sage.knots, sage.groups.braid: Modularization fixes

Author: Matthias Koeppe

src/sage/groups/braid.py

@@ -80,7 +80,6 @@
 from sage.functions.generalized import sign
 from sage.groups.perm_gps.permgroup_named import SymmetricGroup
 from sage.groups.perm_gps.permgroup_named import SymmetricGroupElement
-from sage.knots.knot import Knot
 from sage.libs.gap.libgap import libgap
 from sage.matrix.constructor import identity_matrix, matrix
 from sage.misc.lazy_attribute import lazy_attribute
@@ -99,6 +98,7 @@
              'leastcommonmultiple', 'conjugatingbraid', 'ultrasummitset',
              'thurston_type', 'rigidity', 'sliding_circuits'],
             feature=PythonModule('sage.libs.braiding', spkg='libbraiding', type='standard'))
+lazy_import('sage.knots.knot', 'Knot')
 
 
 class Braid(FiniteTypeArtinGroupElement):

src/sage/knots/knotinfo.py

@@ -97,26 +97,26 @@
     <class 'sage.knots.link.Link'>
 
 If you have `SnapPy <https://snappy.math.uic.edu/index.html>`__ installed inside
-Sage you can obtain an instance of :class:`~spherogram.links.links_base.Link`,
+Sage, you can obtain an instance of :class:`~spherogram.links.links_base.Link`,
 too::
 
+    sage: # optional - snappy
     sage: L6 = KnotInfo.L6a1_0
-    sage: l6s = L6.link(snappy=True); l6s      # optional - snappy
+    sage: l6s = L6.link(snappy=True); l6s
     Plink failed to import tkinter.
     <Link: 2 comp; 6 cross>
-
-    sage: type(l6s)                            # optional - snappy
+    sage: type(l6s)
     <class 'spherogram.links.invariants.Link'>
     sage: l6  = L6.link()
-    sage: l6 == l6s.sage_link()                # optional - snappy
+    sage: l6 == l6s.sage_link()
     True
-    sage: L6.link(L6.items.name, snappy=True)  # optional - snappy
+    sage: L6.link(L6.items.name, snappy=True)
     <Link L6a1: 2 comp; 6 cross>
-    sage: l6sn = _                             # optional - snappy
-    sage: l6s == l6sn                          # optional - snappy
+    sage: l6sn = _
+    sage: l6s == l6sn
     False
-    sage: l6m = l6.mirror_image()              # optional - snappy
-    sage: l6sn.sage_link().is_isotopic(l6m)    # optional - snappy
+    sage: l6m = l6.mirror_image()
+    sage: l6sn.sage_link().is_isotopic(l6m)
     True
 
 But observe that the name conversion to SnapPy does not distinguish orientation
@@ -238,14 +238,16 @@
 
 from enum import Enum
 from sage.misc.cachefunc import cached_method
+from sage.misc.lazy_import import lazy_import
 from sage.misc.sage_eval import sage_eval
 from sage.structure.sage_object import SageObject
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.rings.integer_ring import ZZ
-from sage.groups.braid import BraidGroup
 from sage.knots.knot import Knots
 from sage.databases.knotinfo_db import KnotInfoColumns, db
 
+lazy_import('sage.groups.braid', 'BraidGroup')
+
 
 def eval_knotinfo(string, locals={}, to_tuple=True):
     r"""
@@ -694,8 +696,7 @@ def braid_length(self):
     @cached_method
     def braid(self):
         r"""
-        Return the braid notation of self as an instance of :class:`~sage.groups.braid.Braid`.
-
+        Return the braid notation of ``self`` as an instance of :class:`~sage.groups.braid.Braid`.
 
         EXAMPLES::