Faster implementation of finite dimensional algebras

src/module_list.py

@@ -188,6 +188,8 @@ def uname_specific(name, value, alternative):
 
     Extension('*', sources = ['sage/algebras/letterplace/*.pyx']),
 
+    Extension('*', sources = ['sage/algebras/finite_dimensional_algebras/*.pyx']),
+
     Extension('sage.algebras.quatalg.quaternion_algebra_cython',
                sources = ['sage/algebras/quatalg/quaternion_algebra_cython.pyx'],
                language='c++',

src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra.py

@@ -20,7 +20,7 @@
 from sage.rings.integer_ring import ZZ
 
 from sage.categories.magmatic_algebras import MagmaticAlgebras
-from sage.matrix.constructor import Matrix
+from sage.matrix.constructor import Matrix, matrix
 from sage.matrix.matrix import is_Matrix
 from sage.modules.free_module_element import vector
 from sage.rings.ring import Algebra
@@ -302,7 +302,7 @@ def __iter__(self):
 
             sage: A = FiniteDimensionalAlgebra(GF(3), [Matrix([[1, 0], [0, 1]]), Matrix([[0, 1], [0, 0]])])
             sage: list(A)
-            [0, e0, 2*e0, e1, e0 + e1, 2*e0 + e1, 2*e1, e0 + 2*e1, 2*e0 + 2*e1]
+            [0, e0, e1, 2*e0, e0 + e1, 2*e1, 2*e0 + e1, e0 + 2*e1, 2*e0 + 2*e1]
 
         This is used in the :class:`Testsuite`'s when ``self`` is
         finite.
@@ -554,7 +554,7 @@ def is_unitary(self):
         n = self.degree()
         k = self.base_ring()
         if n == 0:
-            self._one = vector(k, [])
+            self._one = matrix(k, 1, n)
             return True
         B1 = reduce(lambda x, y: x.augment(y),
                     self._table, Matrix(k, n, 0))
@@ -564,7 +564,7 @@ def is_unitary(self):
         # n times n identity matrix:
         kone = k.one()
         kzero = k.zero()
-        v = vector(k, (n - 1) * ([kone] + n * [kzero]) + [kone])
+        v = matrix(k, 1, n**2, (n - 1) * ([kone] + n * [kzero]) + [kone])
         try:
             sol1 = B1.solve_left(v)
             sol2 = B2.solve_left(v)
@@ -719,8 +719,8 @@ def quotient_map(self, ideal):
         pivots = f.pivot_rows()
         table = []
         for p in pivots:
-            v = vector(k, self.degree())
-            v[p] = 1
+            v = matrix(k, 1, self.degree())
+            v[0,p] = 1
             v = self.element_class(self, v)
             table.append(f.solve_right(v.matrix() * f))
         B = FiniteDimensionalAlgebra(k, table)