eja: add a doctest.

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

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 618e09cf41d58eec7ade00aca846eb9677f468ae..a8e16ec94aaa628f26533f654f33468f6a3eace4 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -257,6 +257,35 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
 
     def product_on_basis(self, i, j):
+        r"""
+        Returns the Jordan product of the `i` and `j`th basis elements.
+
+        This completely defines the Jordan product on the algebra, and
+        is used direclty by our superclass machinery to implement
+        :meth:`product`.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import random_eja
+
+        TESTS::
+
+            sage: set_random_seed()
+            sage: J = random_eja()
+            sage: n = J.dimension()
+            sage: ei = J.zero()
+            sage: ej = J.zero()
+            sage: ei_ej = J.zero()*J.zero()
+            sage: if n > 0:
+            ....:     i = ZZ.random_element(n)
+            ....:     j = ZZ.random_element(n)
+            ....:     ei = J.gens()[i]
+            ....:     ej = J.gens()[j]
+            ....:     ei_ej = J.product_on_basis(i,j)
+            sage: ei*ej == ei_ej
+            True
+
+        """
         # We only stored the lower-triangular portion of the
         # multiplication table.
         if j <= i:
@@ -447,13 +476,23 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: J(x.to_vector().column()) == x
             True
 
+        We cannot coerce elements between algebras just because their
+        matrix representations are compatible::
+
+            sage: J1 = HadamardEJA(3)
+            sage: J2 = JordanSpinEJA(3)
+            sage: J2(J1.one())
+            Traceback (most recent call last):
+            ...
+            ValueError: not an element of this algebra
+            sage: J1(J2.zero())
+            Traceback (most recent call last):
+            ...
+            ValueError: not an element of this algebra
+
         """
         msg = "not an element of this algebra"
-        if elt == 0:
-            # The superclass implementation of random_element()
-            # needs to be able to coerce "0" into the algebra.
-            return self.zero()
-        elif elt in self.base_ring():
+        if elt in self.base_ring():
             # Ensure that no base ring -> algebra coercion is performed
             # by this method. There's some stupidity in sage that would
             # otherwise propagate to this method; for example, sage thinks
@@ -461,9 +500,11 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             raise ValueError(msg)
 
         try:
+            # Try to convert a vector into a column-matrix...
             elt = elt.column()
         except (AttributeError, TypeError):
-            # Try to convert a vector into a column-matrix
+            # and ignore failure, because we weren't really expecting
+            # a vector as an argument anyway.
             pass
 
         if elt not in self.matrix_space():
@@ -477,7 +518,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         # could be QQ instead of QQbar.
         #
         # And, we also have to handle Cartesian product bases (when
-        # the matric basis consists of tuples) here. The "good news"
+        # the matrix basis consists of tuples) here. The "good news"
         # is that we're already converting everything to long vectors,
         # and that strategy works for tuples as well.
         #