refactor coercion maps

Author: fchapoton

src/sage/rings/polynomial/integer_valued_polynomials.py

@@ -83,11 +83,6 @@ def __init__(self, R):
         cat = Algebras(R).Commutative().WithBasis()
         Parent.__init__(self, base=R, category=cat.WithRealizations())
 
-        S = self.S()
-        B = self.B()
-        B.module_morphism(S._from_binomial_basis, codomain=S).register_as_coercion()
-        S.module_morphism(B._from_shifted_basis, codomain=B).register_as_coercion()
-
     _shorthands = ["B", "S"]
 
     def _repr_(self) -> str:
@@ -555,6 +550,11 @@ def _element_constructor_(self, x):
                 if P is not self.base_ring():
                     return self.element_class(self, x.monomial_coefficients())
 
+            if isinstance(P, IntegerValuedPolynomialRing.Binomial):
+                phi = P.module_morphism(self._from_binomial_basis,
+                                        codomain=self)
+                return phi(x)
+
             # ok, not a integer-valued polynomial ring element
             R = self.base_ring()
             # coercion via base ring
@@ -655,6 +655,8 @@ def _coerce_map_from_(self, R):
             # that coerces in:
             if isinstance(R, IntegerValuedPolynomialRing.Shifted):
                 return self.base_ring().has_coerce_map_from(R.base_ring())
+            if isinstance(R, IntegerValuedPolynomialRing.Binomial):
+                return self.base_ring().has_coerce_map_from(R.base_ring())
             return self.base_ring().has_coerce_map_from(R)
 
         def _poly(self, i):
@@ -991,6 +993,11 @@ def _element_constructor_(self, x):
                 if P is not self.base_ring():
                     return self.element_class(self, x.monomial_coefficients())
 
+            if isinstance(P, IntegerValuedPolynomialRing.Shifted):
+                psi = P.module_morphism(self._from_shifted_basis,
+                                        codomain=self)
+                return psi(x)
+
             # ok, not a integer-valued polynomial ring element
             R = self.base_ring()
             # coercion via base ring
@@ -1087,6 +1094,8 @@ def _coerce_map_from_(self, R):
             # that coerces in:
             if isinstance(R, IntegerValuedPolynomialRing.Binomial):
                 return self.base_ring().has_coerce_map_from(R.base_ring())
+            if isinstance(R, IntegerValuedPolynomialRing.Shifted):
+                return self.base_ring().has_coerce_map_from(R.base_ring())
             return self.base_ring().has_coerce_map_from(R)
 
         def _poly(self, i):