Fixed doctests

to swap Conversion out for Coercion

Author: Julian Rüth

src/sage/categories/action.pyx

@@ -307,9 +307,8 @@ cdef class PrecomposedAction(Action):
         sage: y = x.modular_symbol_rep()
         sage: A = y.parent().get_action(QQ, self_on_left=False, op=operator.mul)
         sage: A
-        Left scalar multiplication by Rational Field on Abelian Group of all
-        Formal Finite Sums over Rational Field
-        with precomposition on right by Conversion map:
+        Left scalar multiplication by Rational Field on Abelian Group of all Formal Finite Sums over Rational Field
+        with precomposition on right by Coercion map:
           From: Abelian Group of all Formal Finite Sums over Integer Ring
           To:   Abelian Group of all Formal Finite Sums over Rational Field
     """

src/sage/geometry/hyperplane_arrangement/arrangement.py

@@ -3102,15 +3102,13 @@ def _coerce_map_from_(self, P):
             Hyperplane arrangements in 1-dimensional linear space over Real Field with 53 bits of precision with coordinate y
 
             sage: L.coerce_map_from(ZZ)
-            Conversion map:
+            Coercion map:
               From: Integer Ring
               To:   Hyperplane arrangements in 1-dimensional linear space over Rational Field with coordinate x
             sage: M.coerce_map_from(L)
-            Conversion map:
-              From: Hyperplane arrangements in 1-dimensional linear space over
-                    Rational Field with coordinate x
-              To:   Hyperplane arrangements in 1-dimensional linear space over
-                    Real Field with 53 bits of precision with coordinate y
+            Coercion map:
+              From: Hyperplane arrangements in 1-dimensional linear space over Rational Field with coordinate x
+              To:   Hyperplane arrangements in 1-dimensional linear space over Real Field with 53 bits of precision with coordinate y
             sage: L.coerce_map_from(M)
         """
         if self.ambient_space().has_coerce_map_from(P):

src/sage/geometry/linear_expression.py

@@ -733,13 +733,13 @@ def _coerce_map_from_(self, P):
             sage: L.<x> = LinearExpressionModule(QQ)
             sage: M.<y> = LinearExpressionModule(ZZ)
             sage: L.coerce_map_from(M)
-            Conversion map:
+            Coercion map:
               From: Module of linear expressions in variable y over Integer Ring
               To:   Module of linear expressions in variable x over Rational Field
             sage: M.coerce_map_from(L)
 
             sage: M.coerce_map_from(ZZ)
-            Conversion map:
+            Coercion map:
               From: Integer Ring
               To:   Module of linear expressions in variable y over Integer Ring
             sage: M.coerce_map_from(QQ)

src/sage/geometry/polyhedron/parent.py

@@ -647,7 +647,7 @@ def _get_action_(self, other, op, self_is_left):
             Right action by Integer Ring on Polyhedra in ZZ^2
             sage: PZZ2.get_action(QQ)
             Right action by Rational Field on Polyhedra in QQ^2
-            with precomposition on left by Conversion map:
+            with precomposition on left by Coercion map:
               From: Polyhedra in ZZ^2
               To:   Polyhedra in QQ^2
             with precomposition on right by Identity endomorphism of Rational Field

src/sage/manifolds/differentiable/tensorfield_module.py

@@ -172,7 +172,7 @@ class TensorFieldModule(UniqueRepresentation, Parent):
     The coercion::
 
         sage: T20U.coerce_map_from(T20)
-        Conversion map:
+        Coercion map:
           From: Module T^(2,0)(M) of type-(2,0) tensors fields on the 2-dimensional differentiable manifold M
           To:   Free module T^(2,0)(U) of type-(2,0) tensors fields on the Open subset U of the 2-dimensional differentiable manifold M
 
@@ -651,7 +651,7 @@ class TensorFieldFreeModule(TensorFreeModule):
         sage: T20.has_coerce_map_from(T20U)  # the reverse is not true
         False
         sage: T20U.coerce_map_from(T20)
-        Conversion map:
+        Coercion map:
           From: Free module T^(2,0)(R^3) of type-(2,0) tensors fields on the 3-dimensional differentiable manifold R^3
           To:   Free module T^(2,0)(U) of type-(2,0) tensors fields on the Open subset U of the 3-dimensional differentiable manifold R^3
 

src/sage/manifolds/differentiable/vectorfield_module.py

@@ -167,7 +167,7 @@ class VectorFieldModule(UniqueRepresentation, Parent):
         sage: XU.has_coerce_map_from(XM)
         True
         sage: XU.coerce_map_from(XM)
-        Conversion map:
+        Coercion map:
           From: Module X(M) of vector fields on the 2-dimensional differentiable manifold M
           To:   Free module X(U) of vector fields on the Open subset U of the 2-dimensional differentiable manifold M
 
@@ -1149,7 +1149,7 @@ class VectorFieldFreeModule(FiniteRankFreeModule):
         sage: XU.has_coerce_map_from(XM)
         True
         sage: XU.coerce_map_from(XM)
-        Conversion map:
+        Coercion map:
           From: Free module X(S^1) of vector fields on the 1-dimensional differentiable manifold S^1
           To:   Free module X(U) of vector fields on the Open subset U of the 1-dimensional differentiable manifold S^1
 

src/sage/modules/quotient_module.py

@@ -275,23 +275,23 @@ def _coerce_map_from_(self, M):
             Composite map:
               From: Ambient free module of rank 2 over the principal ideal domain Integer Ring
               To:   Vector space quotient V/W of dimension 1 over Rational Field where
-                    V: Vector space of dimension 2 over Rational Field
-                    W: Vector space of degree 2 and dimension 1 over Rational Field
-                    Basis matrix:
-                    [1 2]
-              Defn:   Conversion map:
+            V: Vector space of dimension 2 over Rational Field
+            W: Vector space of degree 2 and dimension 1 over Rational Field
+            Basis matrix:
+            [1 2]
+              Defn:   Coercion map:
                       From: Ambient free module of rank 2 over the principal ideal domain Integer Ring
                       To:   Vector space of dimension 2 over Rational Field
                     then
                       Vector space morphism represented by the matrix:
-                      [   1]
-                      [-1/2]
-                      Domain: Vector space of dimension 2 over Rational Field
-                      Codomain: Vector space quotient V/W of dimension 1 over Rational Field where
-                                V: Vector space of dimension 2 over Rational Field
-                                W: Vector space of degree 2 and dimension 1 over Rational Field
-                                Basis matrix:
-                                [1 2]
+                    [   1]
+                    [-1/2]
+                    Domain: Vector space of dimension 2 over Rational Field
+                    Codomain: Vector space quotient V/W of dimension 1 over Rational Field where
+                    V: Vector space of dimension 2 over Rational Field
+                    W: Vector space of degree 2 and dimension 1 over Rational Field
+                    Basis matrix:
+                    [1 2]
 
         Make sure :trac:`10513` is fixed (no coercion from an abstract
         vector space to an isomorphic quotient vector space)::

src/sage/numerical/linear_functions.pyx

@@ -309,7 +309,7 @@ cdef class LinearFunctionOrConstraint(ModuleElement):
             sage: cm = sage.structure.element.get_coercion_model()
             sage: cm.explain(10, LF(1), operator.le)
             Coercion on left operand via
-                Conversion map:
+                Coercion map:
                   From: Integer Ring
                   To:   Linear functions over Real Double Field
             Arithmetic performed after coercions.

