30352: adding Gauss-code and symmetry type

build/pkgs/knotinfo/SPKG.rst

@@ -20,7 +20,7 @@ https://linkinfo.sitehost.iu.edu'
 
  * #30352: Initial version
 
- The tarbal has been created from the both download files at the
+ The tarball has been created from the both download files at the
  given date:
 
  `knotinfo_data_complete.xls`

build/pkgs/knotinfo/spkg-check.in

@@ -0,0 +1,7 @@
+cd $SAGE_ROOT/src/sage/
+
+echo "Testing databases/knotinfo_db.py"
+sage -t databases/knotinfo_db.py  || sdh_die "Error testing KnotInfo databases"
+
+echo "Testing knots/knotinfo.py"
+sage -t knots/knotinfo.py  || sdh_die "Error testing KnotInfo funcionality"

src/sage/databases/knotinfo_db.py

@@ -35,6 +35,23 @@
 from sage.env import SAGE_SHARE, SAGE_ROOT
 
 
+def is_knotinfo_available():
+    r"""
+    Return wether the KnotInfo databases are installed or not.
+
+    EXAMPLES::
+
+        sage: from sage.databases.knotinfo_db import is_knotinfo_available
+        sage: is_knotinfo_available()
+        True
+    """
+    ki_db = KnotInfoDataBase()
+    try:
+        ki_db.read_num_knots()
+        return True
+    except FileNotFoundError:
+        return False
+
 
 class KnotInfoColumnTypes(Enum):
     r"""
@@ -291,9 +308,6 @@ def __init__(self):
         self._knot_prefix  = 'K'
         self._import_path  = os.path.join(SAGE_SHARE, self._package)
 
-        from sage.misc.misc import sage_makedirs
-        sage_makedirs(self._import_path)
-
         self._knot_list = None
         self._link_list = None
 
@@ -303,7 +317,7 @@ def _create_csv_file(self, filename, path_for_src):
         Return the data fetched from the web-page as a csv file
         such that it can be parsed via pythons ``csv`` class.
 
-        INOUT:
+        INPUT:
 
         - ``filename`` - instance of :class:`KnotInfoDataBase.filename`
         - ``path_for_src`` - string giving the pathname where to store
@@ -365,7 +379,6 @@ def create_spkg_tarball(self, path_for_src=None):
         os.system('cd %s; tar -cvjSf %s/upstream/%s-%s.tar.bz2 src' %(path, SAGE_ROOT, self._package, self._version) )
 
 
-    @cached_method
     def version(self):
         r"""
         Return the current version.
@@ -439,6 +452,9 @@ def create_col_dict_sobj(self):
         link_list = self.link_list()
         link_column_names = link_list[0]
 
+        from sage.misc.misc import sage_makedirs
+        sage_makedirs(self._import_path)
+
         num_knots = len_knots - 1 
         save(num_knots, '%s/%s' %(self._import_path, self.filename.knots.sobj_num_knots()))
 

src/sage/knots/knotinfo.py

@@ -88,16 +88,6 @@ def eval_knotinfo(string, locals={}, to_tuple=True):
 
 
 
-class KnotInfoNotation(Enum):
-    r"""
-    """
-
-    braid = 'braid'
-    PD    = 'planar diagram'
-    DT    = 'Docker Thistlewait'
-    Gauss = 'Gauss code'
-
-
 class KnotInfoBase(Enum):
     r"""
     Enum class to select the knots and links provided by http://www.indiana.edu/~knotinfo
@@ -117,7 +107,7 @@ def items(self):
             sage: from sage.knots.knotinfo import KnotInfo
             sage: L = KnotInfo.L4a1_0
             sage: it = L.items
-            sage: [it.name for it in it if it.name.endswith('notation')]
+            sage: [i.name for i in it if i.name.endswith('notation')]
             ['dt_notation',
              'conway_notation',
              'two_bridge_notation',
@@ -498,6 +488,96 @@ def is_knot(self):
         """
         return self.num_components() == 1
 
