Merge branch 'u/chapoton/28461' in 8.9.b9

Author: fchapoton

src/sage/quivers/algebra.py

@@ -3,7 +3,7 @@
 """
 from __future__ import absolute_import
 
-#*****************************************************************************
+# ****************************************************************************
 #  Copyright (C) 2012 Jim Stark <[email protected]>
 #                2013 Simon King <[email protected]>
 #                2014 Simon King <[email protected]>
@@ -17,14 +17,15 @@
 #  See the GNU General Public License for more details; the full text
 #  is available at:
 #
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 import six
 from sage.misc.cachefunc import cached_method
 from sage.combinat.free_module import CombinatorialFreeModule
 from .algebra_elements import PathAlgebraElement
 
+
 class PathAlgebra(CombinatorialFreeModule):
     r"""
     Create the path algebra of a :class:`quiver <DiGraph>` over a given field.
@@ -50,9 +51,9 @@ class PathAlgebra(CombinatorialFreeModule):
 
     - the path algebra `kP` with the given monomial order
 
-    NOTE:
+    .. NOTE::
 
-    Monomial orders that are not degree orders are not supported.
+        Monomial orders that are not degree orders are not supported.
 
     EXAMPLES::
 
@@ -133,10 +134,11 @@ class PathAlgebra(CombinatorialFreeModule):
     #                                                                         #
     ###########################################################################
 
-    def __init__(self, k, P, order = "negdegrevlex"):
+    def __init__(self, k, P, order="negdegrevlex"):
         """
-        Creates a :class:`PathAlgebra` object.  Type ``PathAlgebra?`` for
-        more information.
+        Create a :class:`PathAlgebra` object.
+
+        Type ``PathAlgebra?`` for more information.
 
         INPUT:
 
@@ -166,10 +168,10 @@ def __init__(self, k, P, order = "negdegrevlex"):
         self._semigroup = P
         self._ordstr = order
         super(PathAlgebra, self).__init__(k, self._semigroup,
-                                             prefix='',
-                                             #element_class=self.Element,
-                                             category=GradedAlgebrasWithBasis(k),
-                                             bracket=False)
+                                          prefix='',
+                                          # element_class=self.Element,
+                                          category=GradedAlgebrasWithBasis(k),
+                                          bracket=False)
         self._assign_names(self._semigroup.variable_names())
 
     def order_string(self):
@@ -223,8 +225,8 @@ def arrows(self):
             sage: A.arrows()
             (a, b, c)
         """
-        return tuple(self._from_dict( {index: self.base_ring().one()},
-                                      remove_zeros=False )
+        return tuple(self._from_dict({index: self.base_ring().one()},
+                                     remove_zeros=False)
                      for index in self._semigroup.arrows())
 
     @cached_method
@@ -240,8 +242,8 @@ def idempotents(self):
             sage: A.idempotents()
             (e_1, e_2, e_3, e_4)
         """
-        return tuple(self._from_dict( {index: self.base_ring().one()},
-                                      remove_zeros=False )
+        return tuple(self._from_dict({index: self.base_ring().one()},
+                                     remove_zeros=False)
                      for index in self._semigroup.idempotents())
 
     @cached_method
@@ -264,8 +266,8 @@ def gen(self, i):
             sage: A.gen(5)
             b
         """
-        return self._from_dict( {self._semigroup.gen(i): self.base_ring().one()},
-                                remove_zeros = False )
+        return self._from_dict({self._semigroup.gen(i): self.base_ring().one()},
+                               remove_zeros=False)
 
     def ngens(self):
         """
@@ -445,7 +447,7 @@ def _repr_monomial(self, data):
         # gives the component in the module, and mid gives the length of the
         # left factor in a two-sided module.
         arrows = self.variable_names()
-        return '*'.join( [arrows[n] for n in data] )
+        return '*'.join(arrows[n] for n in data)
 
     def _latex_monomial(self, data):
         """
@@ -465,7 +467,7 @@ def _latex_monomial(self, data):
 
         """
         arrows = self.variable_names()
-        return '\\cdot '.join( [arrows[n] for n in data] )
+        return '\\cdot '.join(arrows[n] for n in data)
 
     @cached_method
     def one(self):
@@ -482,8 +484,8 @@ def one(self):
             e_1 + e_2 + e_3
         """
         one = self.base_ring().one()
-        D = dict((index,one) for index in self._semigroup.idempotents())
-        return self._from_dict( D )
+        D = {index: one for index in self._semigroup.idempotents()}
+        return self._from_dict(D)
 
     ###########################################################################
     #                                                                         #
@@ -563,19 +565,19 @@ def degree_on_basis(self, x):
 
     def sum(self, iter_of_elements):
         """
-        Returns the sum of all elements in ``iter_of_elements``
+        Return the sum of all elements in ``iter_of_elements``
 
         INPUT:
 
         - ``iter_of_elements``: iterator of elements of ``self``
 
-        NOTE:
+        .. NOTE::
 
-        It overrides a method inherited from
-        :class:`~sage.combinat.free_module.CombinatorialFreeModule`, which
-        relies on a private attribute of elements---an implementation
-        detail that is simply not available for
-        :class:`~sage.quivers.algebra_elements.PathAlgebraElement`.
+            It overrides a method inherited from
+            :class:`~sage.combinat.free_module.CombinatorialFreeModule`,
+            which relies on a private attribute of elements---an
+            implementation detail that is simply not available for
+            :class:`~sage.quivers.algebra_elements.PathAlgebraElement`.
 
