eja: minor improvement to the algebra one() method.

[sage.d.git] / mjo / eja / eja_algebra.py

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index def2028a6a29a0d64733c8ed5c8a38e226c37f81..222b12c9ea0074792c807471eb546d1c45282e71 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -217,7 +217,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         return self.from_vector(coords)
 
     @staticmethod
-    def _max_test_case_size():
+    def _max_random_instance_size():
         """
         Return an integer "size" that is an upper bound on the size of
         this algebra when it is used in a random test
@@ -233,7 +233,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         interpreted to be far less than the dimension) should override
         with a smaller number.
         """
-        return 5
+        raise NotImplementedError
 
     def _repr_(self):
         """
@@ -599,19 +599,20 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         # appeal to the "long vectors" isometry.
         oper_vecs = [ _mat2vec(g.operator().matrix()) for g in self.gens() ]
 
-        # Now we use basis linear algebra to find the coefficients,
+        # Now we use basic linear algebra to find the coefficients,
         # of the matrices-as-vectors-linear-combination, which should
         # work for the original algebra basis too.
-        A = matrix.column(self.base_ring(), oper_vecs)
+        A = matrix(self.base_ring(), oper_vecs)
 
         # We used the isometry on the left-hand side already, but we
         # still need to do it for the right-hand side. Recall that we
         # wanted something that summed to the identity matrix.
         b = _mat2vec( matrix.identity(self.base_ring(), self.dimension()) )
 
-        # Now if there's an identity element in the algebra, this should work.
-        coeffs = A.solve_right(b)
-        return self.linear_combination(zip(self.gens(), coeffs))
+        # Now if there's an identity element in the algebra, this
+        # should work. We solve on the left to avoid having to
+        # transpose the matrix "A".
+        return self.from_vector(A.solve_left(b))
 
 
     def peirce_decomposition(self, c):
@@ -839,12 +840,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         Beware, this will crash for "most instances" because the
         constructor below looks wrong.
         """
-        if cls is TrivialEJA:
-            # The TrivialEJA class doesn't take an "n" argument because
-            # there's only one.
-            return cls(field)
-
-        n = ZZ.random_element(cls._max_test_case_size() + 1)
+        n = ZZ.random_element(cls._max_random_instance_size() + 1)
         return cls(n, field, **kwargs)
 
     @cached_method
@@ -1094,7 +1090,7 @@ class RationalBasisEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebr
 
 class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
     @staticmethod
-    def _max_test_case_size():
+    def _max_random_instance_size():
         # Play it safe, since this will be squared and the underlying
         # field can have dimension 4 (quaternions) too.
         return 2
@@ -1306,7 +1302,7 @@ class RealSymmetricEJA(RealMatrixEuclideanJordanAlgebra):
     The dimension of this algebra is `(n^2 + n) / 2`::
 
         sage: set_random_seed()
-        sage: n_max = RealSymmetricEJA._max_test_case_size()
+        sage: n_max = RealSymmetricEJA._max_random_instance_size()
         sage: n = ZZ.random_element(1, n_max)
         sage: J = RealSymmetricEJA(n)
         sage: J.dimension() == (n^2 + n)/2
@@ -1389,7 +1385,7 @@ class RealSymmetricEJA(RealMatrixEuclideanJordanAlgebra):
 
 
     @staticmethod
-    def _max_test_case_size():
+    def _max_random_instance_size():
         return 4 # Dimension 10
 
 
@@ -1435,7 +1431,7 @@ class ComplexMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
         Embedding is a homomorphism (isomorphism, in fact)::
 
             sage: set_random_seed()
-            sage: n_max = ComplexMatrixEuclideanJordanAlgebra._max_test_case_size()
+            sage: n_max = ComplexMatrixEuclideanJordanAlgebra._max_random_instance_size()
             sage: n = ZZ.random_element(n_max)
             sage: F = QuadraticField(-1, 'I')
             sage: X = random_matrix(F, n)
@@ -1587,7 +1583,7 @@ class ComplexHermitianEJA(ComplexMatrixEuclideanJordanAlgebra):
     The dimension of this algebra is `n^2`::
 
         sage: set_random_seed()
-        sage: n_max = ComplexHermitianEJA._max_test_case_size()
+        sage: n_max = ComplexHermitianEJA._max_random_instance_size()
         sage: n = ZZ.random_element(1, n_max)
         sage: J = ComplexHermitianEJA(n)
         sage: J.dimension() == n^2
@@ -1731,7 +1727,7 @@ class QuaternionMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
         Embedding is a homomorphism (isomorphism, in fact)::
 
             sage: set_random_seed()
-            sage: n_max = QuaternionMatrixEuclideanJordanAlgebra._max_test_case_size()
+            sage: n_max = QuaternionMatrixEuclideanJordanAlgebra._max_random_instance_size()
             sage: n = ZZ.random_element(n_max)
             sage: Q = QuaternionAlgebra(QQ,-1,-1)
             sage: X = random_matrix(Q, n)
@@ -1890,7 +1886,7 @@ class QuaternionHermitianEJA(QuaternionMatrixEuclideanJordanAlgebra):
     The dimension of this algebra is `2*n^2 - n`::
 
         sage: set_random_seed()
-        sage: n_max = QuaternionHermitianEJA._max_test_case_size()
+        sage: n_max = QuaternionHermitianEJA._max_random_instance_size()
         sage: n = ZZ.random_element(1, n_max)
         sage: J = QuaternionHermitianEJA(n)
         sage: J.dimension() == 2*(n^2) - n
@@ -2056,6 +2052,10 @@ class HadamardEJA(RationalBasisEuclideanJordanAlgebra):
                                           **kwargs)
         self.rank.set_cache(n)
 
+    @staticmethod
+    def _max_random_instance_size():
+        return 5
+
     def inner_product(self, x, y):
         """
         Faster to reimplement than to use natural representations.
@@ -2166,6 +2166,10 @@ class BilinearFormEJA(RationalBasisEuclideanJordanAlgebra):
                                               **kwargs)
         self.rank.set_cache(min(n,2))
 
+    @staticmethod
+    def _max_random_instance_size():
+        return 5
+
     def inner_product(self, x, y):
         r"""
         Half of the trace inner product.
@@ -2297,6 +2301,11 @@ class TrivialEJA(FiniteDimensionalEuclideanJordanAlgebra):
         # largest subalgebra generated by any element.
         self.rank.set_cache(0)
 
+    @classmethod
+    def random_instance(cls, field=AA, **kwargs):
+        # We don't take a "size" argument so the superclass method is
+        # inappropriate for us.
+        return cls(field, **kwargs)
 
 class DirectSumEJA(FiniteDimensionalEuclideanJordanAlgebra):
     r"""