src/sage/numerical/linear_tensor_element.pyx

@@ -396,15 +396,15 @@ cdef class LinearTensor(ModuleElement):
             sage: cm = sage.structure.element.get_coercion_model()
             sage: cm.explain(10, lt, operator.le)
             Coercion on left operand via
-                Conversion map:
+                Coercion map:
                   From: Integer Ring
-                  To:   Tensor product of Vector space of dimension 2 over Real 
+                  To:   Tensor product of Vector space of dimension 2 over Real
                         Double Field and Linear functions over Real Double Field
             Arithmetic performed after coercions.
-            Result lives in Tensor product of Vector space of dimension 2 over 
-            Real Double Field and Linear functions over Real Double Field
-            Tensor product of Vector space of dimension 2 over Real Double Field 
-            and Linear functions over Real Double Field
+            Result lives in Tensor product of Vector space of dimension 2 over
+            Real Double Field and Linear functions over Real Double Field +
+            Tensor product of Vector space of dimension 2 over Real Double Field and Linear
+            functions over Real Double Field
         
             sage: operator.le(10, lt)
             (10.0, 10.0) <= (1.0, 2.0)*x_0

src/sage/quivers/algebra.py

@@ -350,7 +350,7 @@ def _coerce_map_from_(self, other):
             sage: A2 = P2.algebra(GF(3))
             sage: A1.coerce_map_from(A2) # indirect doctest
             sage: A2.coerce_map_from(A1) # indirect doctest
-            Conversion map:
+            Coercion map:
               From: Path algebra of Multi-digraph on 2 vertices over Finite Field of size 3
               To:   Path algebra of Multi-digraph on 2 vertices over Finite Field of size 3
             sage: A1.coerce_map_from(ZZ) # indirect doctest
@@ -380,7 +380,7 @@ def _coerce_map_from_(self, other):
         ::
 
             sage: A2.coerce_map_from(P1)
-            Conversion map:
+            Coercion map:
               From: Partial semigroup formed by the directed paths of Multi-digraph on 2 vertices
               To:   Path algebra of Multi-digraph on 2 vertices over Finite Field of size 3
             sage: a = P1(P1.arrows()[0]); a

src/sage/quivers/homspace.py

@@ -211,9 +211,9 @@ def _coerce_map_from_(self, other):
             sage: H1 = P.Hom(S)
             sage: H2 = (P/P.radical()).Hom(S)
             sage: H1.coerce_map_from(H2) # indirect doctest
-            Conversion map:
-                  From: Dimension 1 QuiverHomSpace
-                  To:   Dimension 1 QuiverHomSpace
+            Coercion map:
+              From: Dimension 1 QuiverHomSpace
+              To:   Dimension 1 QuiverHomSpace
         """
 
         if not isinstance(other, QuiverHomSpace):

src/sage/rings/asymptotic/growth_group_cartesian.py

@@ -630,11 +630,11 @@ def _pushout_(self, other):
             Growth Group QQ^x * x^ZZ * log(x)^ZZ
             sage: cm.discover_coercion(A, B)
             ((map internal to coercion system -- copy before use)
-             Conversion map:
+             Coercion map:
                From: Growth Group QQ^x * x^ZZ
                To:   Growth Group QQ^x * x^ZZ * log(x)^ZZ,
              (map internal to coercion system -- copy before use)
-             Conversion map:
+             Coercion map:
                From: Growth Group x^ZZ * log(x)^ZZ
                To:   Growth Group QQ^x * x^ZZ * log(x)^ZZ)
             sage: cm.common_parent(A, B)

src/sage/rings/asymptotic/term_monoid.py

@@ -2903,7 +2903,7 @@ class TermWithCoefficientMonoid(GenericTermMonoid):
         sage: TC_ZZ == TC_QQ or TC_ZZ is TC_QQ
         False
         sage: TC_QQ.coerce_map_from(TC_ZZ)
-        Conversion map:
+        Coercion map:
           From: Generic Term Monoid x^ZZ with (implicit) coefficients in Rational Field
           To:   Generic Term Monoid x^QQ with (implicit) coefficients in Rational Field
     """
@@ -3691,7 +3691,7 @@ class ExactTermMonoid(TermWithCoefficientMonoid):
         sage: ET_QQ = ExactTermMonoid(G_QQ, QQ); ET_QQ
         Exact Term Monoid x^QQ with coefficients in Rational Field
         sage: ET_QQ.coerce_map_from(ET_ZZ)
-        Conversion map:
+        Coercion map:
           From: Exact Term Monoid x^ZZ with coefficients in Integer Ring
           To:   Exact Term Monoid x^QQ with coefficients in Rational Field
 