         EXAMPLES::
 

src/sage/quivers/algebra_elements.pxd

@@ -1,14 +1,14 @@
 """
 Cython types for elements of path algebras
 """
-#*****************************************************************************
+# ****************************************************************************
 #     Copyright (C) 2015 Simon King <[email protected]>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  as published by the Free Software Foundation; either version 2 of
 #  the License, or (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 # This file declares the types. The implementation of the basic on these types
 # is in algebra_elements.pxi, the implementation of the Python class is in

src/sage/quivers/algebra_elements.pxi

@@ -7,14 +7,14 @@ AUTHORS:
 
 """
 
-#*****************************************************************************
+# ****************************************************************************
 #     Copyright (C) 2015 Simon King <[email protected]>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  as published by the Free Software Foundation; either version 2 of
 #  the License, or (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from cysignals.memory cimport check_malloc, check_allocarray, sig_free
 from cysignals.signals cimport sig_check, sig_on, sig_off

src/sage/quivers/algebra_elements.pyx

@@ -7,14 +7,14 @@ AUTHORS:
 
 """
 
-#*****************************************************************************
+# ****************************************************************************
 #     Copyright (C) 2015 Simon King <[email protected]>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  as published by the Free Software Foundation; either version 2 of
 #  the License, or (at your option) any later version.
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
 from __future__ import division, print_function
 
 include "algebra_elements.pxi"
@@ -27,11 +27,12 @@ cdef class PathAlgebraElement(RingElement):
     """
     Elements of a :class:`~sage.quivers.algebra.PathAlgebra`.
 
-    NOTE:
+    .. NOTE::
 
-    Upon creation of a path algebra, one can choose among several monomial
-    orders, which are all positive or negative degree orders. Monomial orders
-    that are not degree orders are not supported.
+        Upon creation of a path algebra, one can choose among several
+        monomial orders, which are all positive or negative degree
+        orders. Monomial orders that are not degree orders are not
+        supported.
 
     EXAMPLES:
 
@@ -148,9 +149,9 @@ cdef class PathAlgebraElement(RingElement):
           :class:`~sage.quivers.paths.QuiverPath`, the value giving its
           coefficient.
 
-        NOTE:
+        .. NOTE::
 
-        Monomial orders that are not degree orders are not supported.
+            Monomial orders that are not degree orders are not supported.
 
         EXAMPLES::
 
@@ -261,10 +262,10 @@ cdef class PathAlgebraElement(RingElement):
         """
         String representation.
 
-        NOTE:
+        .. NOTE::
 
-        The terms are first sorted by initial and terminal vertices, and only
-        then by the given monomial order.
+            The terms are first sorted by initial and terminal
+            vertices, and only then by the given monomial order.
 
         EXAMPLES::
 
@@ -463,7 +464,7 @@ cdef class PathAlgebraElement(RingElement):
 
     cpdef list coefficients(self):
         """
-        Returns the list of coefficients.
+        Return the list of coefficients.
 
         .. NOTE::
 
@@ -498,7 +499,7 @@ cdef class PathAlgebraElement(RingElement):
 
     cpdef list monomials(self):
         """
-        Returns the list of monomials appearing in this element.
+        Return the list of monomials appearing in this element.
 
         .. NOTE::
 
@@ -561,7 +562,7 @@ cdef class PathAlgebraElement(RingElement):
 
     cpdef list terms(self):
         """
-        Returns the list of terms.
+        Return the list of terms.
 
         .. NOTE::
 
@@ -616,7 +617,7 @@ cdef class PathAlgebraElement(RingElement):
 
     cpdef list support(self):
         """
-        Returns the list of monomials, as elements of the underlying partial semigroup.
+        Return the list of monomials, as elements of the underlying partial semigroup.
 
         .. NOTE::
 
@@ -966,12 +967,12 @@ cdef class PathAlgebraElement(RingElement):
         """
         Helper for comparison of path algebra elements.
 
-        NOTE:
+        .. NOTE::
 
-        First, the comparison is by initial vertices of monomials. Then, the
-        terminal vertices are compared. Last, the given monomial order is
-        applied for monomials that have the same initial and terminal
-        vertices.
+            First, the comparison is by initial vertices of
+            monomials. Then, the terminal vertices are compared. Last,
+            the given monomial order is applied for monomials that
+            have the same initial and terminal vertices.
 
         EXAMPLES::