Internals of verified computations ================================== Naming ------ The names of methods containing ``check`` will raise an exception if the desired property cannot be certified. There are different types of Exceptions to indicate how the certification failed. This type can be used by other methods to perform some action such as changing the triangulation or increasing precision or to give up. The user-facing methods have names starting with ``verify`` or ``verified`` and will fail more gracefully returning ``False`` or ``None`` in such a case. Generating certified shape intervals ------------------------------------ The recommended way to obtain certified intervals for the shapes is via ``manifold.tetrahedra_shapes(intervals=True)`` as :doc:`described earlier `. Here we document the ``KrawczykShapesEngine`` and ``IntervalNewtonShapesEngine`` which is implemented internally to generate the intervals. It is of interest for those users who want to understand the underlying interval math and experiment with the Newton interval method or the Krawczyk test. ``CertifiedShapesEngine`` is an alias of either ``KrawczykShapesEngine`` or ``IntervalNewtonShapesEngine`` to determine the default method used by verify. .. automodule:: snappy.verify .. autoclass:: CertifiedShapesEngine :members: :inherited-members: .. autoclass:: IntervalNewtonShapesEngine :members: :inherited-members: .. autoclass:: KrawczykShapesEngine :members: :inherited-members: Verification of hyperbolicity ----------------------------- Methods containing ``check`` will raise an exception if the desired property cannot be certified. Methods containing ``verify`` or ``verified`` will fail more gracefully returning ``False`` or ``None`` in such a case. .. autofunction:: snappy.verify.verifyHyperbolicity.check_logarithmic_gluing_equations_and_positively_oriented_tets Cusp cross sections ------------------- .. autoclass:: snappy.verify.RealCuspCrossSection :members: :inherited-members: .. autoclass:: snappy.verify.ComplexCuspCrossSection :members: :inherited-members: Verified canonical cell decompositions -------------------------------------- .. autofunction:: snappy.verify.verifyCanonical.interval_checked_canonical_triangulation .. autofunction:: snappy.verify.verifyCanonical.exactly_checked_canonical_retriangulation Exact computations for cusp cross sections ------------------------------------------ .. automodule:: snappy.verify.squareExtensions .. autofunction:: snappy.verify.squareExtensions.find_shapes_as_complex_sqrt_lin_combinations .. autoclass:: SqrtLinCombination :members: .. autoclass:: ComplexSqrtLinCombination :members: Exceptions ---------- .. automodule:: snappy.verify.exceptions :members: