Added kernel

vector_bundle/hom_bundle.py

@@ -377,6 +377,51 @@ class HomBundle(VectorBundle):
         image = VectorBundle(K, ideals, g_fi, identity_matrix(K, g_fi.ncols()))
         return image, C_inf
 
+    def kernel(self, f):
+        r"""
+        Return a kernel of global homomorphism ``f`` which is an element of
+        `H^0(\mathrm{self})`.
+
+        That is, a vector bundle `V` together with an injective morphism of `V`
+        into ``self.domain`` such that the image of `V` in ``self.domain``
+        is the kernel of ``f``.
+
+        EXAMPLES ::
+
+            sage: from vector_bundle import trivial_bundle, canonical_bundle
+            sage: F.<x> = FunctionField(GF(7))
+            sage: R.<y> = F[]
+            sage: K.<y> = F.extension(y^2 - x^3 - x)
+            sage: triv = trivial_bundle(K)
+            sage: can = canonical_bundle(K)
+            sage: V1 = triv.direct_sum(can)
+            sage: V2 = can.direct_sum(triv)
+            sage: hom = V1.hom(V2)
+            sage: kernel, map = hom.kernel(matrix(K, [[0, 1], [0, 0]]))
+            sage: kernel.isomorphism_to(triv) is not None
+            True
+            sage: kernel.hom(V1).coordinates_in_h0(map)
+            (1, 0)
+        """
+        dom = self._domain
+        cod = self._codomain
+        ideals, _, U_fi = function_field_utility.pseudo_hermite_form(
+                dom._ideals,
+                f*dom._g_finite,
+                transformation=True)
+        _, U_inf = function_field_utility.hermite_form_infinite_polymod(
+                f*dom._g_infinite,
+                transformation=True)
+        r = f.rank()
+        n = f.ncols()
+        ideals = ideals[:n-r]
+        C_fi = U_fi[:,:n-r]
+        C_inf = U_inf[:,:n-r]
+        g_fi = C_inf.solve_right(C_fi)
+        K = self._function_field
+        image = VectorBundle(K, ideals, g_fi, identity_matrix(K, g_fi.ncols()))
+        return image, C_inf
+
     def is_isomorphism(self, f):
         r"""
         Check if f is an isomorphism from ``self.domain()`` to