eja: demonstration for https://trac.sagemath.org/ticket/31421.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 55b8207ddc3f881e8d98f245bf0275bc4b947334..e6a60929055fccb28fd86765e7743a028b1904a1 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -2690,7 +2690,8 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
 
     SETUP::
 
-        sage: from mjo.eja.eja_algebra import (CartesianProductEJA,
+        sage: from mjo.eja.eja_algebra import (random_eja,
+        ....:                                  CartesianProductEJA,
         ....:                                  HadamardEJA,
         ....:                                  JordanSpinEJA,
         ....:                                  RealSymmetricEJA)
@@ -2740,6 +2741,19 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
         ...
         ValueError: all factors must share the same base field
 
+    The "cached" Jordan and inner products are the componentwise
+    ones::
+
+        sage: set_random_seed()
+        sage: J1 = random_eja()
+        sage: J2 = random_eja()
+        sage: J = cartesian_product([J1,J2])
+        sage: x,y = J.random_elements(2)
+        sage: x*y == J.cartesian_jordan_product(x,y)
+        True
+        sage: x.inner_product(y) == J.cartesian_inner_product(x,y)
+        True
+
     """
     def __init__(self, modules, **kwargs):
         CombinatorialFreeModule_CartesianProduct.__init__(self,
@@ -2765,15 +2779,10 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
         # Use whatever category the superclass came up with. Usually
         # some join of the EJA and Cartesian product
         # categories. There's no need to check the field since it
-        # already came from an EJA. Likewise the axioms are guaranteed
-        # to be satisfied. We can't orthonormalize by default because
-        # there's no way to pass "orthonormalize=False" to
-        # cartesian_product(...) when the base ring is QQ and
-        # orthonormalizing would give us irrational entries.
+        # already came from an EJA.
         #
-        # TODO: create a separate constructor that is capable of
-        # orthonormalizing and is only used by the cartesian_product()
-        # thingy.
+        # If you want the basis to be orthonormalized, orthonormalize
+        # the factors.
         FiniteDimensionalEJA.__init__(self,
                                       basis,
                                       jordan_product,
@@ -2783,16 +2792,6 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
                                       check_field=False,
                                       check_axioms=False,
                                       category=self.category())
-        # TODO:
-        #
-        # Initialize the FDEJA class, too. Does this override the
-        # initialization that we did for the
-        # CombinatorialFreeModule_CartesianProduct class? If not, we
-        # will probably have to duplicate some of the work (i.e. one
-        # of the constructors).  Since the CartesianProduct one is
-        # smaller, that makes the most sense to copy/paste if it comes
-        # down to that.
-        #
 
         self.rank.set_cache(sum(J.rank() for J in modules))
 
@@ -2867,8 +2866,11 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
 
         """
         Ji = self.cartesian_factors()[i]
-        # Requires the fix on Trac 31421/31422 to work!
-        Pi = super().cartesian_projection(i)
+
+        # Required until https://trac.sagemath.org/ticket/31421 is fixed.
+        Pi = self.module_morphism(lambda j_t: Ji.monomial(j_t[1])
+                                  if i == j_t[0] else Ji.zero(),
+                                  codomain=Ji)
         return FiniteDimensionalEJAOperator(self,Ji,Pi.matrix())
 
     @cached_method
@@ -2975,8 +2977,9 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
 
         """
         Ji = self.cartesian_factors()[i]
-        # Requires the fix on Trac 31421/31422 to work!
-        Ei = super().cartesian_embedding(i)
+        # Required until https://trac.sagemath.org/ticket/31421 is fixed.
+        Ei = Ji.module_morphism(lambda t: self.monomial((i, t)),
+                                codomain=self)
         return FiniteDimensionalEJAOperator(Ji,self,Ei.matrix())