X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=8219c5b4ff32b7acdb55de21aac53f657a11b20f;hb=e0031c84e8b7d89071f052f44d1cf28b2370b161;hp=c822d14f6d0900a8b90c24d377fb31196003e0e8;hpb=cda12a746b75b33381325e31afab44c6e9b85950;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index c822d14..8219c5b 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -2111,6 +2111,20 @@ class BilinearFormEJA(RationalBasisEuclideanJordanAlgebra):
         sage: J0.multiplication_table() == J0.multiplication_table()
         True
 
+    An error is raised if the matrix `B` does not correspond to a
+    positive-definite bilinear form::
+
+        sage: B = matrix.random(QQ,2,3)
+        sage: J = BilinearFormEJA(B)
+        Traceback (most recent call last):
+        ...
+        ValueError: bilinear form is not positive-definite
+        sage: B = matrix.zero(QQ,3)
+        sage: J = BilinearFormEJA(B)
+        Traceback (most recent call last):
+        ...
+        ValueError: bilinear form is not positive-definite
+
     TESTS:
 
     We can create a zero-dimensional algebra::
@@ -2151,7 +2165,7 @@ class BilinearFormEJA(RationalBasisEuclideanJordanAlgebra):
         n = B.nrows()
 
         if not B.is_positive_definite():
-            raise TypeError("matrix B is not positive-definite")
+            raise ValueError("bilinear form is not positive-definite")
 
         V = VectorSpace(field, n)
         mult_table = [[V.zero() for j in range(n)] for i in range(n)]
@@ -2181,6 +2195,31 @@ class BilinearFormEJA(RationalBasisEuclideanJordanAlgebra):
     def _max_random_instance_size():
         return 5
 
+    @classmethod
+    def random_instance(cls, field=AA, **kwargs):
+        """
+        Return a random instance of this algebra.
+        """
+        n = ZZ.random_element(cls._max_random_instance_size() + 1)
+        if n == 0:
+            # Special case needed since we use (n-1) below.
+            B = matrix.identity(field, 0)
+            return cls(B, field, **kwargs)
+
+        B11 = matrix.identity(field,1)
+        M = matrix.random(field, n-1)
+        I = matrix.identity(field, n-1)
+        alpha = field.zero()
+        while alpha.is_zero():
+            alpha = field.random_element().abs()
+        B22 = M.transpose()*M + alpha*I
+
+        from sage.matrix.special import block_matrix
+        B = block_matrix(2,2, [ [B11,   ZZ(0) ],
+                                [ZZ(0), B22 ] ])
+
+        return cls(B, field, **kwargs)
+
     def inner_product(self, x, y):
         r"""
         Half of the trace inner product.
@@ -2200,16 +2239,11 @@ class BilinearFormEJA(RationalBasisEuclideanJordanAlgebra):
         paper::
 
             sage: set_random_seed()
-            sage: n = ZZ.random_element(2,5)
-            sage: M = matrix.random(QQ, max(0,n-1), algorithm='unimodular')
-            sage: B11 = matrix.identity(QQ,1)
-            sage: B22 = M.transpose()*M
-            sage: B = block_matrix(2,2,[ [B11,0  ],
-            ....:                        [0, B22 ] ])
-            sage: J = BilinearFormEJA(B)
+            sage: J = BilinearFormEJA.random_instance()
+            sage: n = J.dimension()
             sage: x = J.random_element()
             sage: y = J.random_element()
-            sage: x.inner_product(y) == (x*y).trace()/2
+            sage: (n == 1) or (x.inner_product(y) == (x*y).trace()/2)
             True
 
         """
@@ -2272,6 +2306,16 @@ class JordanSpinEJA(BilinearFormEJA):
         B = matrix.identity(field, n)
         super(JordanSpinEJA, self).__init__(B, field, **kwargs)
 
+    @classmethod
+    def random_instance(cls, field=AA, **kwargs):
+        """
+        Return a random instance of this type of algebra.
+
+        Needed here to override the implementation for ``BilinearFormEJA``.
+        """
+        n = ZZ.random_element(cls._max_random_instance_size() + 1)
+        return cls(n, field, **kwargs)
+
 
 class TrivialEJA(FiniteDimensionalEuclideanJordanAlgebra):
     """