eja: rename operator_inner_product -> operator_trace inner_product.

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

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 68f1ce4cf8b5f07087e4474069ad4ebe5c6a4998..97a79789750197fafbb39e8e3fd9e1a7710e98d3 100644 (file)
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -1,10 +1,11 @@
 from sage.matrix.constructor import matrix
 from sage.misc.cachefunc import cached_method
 
-from mjo.eja.eja_algebra import FiniteDimensionalEJA
-from mjo.eja.eja_element import FiniteDimensionalEJAElement
+from mjo.eja.eja_algebra import EJA
+from mjo.eja.eja_element import (EJAElement,
+                                 CartesianProductParentEJAElement)
 
-class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement):
+class EJASubalgebraElement(EJAElement):
     """
     SETUP::
 
@@ -15,7 +16,6 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement):
     The matrix representation of an element in the subalgebra is
     the same as its matrix representation in the superalgebra::
 
-        sage: set_random_seed()
         sage: x = random_eja(field=QQ,orthonormalize=False).random_element()
         sage: A = x.subalgebra_generated_by(orthonormalize=False)
         sage: y = A.random_element()
@@ -28,11 +28,10 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement):
     works like it does in the superalgebra, even if we orthonormalize
     our basis::
 
-        sage: set_random_seed()
-        sage: x = random_eja(field=AA).random_element()
-        sage: A = x.subalgebra_generated_by(orthonormalize=True)
-        sage: y = A.random_element()
-        sage: y.operator()(A.one()) == y
+        sage: x = random_eja(field=AA).random_element()           # long time
+        sage: A = x.subalgebra_generated_by(orthonormalize=True)  # long time
+        sage: y = A.random_element()                              # long time
+        sage: y.operator()(A.one()) == y                          # long time
         True
 
     """
@@ -71,7 +70,6 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement):
 
         We can convert back and forth faithfully::
 
-            sage: set_random_seed()
             sage: J = random_eja(field=QQ, orthonormalize=False)
             sage: x = J.random_element()
             sage: A = x.subalgebra_generated_by(orthonormalize=False)
@@ -90,7 +88,7 @@ class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement):
 
 
 
-class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
+class EJASubalgebra(EJA):
     """
     A subalgebra of an EJA with a given basis.
 
@@ -99,7 +97,7 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
         sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
         ....:                                  JordanSpinEJA,
         ....:                                  RealSymmetricEJA)
-        sage: from mjo.eja.eja_subalgebra import FiniteDimensionalEJASubalgebra
+        sage: from mjo.eja.eja_subalgebra import EJASubalgebra
 
     EXAMPLES:
 
@@ -111,11 +109,11 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
         ....:                    [0,0] ])
         sage: E22 = matrix(AA, [ [0,0],
         ....:                    [0,1] ])
-        sage: K1 = FiniteDimensionalEJASubalgebra(J, (J(E11),), associative=True)
+        sage: K1 = EJASubalgebra(J, (J(E11),), associative=True)
         sage: K1.one().to_matrix()
         [1 0]
         [0 0]
-        sage: K2 = FiniteDimensionalEJASubalgebra(J, (J(E22),), associative=True)
+        sage: K2 = EJASubalgebra(J, (J(E22),), associative=True)
         sage: K2.one().to_matrix()
         [0 0]
         [0 1]
@@ -187,7 +185,7 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
         SETUP::
 
             sage: from mjo.eja.eja_algebra import RealSymmetricEJA
-            sage: from mjo.eja.eja_subalgebra import FiniteDimensionalEJASubalgebra
+            sage: from mjo.eja.eja_subalgebra import EJASubalgebra
 
         EXAMPLES::
 
@@ -197,7 +195,7 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
             ....:                  [1,0,0] ])
             sage: x = J(X)
             sage: basis = ( x, x^2 ) # x^2 is the identity matrix
-            sage: K = FiniteDimensionalEJASubalgebra(J,
+            sage: K = EJASubalgebra(J,
             ....:                                    basis,
             ....:                                    associative=True,
             ....:                                    orthonormalize=False)
@@ -210,7 +208,17 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
 
         """
         if elt in self.superalgebra():
-            return super()._element_constructor_(elt.to_matrix())
+            # If the subalgebra is trivial, its _matrix_span will be empty
+            # but we still want to be able convert the superalgebra's zero()
+            # element into the subalgebra's zero() element. There's no great
+            # workaround for this because sage checks that your basis is
+            # linearly-independent everywhere, so we can't just give it a
+            # basis consisting of the zero element.
+            m = elt.to_matrix()
+            if self.is_trivial() and m.is_zero():
+                return self.zero()
+            else:
+                return super()._element_constructor_(m)
         else:
             return super()._element_constructor_(elt)
 
@@ -227,6 +235,10 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
         r"""
         Return the embedding from this subalgebra into the superalgebra.
 
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import HadamardEJA
+
         EXAMPLES::
 
             sage: J = HadamardEJA(4)
@@ -244,13 +256,52 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
             True
 
         """
-        from mjo.eja.eja_operator import FiniteDimensionalEJAOperator
+        from mjo.eja.eja_operator import EJAOperator
         mm = self._module_morphism(lambda j: self.superalgebra()(self.monomial(j).to_matrix()),
                                    codomain=self.superalgebra())
-        return FiniteDimensionalEJAOperator(self,
+        return EJAOperator(self,
                                             self.superalgebra(),
                                             mm.matrix())
 
 
 
-    Element = FiniteDimensionalEJASubalgebraElement
+    Element = EJASubalgebraElement
+
+
+
+class CartesianProductEJASubalgebraElement(EJASubalgebraElement,
+                                           CartesianProductParentEJAElement):
+    r"""
+    The class for elements that both belong to a subalgebra and
+    have a Cartesian product algebra as their parent. By inheriting
+    :class:`CartesianProductParentEJAElement` in addition to
+    :class:`EJASubalgebraElement`, we allow the
+    ``to_matrix()`` method to be overridden with the version that
+    works on Cartesian products.
+
+    SETUP::
+
+        sage: from mjo.eja.eja_algebra import (HadamardEJA,
+        ....:                                  RealSymmetricEJA)
+
+    TESTS:
+
+    This used to fail when ``subalgebra_idempotent()`` tried to
+    embed the subalgebra element back into the original EJA::
+
+        sage: J1 = HadamardEJA(0, field=QQ, orthonormalize=False)
+        sage: J2 = RealSymmetricEJA(2, field=QQ, orthonormalize=False)
+        sage: J = cartesian_product([J1,J2])
+        sage: J.one().subalgebra_idempotent() == J.one()
+        True
+
+    """
+    pass
+
+class CartesianProductEJASubalgebra(EJASubalgebra):
+    r"""
+    Subalgebras whose parents are Cartesian products. Exists only
+    to specify a special element class that will (in addition)
+    inherit from ``CartesianProductParentEJAElement``.
+    """
+    Element = CartesianProductEJASubalgebraElement