Ticket #12733: trac_12733_symbolic_matrix_norm.patch

sage/matrix/matrix2.pyx

@@ -10284 +10284 @@
             0.0
             sage: a.norm(Infinity) == a.norm(1)
             True
+
+        Norms of symbolic matrices can also be calculated, except for the norm p=2.  ::
+
+            sage: var('a, b, c, d')
+            (a, b, c, d)
+            sage: m = matrix(SR, [[a, b], [c, d]])
+            sage: m
+            [a b]
+            [c d]
+            sage: m.norm(1)
+            a + c
+            sage: m.norm(infinity)
+            a + b
+            sage: m.norm('frob')
+            sqrt(a^2 + b^2 + c^2 + d^2)
         """ 
 
+        from sage.symbolic.all import SR
+
         if self._nrows == 0 or self._ncols == 0:
             return RDF(0)
         
         # 2-norm: 
         if p == 2:
+            if self.base_ring() == SR:
+                raise NotImplementedError 
             A = self.change_ring(CDF)
             A = A.conjugate().transpose() * A
             U, S, V = A.SVD() 
             return max(S.list()).real().sqrt() 
 
-        A = self.apply_map(abs).change_ring(RDF)
+        if self.base_ring() != SR:
+            A = self.apply_map(abs).change_ring(RDF)
+        else:
+            A = self
 
         # 1-norm: largest column-sum 
-        if p == 1: 
+        if p == 1:
             A = A.transpose() 
             return max([sum(i) for i in list(A)]) 
 

sage/misc/functional.py

@@ -1136 +1136 @@
     The norm of matrices::
 
         sage: z = 1 + 2*I
-        sage: norm(matrix([[z]]))
+        sage: matrix(CC, [[z]]).norm()
         2.2360679775
         sage: M = matrix(ZZ, [[1,2,4,3], [-1,0,3,-10]])
         sage: norm(M)