+    @cached_method
+    def symmetry_type(self):
+        r"""
+        Return the symmetry type of ``self``.
+
+        From the KnotInfo description page:
+
+            If a knot is viewed as the oriented diffeomorphism
+            class of an oriented pair, `K = (S_3, S_1), with `S_i`
+            diffeomorphic to `S^i`, there are four oriented knots
+            associated to any particular knot `K`. In addition to
+            `K` itself, there is the reverse, `K^r = (S_3, -S_1)`,
+            the concordance inverse, `-K = (-S_3, -S_1)`, and the
+            mirror image, `K^m = (-S3, S1)`. A knot is called
+            reversible if `K = K^r`, negative amphicheiral if
+            `K = -K`, and positive amphicheiral if `K = K^m`.
+
+            A knot possessing any two of these types of symmetry
+            has all three. Thus, in the table, a knot is called
+            reversible if that is the only type of symmetry it has,
+            and likewise for negative amphicheiral. If it has none
+            of these types of symmetry it is called chiral, and if
+            it has all three it is called fully amphicheiral.
+
+            For prime knots with fewer than 12 crossings, all
+            amphicheiral knots are negative amphicheiral.
+
+        EXAMPLES::
+
+            sage: from sage.knots.knotinfo import KnotInfo
+            sage: [(L.name, L.symmetry_type()) for L in KnotInfo if L.is_knot() and L.crossing_number() < 6]
+            [('K0_1', 'fully amphicheiral'),
+            ('K3_1', 'reversible'),
+            ('K4_1', 'fully amphicheiral'),
+            ('K5_1', 'reversible'),
+            ('K5_2', 'reversible')]
+        """
+        if not self.is_knot():
+            raise NotImplementedError('This is only available for knots')
+        if not self[self.items.symmetry_type] and self.crossing_number() == 0:
+            return 'fully amphicheiral'
+        return self[self.items.symmetry_type]
+
+
+    def is_reversible(self):
+        r"""
+        Return wether ``self`` is reversible.
+
+        EXAMPLES::
+
+            sage: from sage.knots.knotinfo import KnotInfo
+            sage: KnotInfo.K6_3.is_reversible()
+            True
+        """
+        if self.symmetry_type() == 'reversible':
+            return True
+        if self.symmetry_type() == 'fully amphicheiral':
+            return True
+        return False
+
+    def is_amphicheiral(self, positive=False):
+        r"""
+        Return wether ``self`` is amphicheiral.
+
+        INPUT:
+
+        - ``positive`` -- Boolean (default False) wether to check
+          if ``self`` is positive or negative amphicheiral (see
+          doctest of :meth:`symmetry_type`)
+
+        EXAMPLES::
+
+            sage: from sage.knots.knotinfo import KnotInfo
+            sage: K = KnotInfo.K12a_427
+            sage: K.is_amphicheiral()
+            False
+            sage: K.is_amphicheiral(positive=True)
+            True
+        """
+        if positive:
+            if self.symmetry_type() == 'positive amphicheiral':
+                return True
+        else:
+            if self.symmetry_type() == 'negative amphicheiral':
+                return True
+        if self.symmetry_type() == 'fully amphicheiral':
+            return True
+        return False
+
+
     @cached_method
     def homfly_polynomial(self, var1='L', var2='M', original=False):
         r"""
@@ -611,7 +691,8 @@ def link(self, use_item=db.columns().pd_notation):
           that should be used to construct the link. Allowed values
           are:
           -- self.items.pd_notation
-          -- self.items.dt_notation (only for knots)
+          -- self.items.dt_notation    (only for knots)
+          -- self.items.gauss_notation (only for knots)
           -- self.items.braid_notation
 
         .. NOTE::
@@ -631,6 +712,11 @@ def link(self, use_item=db.columns().pd_notation):
             Therefore, we have to take the mirror_image of the
             link!
 
+            Furthermore, note that the mirror version may depend
+            on the used KnotInfo-notation. For example for the
+            knot `5_1` the Gauss- and the DT-notation refer to
+            the mirror image (see example below).
+
         EXAMPLES::
 
             sage: from sage.knots.knotinfo import KnotInfo
@@ -670,6 +756,14 @@ def link(self, use_item=db.columns().pd_notation):
             [[4, 1, 5, 2], [8, 5, 1, 6], [6, 4, 7, 3], [2, 8, 3, 7]]
             sage: K4_1.pd_notation()
             [[4, 2, 5, 1], [8, 6, 1, 5], [6, 3, 7, 4], [2, 7, 3, 8]]
+
+            sage: K5_1 = KnotInfo.K5_1
+            sage: K5_1.link().braid()
+            s^5
+            sage: K5_1.link(K5_1.items.dt_notation).braid()
+            s^-5
+            sage: K5_1.link(K5_1.items.gauss_notation).braid()
+            s^-5
         """
         if not isinstance(use_item, KnotInfoColumns):
             raise TypeError('%s must be an instance of %s' %(use_item, KnotInfoColumns))
@@ -688,6 +782,11 @@ def link(self, use_item=db.columns().pd_notation):
                 raise NotImplementedError('%s only implemented for knots' %use_item)
             from sage.knots.knot import Knots
             return Knots().from_dowker_code(self.dt_notation())
+        elif use_item == self.items.gauss_notation:
+            if not self.is_knot():
+                raise NotImplementedError('%s only implemented for knots' %use_item)
+            from sage.knots.knot import Knots
+            return Knots().from_gauss_code(self.gauss_notation())
         else:
             raise ValueError('Construction using %s not possible' %use_item)