eja: move the TrivialEJA random_instance() into an override method.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 183e4cb978c233dbac31e321e855978309b27687..7089c50ab81c222b5be8ddca3c6667da9699cf98 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):
         """
@@ -839,12 +839,7 @@ 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 +1089,7 @@ 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 +1301,7 @@ 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 +1384,7 @@ class RealSymmetricEJA(RealMatrixEuclideanJordanAlgebra):
 
 
     @staticmethod
-    def _max_test_case_size():
+    def _max_random_instance_size():
         return 4 # Dimension 10
 
 
@@ -1435,7 +1430,7 @@ 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 +1582,7 @@ 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 +1726,7 @@ 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 +1885,7 @@ 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 +2051,10 @@ 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 +2165,10 @@ 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 +2300,11 @@ 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"""
@@ -2440,3 +2448,42 @@ class DirectSumEJA(FiniteDimensionalEuclideanJordanAlgebra):
         iota_left = lambda x: self.from_vector(I1*x.to_vector())
         iota_right = lambda x: self.from_vector(I2*+x.to_vector())
         return (iota_left, iota_right)
+
+    def inner_product(self, x, y):
+        r"""
+        The standard Cartesian inner-product.
+
+        We project ``x`` and ``y`` onto our factors, and add up the
+        inner-products from the subalgebras.
+
+        SETUP::
+
+
+            sage: from mjo.eja.eja_algebra import (HadamardEJA,
+            ....:                                  QuaternionHermitianEJA,
+            ....:                                  DirectSumEJA)
+
+        EXAMPLE::
+
+            sage: J1 = HadamardEJA(3)
+            sage: J2 = QuaternionHermitianEJA(2,QQ,normalize_basis=False)
+            sage: J = DirectSumEJA(J1,J2)
+            sage: x1 = J1.one()
+            sage: x2 = x1
+            sage: y1 = J2.one()
+            sage: y2 = y1
+            sage: x1.inner_product(x2)
+            3
+            sage: y1.inner_product(y2)
+            2
+            sage: J.one().inner_product(J.one())
+            5
+
+        """
+        (pi_left, pi_right) = self.projections()
+        x1 = pi_left(x)
+        x2 = pi_right(x)
+        y1 = pi_left(y)
+        y2 = pi_right(y)
+
+        return (x1.inner_product(y1) + x2.inner_product(y2))