src/sage/rings/complex_arb.pyx

@@ -272,27 +272,27 @@ class ComplexBallField(UniqueRepresentation, Field):
         construction functions)::
 
             sage: CBF.coerce_map_from(ZZ)
-            Conversion map:
-            From: Integer Ring
-            To:   Complex ball field with 53 bits precision
+            Coercion map:
+              From: Integer Ring
+              To:   Complex ball field with 53 bits precision
             sage: CBF.coerce_map_from(QQ)
-            Conversion map:
-            From: Rational Field
-            To:   Complex ball field with 53 bits precision
+            Coercion map:
+              From: Rational Field
+              To:   Complex ball field with 53 bits precision
 
         Various other coercions are available through real ball fields or CLF::
 
             sage: CBF.coerce_map_from(RLF)
             Composite map:
-            From: Real Lazy Field
-            To:   Complex ball field with 53 bits precision
-            Defn:   Conversion map:
-                    From: Real Lazy Field
-                    To:   Real ball field with 53 bits precision
+              From: Real Lazy Field
+              To:   Complex ball field with 53 bits precision
+              Defn:   Coercion map:
+                      From: Real Lazy Field
+                      To:   Real ball field with 53 bits precision
                     then
-                    Conversion map:
-                    From: Real ball field with 53 bits precision
-                    To:   Complex ball field with 53 bits precision
+                      Coercion map:
+                      From: Real ball field with 53 bits precision
+                      To:   Complex ball field with 53 bits precision
             sage: CBF.has_coerce_map_from(AA)
             True
             sage: CBF.has_coerce_map_from(QuadraticField(-1))
@@ -422,9 +422,9 @@ class ComplexBallField(UniqueRepresentation, Field):
             sage: CBF.coerce_map_from(CBF)
             Identity endomorphism of Complex ball field with 53 bits precision
             sage: CBF.coerce_map_from(ComplexBallField(100))
-            Conversion map:
-            From: Complex ball field with 100 bits precision
-            To:   Complex ball field with 53 bits precision
+            Coercion map:
+              From: Complex ball field with 100 bits precision
+              To:   Complex ball field with 53 bits precision
             sage: CBF.has_coerce_map_from(ComplexBallField(42))
             False
             sage: CBF.has_coerce_map_from(RealBallField(54))

src/sage/rings/homset.py

@@ -285,7 +285,7 @@ def _coerce_impl(self, x):
             Composite map:
               From: Multivariate Polynomial Ring in x, y over Integer Ring
               To:   Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2)
-              Defn:   Conversion map:
+              Defn:   Coercion map:
                       From: Multivariate Polynomial Ring in x, y over Integer Ring
                       To:   Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2)
                     then
@@ -295,7 +295,7 @@ def _coerce_impl(self, x):
                       Defn: a |--> b
                             b |--> a
                     then
-                      Conversion map:
+                      Coercion map:
                       From: Multivariate Polynomial Ring in x, y over Rational Field
                       To:   Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2)
 

src/sage/rings/infinity.py

@@ -1209,7 +1209,7 @@ def _coerce_map_from_(self, R):
             sage: cm = get_coercion_model()
             sage: cm.explain(AA(3), oo, operator.lt)
             Coercion on left operand via
-                Conversion map:
+                Coercion map:
                   From: Algebraic Real Field
                   To:   The Infinity Ring
             Arithmetic performed after coercions.

