more fixes in Pieri factors

Author: fchapoton

src/doc/en/reference/references/index.rst

@@ -3250,7 +3250,7 @@ REFERENCES:
 
 **L**
 
-.. [Lab2008] S. Labbé, *Propriétés combinatoires des `f`-palindromes*,
+.. [Lab2008] \S. Labbé, *Propriétés combinatoires des* `f`-*palindromes*,
              Mémoire de maîtrise en Mathématiques, Montréal, UQAM,
              2008, 109 pages.
 
@@ -3270,15 +3270,15 @@ REFERENCES:
 .. [Lan2002] \S. Lang : *Algebra*, 3rd ed., Springer (New York) (2002);
              :doi:`10.1007/978-1-4613-0041-0`
 
-.. [Lan2008] \E. Lanneau "Connected components of the strata of the
-             moduli spaces of quadratic differentials", Annales
+.. [Lan2008] \E. Lanneau, *Connected components of the strata of the
+             moduli spaces of quadratic differentials*, Annales
              sci. de l'ENS, serie 4, fascicule 1, 41, 1-56 (2008)
 
 .. [Lasc] \A. Lascoux. *Chern and Yang through ice*.
           Preprint.
 
-.. [Lau2011] Alan G.B. Lauder, "Computations with classical and p-adic
-             modular forms", LMS J. of Comput. Math. 14 (2011),
+.. [Lau2011] Alan G.B. Lauder, *Computations with classical and p-adic
+             modular forms*, LMS J. of Comput. Math. 14 (2011),
              214-231.
 
 .. [Laz1992] Daniel Lazard, *Solving Zero-dimensional Algebraic

src/sage/combinat/root_system/pieri_factors.py

@@ -439,7 +439,7 @@ class PieriFactors_type_B(PieriFactors_finite_type):
     r"""
     The type B finite Pieri factors are realized as the set of
     elements that have a reduced word that is a subword of
-    12...(n-1)n(n-1)...21.  They are the restriction of the type C
+    `12...(n-1)n(n-1)...21`. They are the restriction of the type C
     affine Pieri factors to the set of finite Weyl group elements
     under the usual embedding.
     """
@@ -476,10 +476,9 @@ def maximal_elements_combinatorial(self):
         li = list(range(1, N)) + list(range(N, 0, -1))
         return [self.W.from_reduced_word(li)]
 
-    def stanley_symm_poly_weight(self,w):
+    def stanley_symm_poly_weight(self, w):
         r"""
-        Weight used in computing Stanley symmetric polynomials of type
-        `B`.
+        Weight used in computing Stanley symmetric polynomials of type `B`.
 
         The weight for finite type B is the number of components
         of the support of an element minus the number of occurrences
@@ -648,13 +647,13 @@ def _test_maximal_elements(self, **options):
             sage: W = WeylGroup(['A',4,1])
             sage: W.pieri_factors()._test_maximal_elements(verbose = True)
             sage: W.pieri_factors(min_length = 1)._test_maximal_elements(verbose = True)
-            Strict subset of the pieri factors; skipping test
+            Strict subset of the Pieri factors; skipping test
 
         """
         tester = self._tester(**options)
         index_set = self.W.index_set()
         if self._min_length > 0 or self._max_length < len(self.W.index_set())-1 or self._max_support != frozenset(index_set):
-            tester.info("\n  Strict subset of the pieri factors; skipping test")
+            tester.info("\n  Strict subset of the Pieri factors; skipping test")
             return
         return super(PieriFactors_type_A_affine, self)._test_maximal_elements(**options)
 
@@ -821,7 +820,7 @@ class PieriFactors_type_C_affine(PieriFactors_affine_type):
     r"""
     The type C affine Pieri factors are realized as the order ideal (in Bruhat
     order) generated by cyclic rotations of the element with unique reduced word
-    123...(n-1)n(n-1)...3210.
+    `123...(n-1)n(n-1)...3210`.
 
