more fine-tuning details in MZV

Author: fchapoton

src/sage/modular/multiple_zeta.py

@@ -2614,7 +2614,6 @@ def rho_inverse(elt):
         sage: from sage.modular.multiple_zeta_F_algebra import F_algebra
         sage: A = F_algebra(QQ)
         sage: f = A.custom_gen
-        sage: W = A.basis().keys()
         sage: rho_inverse(f(3))
         ζ(3)
         sage: rho_inverse(f(9))

src/sage/modular/multiple_zeta_F_algebra.py

@@ -312,11 +312,11 @@ def one_basis(self):
 
     def product_on_basis(self, pw1, pw2):
         r"""
-        Return the product of basis elements ``w1`` and ``w2``.
+        Return the product of basis elements ``pw1`` and ``pw2``.
 
         INPUT:
 
-        - ``w1``, ``w2`` -- basis elements
+        - ``pw1``, ``pw2`` -- basis elements
 
         EXAMPLES::
 
@@ -333,13 +333,13 @@ def product_on_basis(self, pw1, pw2):
 
     def half_product_on_basis(self, pw1, pw2):
         r"""
-        Return the half product of basis elements ``w1`` and ``w2``.
+        Return the half product of basis elements ``pw1`` and ``pw2``.
 
         This is an extension of the zinbiel product of the shuffle algebra.
 
         INPUT:
 
-        - ``w1``, ``w2`` -- Basis elements
+        - ``pw1``, ``pw2`` -- Basis elements
 
         EXAMPLES::
 
@@ -408,7 +408,7 @@ def custom_gen(self, i):
 
         INPUT:
 
-        - ``i`` -- a nonnegative integer
+        - ``i`` -- a nonnegative integer (at least 2)
 
         If ``i`` is odd, this returns a single generator `f_i` of the free
         shuffle algebra.
@@ -463,7 +463,7 @@ def some_elements(self):
 
     def coproduct_on_basis(self, pw):
         r"""
-        Return the coproduct of the basis element indexed by the word ``w``.
+        Return the coproduct of the basis element indexed by the pair ``pw``.
 
         The coproduct is given by deconcatenation on the shuffle part,
         and extended by the value
@@ -474,7 +474,7 @@ def coproduct_on_basis(self, pw):
 
         INPUT:
 
-        - ``w`` -- a word
+        - ``pw`` -- an index
 
         EXAMPLES::
 
@@ -695,10 +695,6 @@ def homogeneous_to_vector(self):
 
             This is using a fixed enumeration of the basis.
 
-            INPUT:
-
-            an homogeneous element of :func:`F_ring` over some base ring
-
             OUTPUT:
 
             a vector with coefficients in the base ring