src/sage/rings/number_field/number_field.py

@@ -2414,14 +2414,14 @@ def maximal_totally_real_subfield(self):
               Defn: a0 |--> -a^27 - a^26 - a^25 - a^24 - a^23 - a^22 - a^21 - a^20 - a^19 - a^18 - a^17 - a^16 - a^15 - a^14 - a^13 - a^12 - a^11 - a^10 - a^9 - a^8 - a^7 - a^6 - a^5 - a^4 - a^3 - a^2 - 1)
             sage: F.<a> = NumberField(x^3 - 2)
             sage: F.maximal_totally_real_subfield()
-            [Rational Field, Conversion map:
-              From: Rational Field
-              To:   Number Field in a with defining polynomial x^3 - 2]
+            [Rational Field, Coercion map:
+               From: Rational Field
+               To:   Number Field in a with defining polynomial x^3 - 2]
             sage: F.<a> = NumberField(x^4 - x^3 - x^2 + x + 1)
             sage: F.maximal_totally_real_subfield()
-            [Rational Field, Conversion map:
-              From: Rational Field
-              To:   Number Field in a with defining polynomial x^4 - x^3 - x^2 + x + 1]
+            [Rational Field, Coercion map:
+               From: Rational Field
+               To:   Number Field in a with defining polynomial x^4 - x^3 - x^2 + x + 1]
             sage: F.<a> = NumberField(x^4 - x^3 + 2*x^2 + x + 1)
             sage: F.maximal_totally_real_subfield()
             [Number Field in a1 with defining polynomial x^2 - x - 1, Ring morphism:

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -471,9 +471,9 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
             sage: R.has_coerce_map_from(ZZ['t'])
             False
             sage: R.coerce_map_from(ZZ['x'])
-            Conversion map:
-            From: Univariate Polynomial Ring in x over Integer Ring
-            To:   Multivariate Polynomial Ring in x, y over Rational Field
+            Coercion map:
+              From: Univariate Polynomial Ring in x over Integer Ring
+              To:   Multivariate Polynomial Ring in x, y over Rational Field
 
         """
         base_ring = self.base_ring()

src/sage/structure/coerce.pyx

@@ -1307,14 +1307,14 @@ cdef class CoercionModel_cache_maps(CoercionModel):
             sage: cm = sage.structure.element.get_coercion_model()
             sage: cm.coercion_maps(V, W)
             (None, (map internal to coercion system -- copy before use)
-            Conversion map:
-              From: Vector space of dimension 3 over Rational Field
-              To:   Vector space of dimension 3 over Rational Field)
+             Coercion map:
+               From: Vector space of dimension 3 over Rational Field
+               To:   Vector space of dimension 3 over Rational Field)
             sage: cm.coercion_maps(W, V)
             (None, (map internal to coercion system -- copy before use)
-            Conversion map:
-              From: Vector space of dimension 3 over Rational Field
-              To:   Vector space of dimension 3 over Rational Field)
+             Coercion map:
+               From: Vector space of dimension 3 over Rational Field
+               To:   Vector space of dimension 3 over Rational Field)
             sage: v = V([1,2,3])
             sage: w = W([1,2,3])
             sage: parent(v+w) is V

src/sage/structure/coerce_actions.pyx

@@ -523,13 +523,11 @@ cdef class ModuleAction(Action):
             sage: cm = sage.structure.element.get_coercion_model()
             sage: cm.explain(x, 1, operator.div)
             Action discovered.
-                Right inverse action by Symbolic Constants Subring on
-                Univariate Polynomial Ring in x over Symbolic Constants Subring
-                with precomposition on right by Conversion map:
+                Right inverse action by Symbolic Constants Subring on Univariate Polynomial Ring in x over Symbolic Constants Subring
+                with precomposition on right by Coercion map:
                   From: Integer Ring
                   To:   Symbolic Constants Subring
-            Result lives in Univariate Polynomial Ring in x over
-            Symbolic Constants Subring
+            Result lives in Univariate Polynomial Ring in x over Symbolic Constants Subring
             Univariate Polynomial Ring in x over Symbolic Constants Subring
         """
         K = self.G._pseudo_fraction_field()