matrix_algebra.py: speed up __getitem__() and trace().

diff --git a/mjo/matrix_algebra.py b/mjo/matrix_algebra.py
index bc46c2a67c5dacb69387592d3593ecfd29123779..6817af1e046d65efeab32f45dc17396cd7fb4906 100644 (file)
--- a/mjo/matrix_algebra.py
+++ b/mjo/matrix_algebra.py
@@ -111,7 +111,12 @@ class MatrixAlgebraElement(IndexedFreeModuleElement):
 
         """
         i,j = indices
-        return self.rows()[i][j]
+        d = self.monomial_coefficients()
+        A = self.parent().entry_algebra()
+        return A.sum( d[k]*k[2]
+                      for k in d
+                      if k[0] == i and k[1] == j )
+
 
     def trace(self):
         r"""
@@ -136,8 +141,9 @@ class MatrixAlgebraElement(IndexedFreeModuleElement):
             [0 2]
 
         """
-        zero = self.parent().entry_algebra().zero()
-        return sum( (self[i,i] for i in range(self.nrows())), zero )
+        d = self.monomial_coefficients()
+        A = self.parent().entry_algebra()
+        return A.sum( d[k]*k[2] for k in d if k[0] == k[1] )
 
     def matrix_space(self):
         r"""
@@ -203,7 +209,7 @@ class MatrixAlgebra(CombinatorialFreeModule):
 
         self._nrows = n
 
-        # Since the scalar ring is real but the entries are not,
+        # Since the scalar ring is (say) real but the entries are not,
         # 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.