Trac #32893: Features for palp, polytopes_db, polytopes_db_4d

`palp` is a standard package, but with modularization that does not mean
that everyone has it. In particular, '''sagemath-polyhedra''' (#32432)
will not ship it.

We add a feature test along the lines of the palp `spkg-configure.m4`
script and mark many doctests in `sage.geometry` as `# optional - palp`.

To help construct doctest examples without having to rely on `palp`, we
endow several classes with `_sage_input_` methods.

As a cosmetic change, nef-partitions now use a unicode symbol.
{{{
-            Nef-partition {0, 1, 3} U {2, 4, 5}
+            Nef-partition {0, 1, 3} ⊔ {2, 4, 5}
}}}

We also add feature tests for `polytopes_db`, `polytopes_db_4d`.

URL: https://trac.sagemath.org/32893
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe
Reviewer(s): Dima Pasechnik

src/sage/features/databases.py

@@ -7,7 +7,8 @@
 from . import StaticFile, PythonModule
 from sage.env import (
     CONWAY_POLYNOMIALS_DATA_DIR,
-    CREMONA_MINI_DATA_DIR, CREMONA_LARGE_DATA_DIR)
+    CREMONA_MINI_DATA_DIR, CREMONA_LARGE_DATA_DIR,
+    POLYTOPE_DATA_DIR)
 
 
 class DatabaseConwayPolynomials(StaticFile):
@@ -127,8 +128,35 @@ def __init__(self):
         PythonModule.__init__(self, 'database_knotinfo', spkg='database_knotinfo')
 
 
+class DatabaseReflexivePolytopes(StaticFile):
+    r"""
+    A :class:`~sage.features.Feature` which describes the presence of the PALP database
+    of reflexive lattice polytopes.
+
+    EXAMPLES::
+
+        sage: from sage.features.databases import DatabaseReflexivePolytopes
+        sage: bool(DatabaseReflexivePolytopes().is_present())                              # optional - polytopes_db
+        True
+        sage: bool(DatabaseReflexivePolytopes('polytopes_db_4d', 'Hodge4d').is_present())  # optional - polytopes_db_4d
+        True
+    """
+    def __init__(self, name='polytopes_db', dirname='Full3D'):
+        """
+        TESTS::
+
+            sage: from sage.features.databases import DatabaseReflexivePolytopes
+            sage: isinstance(DatabaseReflexivePolytopes(), DatabaseReflexivePolytopes)
+            True
+        """
+        StaticFile.__init__(self, name, dirname,
+                            search_path=[POLYTOPE_DATA_DIR])
+
+
 def all_features():
     return [DatabaseConwayPolynomials(),
             DatabaseCremona(), DatabaseCremona('cremona_mini'),
             DatabaseJones(),
-            DatabaseKnotInfo()]
+            DatabaseKnotInfo(),
+            DatabaseReflexivePolytopes(),
+            DatabaseReflexivePolytopes('polytopes_db_4d', 'Hodge4d')]

src/sage/features/palp.py

@@ -0,0 +1,64 @@
+r"""
+Feature for testing the presence of ``palp``
+"""
+# ****************************************************************************
+#       Copyright (C) 2022 Matthias Koeppe
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
+
+from . import Executable
+from .join_feature import JoinFeature
+
+
+class PalpExecutable(Executable):
+    r"""
+    A :class:`~sage.features.Feature` describing the presence of a PALP executable.
+
+    INPUT:
+
+    - ``palpprog`` -- string, one of "poly", "class", "nef", "cws".
+
+    - ``suff`` -- string or ``None``.
+    """
+    def __init__(self, palpprog, suff=None):
+        r"""
+        TESTS::
+
+            sage: from sage.features.palp import PalpExecutable
+            sage: isinstance(PalpExecutable("poly", 5), PalpExecutable)
+            True
+        """
+        if suff:
+            Executable.__init__(self, f"palp_{palpprog}_{suff}d",
+                                executable=f"{palpprog}-{suff}d.x",
+                                spkg="palp")
+        else:
+            Executable.__init__(self, f"palp_{palpprog}",
+                                executable=f"{palpprog}.x",
+                                spkg="palp")
+
+class Palp(JoinFeature):
+    r"""
+    A :class:`~sage.features.Feature` describing the presence of ``PALP``.
+    """
+    def __init__(self):
+        r"""
+        TESTS::
+
+            sage: from sage.features.palp import Palp
+            sage: isinstance(Palp(), Palp)
+            True
+        """
+        JoinFeature.__init__(self, "palp",
+                             [PalpExecutable(palpprog, suff)
+                              for palpprog in ("poly", "class", "nef", "cws")
+                              for suff in (None, 4, 5, 6, 11)],
+                             description="PALP")
+
+def all_features():
+    return [Palp()]

src/sage/geometry/cone.py

@@ -2745,17 +2745,16 @@ def faces(self, dim=None, codim=None):
         We also ensure that a call to this function does not break
         :meth:`facets` method (see :trac:`9780`)::
 
-            sage: cone = toric_varieties.dP8().fan().generating_cone(0)
-            sage: cone
+            sage: cone = toric_varieties.dP8().fan().generating_cone(0); cone   # optional - palp
             2-d cone of Rational polyhedral fan in 2-d lattice N
-            sage: for f in cone.facets(): print(f.rays())
+            sage: for f in cone.facets(): print(f.rays())                       # optional - palp
             N(1, 1)
             in 2-d lattice N
             N(0, 1)
             in 2-d lattice N
-            sage: len(cone.faces())
+            sage: len(cone.faces())                                             # optional - palp
             3
-            sage: for f in cone.facets(): print(f.rays())
+            sage: for f in cone.facets(): print(f.rays())                       # optional - palp
             N(1, 1)
             in 2-d lattice N
             N(0, 1)