matrix_algebra: put basis in the usual (row,column) order.

[sage.d.git] / mjo / matrix_algebra.py

diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py
index 94a8410f9929986a8737f9bbb846c04490751fe5..84aa8d28bb3de9e6797b9b0a209eb96c3a14dc22 100644 (file)
--- a/mjo/matrix_algebra.py
+++ b/mjo/matrix_algebra.py
@@ -18,7 +18,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement):
 
         EXAMPLES::
 
-            sage: M = MatrixAlgebra(QQbar,RDF,2)
+            sage: M = MatrixAlgebra(2, QQbar,RDF)
             sage: A = M.monomial((0,0,1)) + 4*M.monomial((0,1,1))
             sage: A
             +-----+-----+
@@ -50,7 +50,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement):
 
         EXAMPLES::
 
-            sage: MatrixAlgebra(ZZ,ZZ,2).zero()
+            sage: MatrixAlgebra(2,ZZ,ZZ).zero()
             +---+---+
             | 0 | 0 |
             +---+---+
@@ -71,7 +71,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement):
 
         EXAMPLES::
 
-            sage: A = MatrixAlgebra(ZZ,ZZ,2)
+            sage: A = MatrixAlgebra(2,ZZ,ZZ)
             sage: A([[1,2],[3,4]]).list()
             [1, 2, 3, 4]
 
@@ -88,7 +88,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement):
 
         EXAMPLES::
 
-            sage: M = MatrixAlgebra(ZZ,ZZ,2)([[1,2],[3,4]])
+            sage: M = MatrixAlgebra(2,ZZ,ZZ)([[1,2],[3,4]])
             sage: M[0,0]
             1
             sage: M[0,1]
@@ -117,7 +117,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement):
 
             sage: entries = MatrixSpace(ZZ,2)
             sage: scalars = ZZ
-            sage: M = MatrixAlgebra(entries, scalars, 2)
+            sage: M = MatrixAlgebra(2, entries, scalars)
             sage: I = entries.one()
             sage: Z = entries.zero()
             sage: M([[I,Z],[Z,I]]).trace()
@@ -139,7 +139,7 @@ class MatrixAlgebraElement(IndexedFreeModuleElement):
 
             sage: set_random_seed()
             sage: entries = QuaternionAlgebra(QQ,-1,-1)
-            sage: M = MatrixAlgebra(entries, QQ, 3)
+            sage: M = MatrixAlgebra(3, entries, QQ)
             sage: M.random_element().matrix_space() == M
             True
 
@@ -167,7 +167,7 @@ class MatrixAlgebra(CombinatorialFreeModule):
 
     The existence of a unit element is determined dynamically::
 
-        sage: MatrixAlgebra(ZZ,ZZ,2).one()
+        sage: MatrixAlgebra(2,ZZ,ZZ).one()
         +---+---+
         | 1 | 0 |
         +---+---+
@@ -177,7 +177,7 @@ class MatrixAlgebra(CombinatorialFreeModule):
     """
     Element = MatrixAlgebraElement
 
-    def __init__(self, entry_algebra, scalars, n, prefix="A", **kwargs):
+    def __init__(self, n, entry_algebra, scalars, prefix="A", **kwargs):
 
         category = MagmaticAlgebras(scalars).FiniteDimensional()
         category = category.WithBasis()
@@ -198,14 +198,16 @@ class MatrixAlgebra(CombinatorialFreeModule):
         # sticking a "1" in each position doesn't give us a basis for
         # the space. We actually need to stick each of e0, e1, ...  (a
         # basis for the entry algebra itself) into each position.
-        I = range(n)
-        J = range(n)
         self._entry_algebra = entry_algebra
-        entry_basis = entry_algebra.gens()
 
-        basis_indices = [(i,j,e) for i in range(n)
-                                 for j in range(n)
-                                 for e in entry_algebra.gens()]
+        # Needs to make the (overridden) method call when, for example,
+        # the entry algebra is the complex numbers and its gens() method
+        # lies to us.
+        entry_basis = self.entry_algebra_gens()
+
+        basis_indices = [(i,j,e) for j in range(n)
+                                 for i in range(n)
+                                 for e in entry_basis]
 
         super().__init__(scalars,
                          basis_indices,
@@ -227,6 +229,17 @@ class MatrixAlgebra(CombinatorialFreeModule):
         """
         return self._entry_algebra
 
+    def entry_algebra_gens(self):
+        r"""
+        Return a tuple of the generators of (that is, a basis for) the
+        entries of this matrix algebra.
+
+        This can be overridden in subclasses to work around the
+        inconsistency in the ``gens()`` methods of the various
+        entry algebras.
+        """
+        return self.entry_algebra().gens()
+
     def nrows(self):
         return self._nrows
     ncols = nrows
@@ -245,7 +258,7 @@ class MatrixAlgebra(CombinatorialFreeModule):
             sage: e = O.gens()
             sage: e[2]*e[1]
             -e3
-            sage: A = MatrixAlgebra(O,QQ,2)
+            sage: A = MatrixAlgebra(2,O,QQ)
             sage: A.product_on_basis( (0,0,e[2]), (0,0,e[1]) )
             +-----+---+
             | -e3 | 0 |
@@ -278,7 +291,7 @@ class MatrixAlgebra(CombinatorialFreeModule):
 
         EXAMPLES::
 
-            sage: A = MatrixAlgebra(QQbar, ZZ, 2)
+            sage: A = MatrixAlgebra(2, QQbar, ZZ)
             sage: A.from_list([[0,I],[-I,0]])
             +----+---+
             | 0  | I |