move single_valued method of MZV to auxiliary F ring

Author: fchapoton

src/sage/modular/multiple_zeta.py

@@ -1108,13 +1108,7 @@ def single_valued(self):
                 sage: Z(5,3).single_valued() == 14*Z(3)*Z(5)
                 True
             """
-            phi_im = self.phi()
-            zin = phi_im.parent()
-            phi_no_f2 = phi_im.without_f2()
-            sv = zin.sum_of_terms(((0, w), cf)
-                                  for (a, b), cf in phi_no_f2.coproduct()
-                                  for w in shuffle(a[1], b[1].reversal(), False))
-            return rho_inverse(sv)
+            return rho_inverse(self.phi().single_valued())
 
         def simplify(self):
             """

src/sage/modular/multiple_zeta_F_algebra.py

@@ -31,6 +31,7 @@
 from sage.combinat.free_module import CombinatorialFreeModule
 from sage.combinat.words.words import Words
 from sage.combinat.words.finite_word import FiniteWord_class
+from sage.combinat.words.shuffle_product import ShuffleProduct_w1w2 as shuffle
 from sage.misc.cachefunc import cached_method
 from sage.misc.lazy_attribute import lazy_attribute
 from sage.sets.integer_range import IntegerRange
@@ -721,3 +722,24 @@ def without_f2(self):
             """
             F = self.parent()
             return F._from_dict({(0, w): cf for (p, w), cf in self if not p})
+
+        def single_valued(self):
+            """
+            Return the single-valued version of ``self``.
+
+            EXAMPLES::
+
+                sage: from sage.modular.multiple_zeta_F_algebra import F_algebra
+                sage: F = F_algebra(QQ)
+                sage: t = 4*F("2")+F("3")
+                sage: t.single_valued()
+                2*f3
+                sage: t = 4*F("35")+F("27")
+                sage: t.single_valued()
+                8*f3f5 + 8*f5f3
+            """
+            F = self.parent()
+            no_f2 = self.without_f2()
+            return F.sum_of_terms(((0, w), cf)
+                                  for (a, b), cf in no_f2.coproduct()
+                                  for w in shuffle(a[1], b[1].reversal(), False))