";
 }
 
@@ -136,7 +136,7 @@ TEST(HyperIdealFunctional, EnergyFiniteAtTestPoint)
 {
     auto mesh = make_quad_strip();
     auto maps = setup_hyper_ideal_maps(mesh);
-    int  n    = assign_all_dof_indices(mesh, maps);
+    int  n    = assign_hyper_ideal_all_dof_indices(mesh, maps);
 
     // Values taken from the Java testFunctionalAtNaNValue spirit:
     // large-ish but positive DOF values that could expose degenerate paths.
@@ -177,7 +177,7 @@ TEST(HyperIdealFunctional, GradientCheck_MixedIdealHyperIdeal)
     // DOF vector: [b1, b2, a_e0, a_e1, a_e2]
     std::vector<double> x = {1.0, 1.0, 0.5, 0.5, 0.5};
 
-    EXPECT_TRUE(gradient_check(mesh, x, maps))
+    EXPECT_TRUE(gradient_check_hyper_ideal(mesh, x, maps))
         << "Finite-difference gradient check failed for mixed ideal / hyper-ideal";
 }
 
@@ -194,7 +194,7 @@ TEST(HyperIdealFunctional, GradientCheck_Fan6AllVariable)
     auto maps = setup_hyper_ideal_maps(mesh);
     auto x    = make_x_all_variable(mesh, maps, /*b=*/1.0, /*a=*/0.5);
 
-    EXPECT_TRUE(gradient_check(mesh, x, maps))
+    EXPECT_TRUE(gradient_check_hyper_ideal(mesh, x, maps))
         << "Finite-difference gradient check failed on fan-6 mesh";
 }