trac #27937. fix functorial construction of monoid algebras

src/sage/categories/sets_cat.py

@@ -2470,11 +2470,29 @@ def construction(self):
                 EXAMPLES::
 
                     sage: A = GroupAlgebra(KleinFourGroup(), QQ)
-                    sage: A.construction()
+                    sage: F, arg = A.construction(); F, arg
                     (GroupAlgebraFunctor, Rational Field)
+                    sage: F(arg) is A
+                    True
+
+                This also works for structures such as monoid algebras (see
+                :trac:`27937`)::
+
+                    sage: A = FreeAbelianMonoid('x,y').algebra(QQ)
+                    sage: F, arg = A.construction(); F, arg
+                    (The algebra functorial construction,
+                     Free abelian monoid on 2 generators (x, y))
+                    sage: F(arg) is A
+                    True
                 """
-                from sage.categories.algebra_functor import GroupAlgebraFunctor
-                return GroupAlgebraFunctor(self.group()), self.base_ring()
+                from sage.categories.algebra_functor import (
+                        GroupAlgebraFunctor, AlgebraFunctor)
+                try:
+                    group = self.group()
+                except AttributeError:
+                    return (AlgebraFunctor(self.base_ring()),
+                            self.basis().keys())
+                return GroupAlgebraFunctor(group), self.base_ring()
 
             def _repr_(self):
                 r"""

src/sage/matrix/matrix2.pyx

@@ -2426,6 +2426,12 @@ cdef class Matrix(Matrix1):
             sage: A._charpoly_df()
             x - 23
 
+        Test that :trac:`27937` is fixed::
+
+            sage: R = FreeAbelianMonoid('u,v').algebra(QQ)
+            sage: matrix(4, 4, lambda i, j: R.an_element())._charpoly_df()
+            B[1]*x^4 - 4*B[u]*x^3
+
         .. NOTE::
 
             The key feature of this implementation is that it is division-free.
@@ -2457,7 +2463,7 @@ cdef class Matrix(Matrix1):
         # test for 0 x n or m x 0 matrices.
         #
         if n == 0:
-            return S(1)
+            return S.one()
 
         # In the notation of Algorithm 3.1,
         #
@@ -2474,9 +2480,9 @@ cdef class Matrix(Matrix1):
         #
         from sage.matrix.constructor import matrix
 
-        F = [R(0) for i in xrange(n)]
+        F = [R.zero()] * n
         cdef Matrix a = <Matrix> matrix(R, n-1, n)
-        A = [R(0) for i in xrange(n)]
+        A = [R.zero()] * n
 
         F[0] = - M.get_unsafe(0, 0)
         for t in xrange(1,n):
@@ -2495,7 +2501,7 @@ cdef class Matrix(Matrix1):
                 # Set a(p, t) to the product of M[<=t, <=t] * a(p-1, t)
                 #
                 for i in xrange(t+1):
-                    s = R(0)
+                    s = R.zero()
                     for j in xrange(t+1):
                         s = s + M.get_unsafe(i, j) * a.get_unsafe(p-1, j)
                     a.set_unsafe(p, i, s)
@@ -2506,7 +2512,7 @@ cdef class Matrix(Matrix1):
 
             # Set A[t, t] to be M[t, <=t] * a(p-1, t)
             #
-            s = R(0)
+            s = R.zero()
             for j in xrange(t+1):
                 s = s + M.get_unsafe(t, j) * a.get_unsafe(t-1, j)
             A[t] = s
@@ -2518,9 +2524,7 @@ cdef class Matrix(Matrix1):
                 F[p] = s - A[p]
 
         X = S.gen(0)
-        f = X ** n
-        for p in xrange(n):
-            f = f + F[p] * X ** (n-1-p)
+        f = X ** n + S(list(reversed(F)))
 
         return f