use in_base in invert method

Author: xcaruso

src/sage/rings/function_field/drinfeld_modules/finite_drinfeld_module.py

@@ -437,37 +437,38 @@ def invert(self, ore_pol):
         """
         deg = ore_pol.degree()
         r = self.rank()
-        base_over_Fq = self.base_over_constants_field()
+        E = self.base()
+        K = self.base_over_constants_field()
         if ore_pol not in self._ore_polring:
             raise TypeError('input must be an Ore polynomial')
-        if ore_pol.degree() == 0:
-            coord = base_over_Fq(self._base(ore_pol)).vector()
-            if coord.nonzero_positions == [0]:
-                return self._Fq(coord[0])
-        if ore_pol == 0:
-            return self._Fq.zero()
         if deg % r != 0:
-            raise ValueError('input must be in the image of the Drinfeld '
-                             'module')
+            raise ValueError('input must be in the image of the Drinfeld module')
+
+        if ore_pol.degree() <= 0:
+            return K(ore_pol[0]).in_base()
 
         k = deg // r
-        T = self._function_ring.gen()
-        mat_lines = [[0 for _ in range(k+1)] for _ in range(k+1)]
-        for i in range(k+1):
-            phi_T_i = self(T**i)
+        A = self._function_ring
+        T = A.gen()
+        mat_rows = [[E.zero() for _ in range(k+1)] for _ in range(k+1)]
+        mat_rows[0][0] = E.one()
+        phiT = self.gen()
+        phiTi = self.ore_polring().one()
+        for i in range(1, k+1):
+            phiTi *= phiT
             for j in range(i+1):
-                mat_lines[j][i] = phi_T_i[r*j]
-        mat = Matrix(mat_lines)
-        vec = vector([list(ore_pol)[r*j] for j in range(k+1)])
-        coeffs_K = list((mat**(-1)) * vec)
-        coeffs_Fq = list(map(lambda x: base_over_Fq(x).vector()[0], coeffs_K))
-        pre_image = self._function_ring(coeffs_Fq)
-
-        if self(pre_image) == ore_pol:
-            return pre_image
-        else:
-            raise ValueError('input must be in the image of the Drinfeld '
-                             'module')
+                mat_rows[j][i] = phiTi[r*j]
+        mat = Matrix(mat_rows)
+        vec = vector([ore_pol[r*j] for j in range(k+1)])
+        coeffs_K = list(mat.inverse() * vec)
+        try:
+            coeffs_Fq = [K(c).in_base() for c in coeffs_K]
+            pre_image = A(coeffs_Fq)
+            if self(pre_image) == ore_pol:
+                return pre_image
+        except ValueError:
+            pass
+        raise ValueError('input must be in the image of the Drinfeld module')
 
     def is_ordinary(self):
         r"""

src/sage/rings/function_field/drinfeld_modules/homset.py

@@ -200,10 +200,9 @@ class DrinfeldModuleHomset(Homset):
         False
         sage: frobenius_endomorphism in H
         False
-    """
 
+    """
     Element = DrinfeldModuleMorphism
-    __contains__ = Parent.__contains__
 
     def __init__(self, X, Y, category=None, check=True):
         """
@@ -238,8 +237,7 @@ def __init__(self, X, Y, category=None, check=True):
         if check:
             if X.category() != Y.category() \
                     or not isinstance(X.category(), DrinfeldModules):
-                raise ValueError('Drinfeld modules must be in the same '
-                                 'category')
+                raise ValueError('Drinfeld modules must be in the same category')
             if category != X.category():
                 raise ValueError('category should be DrinfeldModules')
         base = category.base()

src/sage/rings/function_field/drinfeld_modules/morphism.py

@@ -96,8 +96,13 @@ class DrinfeldModuleMorphism(Morphism, UniqueRepresentation,
 
     TESTS::
 
-        sage: morphism.parent() == Hom(phi, psi)
+        sage: morphism.parent() is Hom(phi, psi)
         True
+        sage: Hom(phi, psi)(morphism) == morphism
+        True
+
+    ::
+
         sage: phi.frobenius_endomorphism().parent() == End(phi)
         True
         sage: End(phi)(0).parent() == End(phi)
@@ -115,8 +120,8 @@ class DrinfeldModuleMorphism(Morphism, UniqueRepresentation,
           Defn: t + z^5 + z^3 + z + 1
         sage: DrinfeldModuleMorphism(Hom(phi, psi), ore_pol) is morphism
         True
-    """
 
+    """
     @staticmethod
     def __classcall_private__(cls, parent, x):
         """
@@ -627,6 +632,14 @@ def dual_isogeny(self):
             sage: f * g == psi.hom(a)
             True
 
+        TESTS::
+
+            sage: zero = phi.hom(0)
+            sage: zero.dual_isogeny()
+            Traceback (most recent call last):
+            ...
+            ValueError: the dual isogeny of the zero morphism is not defined
+
         """
         if not self.is_isogeny():
             raise ValueError("the dual isogeny of the zero morphism is not defined")
@@ -670,6 +683,15 @@ def characteristic_polynomial(self, var='X'):
             sage: f.characteristic_polynomial(var='Y')
             Y^3 + (T + 1)*Y^2 + (2*T + 3)*Y + 2*T^3 + T + 1
 
+        TESTS::
+
+            sage: t = phi.ore_variable()
+            sage: isog = phi.hom(t + 1)
+            sage: isog.characteristic_polynomial()
+            Traceback (most recent call last):
+            ...
+            ValueError: characteristic polynomial is only defined for endomorphisms
+
         """
         if self.domain() is not self.codomain():
             raise ValueError("characteristic polynomial is only defined for endomorphisms")