     EXAMPLES::
 
@@ -897,10 +896,11 @@ class PieriFactors_type_B_affine(PieriFactors_affine_type):
     The type B affine Pieri factors are realized as the order ideal (in Bruhat
     order) generated by the following elements:
 
-    - cyclic rotations of the element with reduced word 234...(n-1)n(n-1)...3210,
-      except for 123...n...320 and 023...n...321.
-    - 123...(n-1)n(n-1)...321
-    - 023...(n-1)n(n-1)...320
+    - cyclic rotations of the element with reduced word
+      `234...(n-1)n(n-1)...3210`,
+      except for `123...n...320` and `023...n...321`.
+    - `123...(n-1)n(n-1)...321`
+    - `023...(n-1)n(n-1)...320`
 
     EXAMPLES::
 
@@ -952,7 +952,7 @@ def maximal_elements_combinatorial(self):
         rotations.append(self.W.from_reduced_word([0])*self.W.from_reduced_word(range(2,n-1))*self.W.from_reduced_word(range(n-1,1,-1))*self.W.from_reduced_word([0]))
         return rotations
 
-    def stanley_symm_poly_weight(self,w):
+    def stanley_symm_poly_weight(self, w):
         r"""
         Return the weight of a Pieri factor to be used in the definition of
         Stanley symmetric functions.
@@ -964,12 +964,12 @@ def stanley_symm_poly_weight(self,w):
         and 1 to be one node for the purpose of counting components of
         the complement (as if the Dynkin diagram were that of type C).
         Let n be the rank of the affine Weyl group in question (if
-        type ['B',k,1] then we have n = k+1).  Let chi(v.length() < n-1)
+        type ``['B',k,1]`` then we have n = k+1).  Let ``chi(v.length() < n-1)``
         be the indicator function that is 1 if the length of v is
         smaller than n-1, and 0 if the length of v is greater than or
-        equal to n-1.  If we say c'(v) = the number of components of
+        equal to n-1.  If we call ``c'(v)`` the number of components of
         the complement of the support of v, then the type B weight is
-        given by weight = c'(v) - chi(v.length() < n-1).
+        given by ``weight = c'(v) - chi(v.length() < n-1)``.
 
         EXAMPLES::
 
@@ -1004,12 +1004,13 @@ class PieriFactors_type_D_affine(PieriFactors_affine_type):
     The type D affine Pieri factors are realized as the order ideal
     (in Bruhat order) generated by the following elements:
 
-     * cyclic rotations of the element with reduced word 234...(n-2)n(n-1)(n-2)...3210
+     * cyclic rotations of the element with reduced word
+       `234...(n-2)n(n-1)(n-2)...3210`
        such that 1 and 0 are always adjacent and (n-1) and n are always adjacent.
-     * 123...(n-2)n(n-1)(n-2)...321
-     * 023...(n-2)n(n-1)(n-2)...320
-     * n(n-2)...2102...(n-2)n
-     * (n-1)(n-2)...2102...(n-2)(n-1)
+     * `123...(n-2)n(n-1)(n-2)...321`
+     * `023...(n-2)n(n-1)(n-2)...320`
+     * `n(n-2)...2102...(n-2)n`
+     * `(n-1)(n-2)...2102...(n-2)(n-1)`
 
     EXAMPLES::
 
@@ -1075,16 +1076,16 @@ def stanley_symm_poly_weight(self, w):
 
         INPUT:
 
-         - ``w`` -- a pieri factor for this type
+        - ``w`` -- a Pieri factor for this type
 
-        For type D, this weight involves
+        For type `D`, this weight involves
         the number of components of the complement of the support of
-        an element, where we consider 0 and 1 to be one node -- if 1
-        is in the support, then we pretend 0 in the support, and vice
-        versa.  Similarly with `n-1` and `n`.  We also consider 0 and
-        1, n-1 and n to be one node for the purpose of counting
+        an element, where we consider `0` and `1` to be one node -- if `1`
+        is in the support, then we pretend `0` in the support, and vice
+        versa.  Similarly with `n-1` and `n`.  We also consider `0` and
+        `1`, `n-1` and `n` to be one node for the purpose of counting
         components of the complement (as if the Dynkin diagram were
-        that of type C).
+        that of type `C`).
 
         Type D Stanley symmetric polynomial weights are still
         conjectural.  The given weight comes from conditions on
@@ -1116,9 +1117,9 @@ def stanley_symm_poly_weight(self, w):
         if 1 in support or 0 in support:
             support = support.union(set([1])).difference(set([0]))
         if n in support or n - 1 in support:
-            support = support.union(set([n-2])).difference(set([n - 1]))
-        support_complement = set(range(1,n-1)).difference(support)
-        return DiGraph(DynkinDiagram(ct)).subgraph(support_complement).connected_components_number()-1
+            support = support.union(set([n - 2])).difference(set([n - 1]))
+        support_complement = set(range(1, n - 1)).difference(support)
+        return DiGraph(DynkinDiagram(ct)).subgraph(support_complement).connected_components_number() - 1
 
 
 # Inserts those classes in CartanTypes