eja: begin major overhaul of class hierarchy and naming.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index d99a7d873ab69e511186b7f0bc3ba3127a45c85a..6181f032e644423989cf135cd65eeafcb943585f 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -2,10 +2,10 @@ from sage.matrix.constructor import matrix
 from sage.modules.free_module import VectorSpace
 from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement
 
-from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator
+from mjo.eja.eja_operator import FiniteDimensionalEJAOperator
 from mjo.eja.eja_utils import _mat2vec
 
-class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
+class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
     """
     An element of a Euclidean Jordan algebra.
     """
@@ -444,8 +444,13 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         ALGORITHM:
 
-        We appeal to the quadratic representation as in Koecher's
-        Theorem 12 in Chapter III, Section 5.
+        In general we appeal to the quadratic representation as in
+        Koecher's Theorem 12 in Chapter III, Section 5. But if the
+        parent algebra's "characteristic polynomial of" coefficients
+        happen to be cached, then we use Proposition II.2.4 in Faraut
+        and Korányi which gives a formula for the inverse based on the
+        characteristic polynomial and the Cayley-Hamilton theorem for
+        Euclidean Jordan algebras::
 
         SETUP::
 
@@ -515,22 +520,19 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             ....:    x.operator().inverse()(J.one()) == x.inverse() )
             True
 
-        Proposition II.2.4 in Faraut and Korányi gives a formula for
-        the inverse based on the characteristic polynomial and the
-        Cayley-Hamilton theorem for Euclidean Jordan algebras::
+        Check that the fast (cached) and slow algorithms give the same
+        answer::
 
-            sage: set_random_seed()
-            sage: J = ComplexHermitianEJA(3)
-            sage: x = J.random_element()
-            sage: while not x.is_invertible():
-            ....:     x = J.random_element()
-            sage: r = J.rank()
-            sage: a = x.characteristic_polynomial().coefficients(sparse=False)
-            sage: expected  = (-1)^(r+1)/x.det()
-            sage: expected *= sum( a[i+1]*x^i for i in range(r) )
-            sage: x.inverse() == expected
+            sage: set_random_seed()                              # long time
+            sage: J = random_eja(field=QQ, orthonormalize=False) # long time
+            sage: x = J.random_element()                         # long time
+            sage: while not x.is_invertible():                   # long time
+            ....:     x = J.random_element()                     # long time
+            sage: slow = x.inverse()                             # long time
+            sage: _ = J._charpoly_coefficients()                 # long time
+            sage: fast = x.inverse()                             # long time
+            sage: slow == fast                                   # long time
             True
-
         """
         if not self.is_invertible():
             raise ValueError("element is not invertible")
@@ -587,6 +589,18 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: (not J.is_trivial()) and J.zero().is_invertible()
             False
 
+        Test that the fast (cached) and slow algorithms give the same
+        answer::
+
+            sage: set_random_seed()                              # long time
+            sage: J = random_eja(field=QQ, orthonormalize=False) # long time
+            sage: x = J.random_element()                         # long time
+            sage: slow = x.is_invertible()                       # long time
+            sage: _ = J._charpoly_coefficients()                 # long time
+            sage: fast = x.is_invertible()                       # long time
+            sage: slow == fast                                   # long time
+            True
+
         """
         if self.is_zero():
             if self.parent().is_trivial():
@@ -1108,10 +1122,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         P = self.parent()
         left_mult_by_self = lambda y: self*y
         L = P.module_morphism(function=left_mult_by_self, codomain=P)
-        return FiniteDimensionalEuclideanJordanAlgebraOperator(
-                 P,
-                 P,
-                 L.matrix() )
+        return FiniteDimensionalEJAOperator(P, P, L.matrix() )
 
 
     def quadratic_representation(self, other=None):
@@ -1356,8 +1367,8 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             True
 
         """
-        from mjo.eja.eja_element_subalgebra import FiniteDimensionalEuclideanJordanElementSubalgebra
-        return FiniteDimensionalEuclideanJordanElementSubalgebra(self, orthonormalize_basis)
+        from mjo.eja.eja_element_subalgebra import FiniteDimensionalEJAElementSubalgebra
+        return FiniteDimensionalEJAElementSubalgebra(self, orthonormalize_basis)
 
 
     def subalgebra_idempotent(self):