diff --git a/doc_src/verify_internals.rst b/doc_src/verify_internals.rst
index 149bc978..c32c38dc 100644
--- a/doc_src/verify_internals.rst
+++ b/doc_src/verify_internals.rst
@@ -64,9 +64,9 @@ Verified canonical cell decompositions
 Exact computations for cusp cross sections
 ------------------------------------------
 
-..   automodule:: snappy.verify.squareExtensions
+..   automodule:: snappy.verify.square_extensions
 
-..   autofunction:: snappy.verify.squareExtensions.find_shapes_as_complex_sqrt_lin_combinations
+..   autofunction:: snappy.verify.square_extensions.find_shapes_as_complex_sqrt_lin_combinations
 ..   autoclass:: SqrtLinCombination
      :members:
 ..   autoclass:: ComplexSqrtLinCombination
diff --git a/python/verify/realAlgebra.py b/python/verify/real_algebra.py
similarity index 100%
rename from python/verify/realAlgebra.py
rename to python/verify/real_algebra.py
diff --git a/python/verify/squareExtensions.py b/python/verify/square_extensions.py
similarity index 99%
rename from python/verify/squareExtensions.py
rename to python/verify/square_extensions.py
index 2b03e9d2..46e88696 100644
--- a/python/verify/squareExtensions.py
+++ b/python/verify/square_extensions.py
@@ -1,5 +1,5 @@
 """
-The squareExtensions module provides
+The square_extensions module provides
 two special classes to give exact representations of the values
 involved when computing a cusp cross section.
 
@@ -39,7 +39,7 @@
 
     from ..snap import find_field
 
-from .realAlgebra import field_containing_real_and_imaginary_part_of_number_field
+from .real_algebra import field_containing_real_and_imaginary_part_of_number_field
 
 
 def eval_number_field_elt(elt, root):
@@ -75,7 +75,7 @@ def eval_number_field_elt(elt, root):
 #    _field_containing_real_and_imaginary_part_of_algebraic_number_LLL.
 # This was still very slow and failed on t11669 and 9 manifolds with 9 tetrahedra.
 #
-# The fastest implementation so far is in realAlgebra. The implementation there
+# The fastest implementation so far is in real_algebra. The implementation there
 # turns the one complex equation p(z) = 0 defining the number field into two
 # real equations for the real and imaginary part of the complex equation and
 # then uses the resultant to find exact solutions.
diff --git a/python/verify/test.py b/python/verify/test.py
index 01091feb..7212ee12 100644
--- a/python/verify/test.py
+++ b/python/verify/test.py
@@ -70,8 +70,8 @@ def run_doctests(verbose=False, print_info=True):
             verify.maximal_cusp_area_matrix,
             verify.maximal_cusp_area_matrix.cusp_tiling_engine,
             verify.maximal_cusp_area_matrix.cusp_translate_engine,
-            verify.squareExtensions,
-            verify.realAlgebra ],
+            verify.square_extensions,
+            verify.real_algebra ],
         extraglobs=globs,
         verbose=verbose, print_info=print_info)
 
diff --git a/python/verify/verify_canonical.py b/python/verify/verify_canonical.py
index ea3cb573..e50d0857 100644
--- a/python/verify/verify_canonical.py
+++ b/python/verify/verify_canonical.py
@@ -3,7 +3,7 @@
 from ..geometric_structure.cusp_neighborhood.cusp_cross_section import RealCuspCrossSection
 from ..snap.t3mlite import simplex
 
-from .squareExtensions import find_shapes_as_complex_sqrt_lin_combinations
+from .square_extensions import find_shapes_as_complex_sqrt_lin_combinations
 from . import edge_equations
 from . import verifyHyperbolicity
 from . import exceptions