eja: special subalgebra handling for Cartesian product EJAs.

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

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 68f1ce4cf8b5f07087e4474069ad4ebe5c6a4998..c9abada53cf3fbd3803601fa0e7b430a0b506fd1 100644 (file)
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -2,7 +2,8 @@ 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_element import (FiniteDimensionalEJAElement,
+                                 CartesianProductParentEJAElement)
 
 class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement):
     """
@@ -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)
@@ -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)
@@ -254,3 +266,41 @@ class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA):
 
 
     Element = FiniteDimensionalEJASubalgebraElement
+
+
+
+class FiniteDimensionalCartesianProductEJASubalgebraElement(FiniteDimensionalEJASubalgebraElement, 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:`FiniteDimensionalEJASubalgebraElement`, 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 FiniteDimensionalCartesianProductEJASubalgebra(FiniteDimensionalEJASubalgebra):
+    r"""
+    Subalgebras whose parents are Cartesian products. Exists only
+    to specify a special element class that will (in addition)
+    inherit from ``CartesianProductParentEJAElement``.
+    """
+    Element = FiniteDimensionalCartesianProductEJASubalgebraElement