eja: override product_on_basis() for Cartesian products.

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index db1e63d1b56ade8d29a33d256ee7e1f2b5e97d31..00de418a36cca4ecdf7bd6c6e70daf7cc8531344 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -3196,6 +3196,47 @@ class CartesianProductEJA(CombinatorialFreeModule_CartesianProduct,
         self.one.set_cache(self._cartesian_product_of_elements(ones))
         self.rank.set_cache(sum(J.rank() for J in algebras))
 
+    def product_on_basis(self, i, j):
+        r"""
+        Return the product of the monomials indexed by ``i`` and ``j``.
+
+        This overrides the superclass method because here, both ``i``
+        and ``j`` will be ordered pairs.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
+            ....:                                  JordanSpinEJA,
+            ....:                                  RealSymmetricEJA)
+
+        TESTS::
+
+            sage: J1 = RealSymmetricEJA(2,field=QQ,orthonormalize=False)
+            sage: J2 = ComplexHermitianEJA(0,field=QQ,orthonormalize=False)
+            sage: J3 = JordanSpinEJA(2,field=QQ,orthonormalize=False)
+            sage: J = cartesian_product([J1,J2,J3])
+            sage: x = sum(J.gens())
+            sage: x*J.one()
+            e(0, 0) + e(0, 1) + e(0, 2) + e(2, 0) + e(2, 1)
+            sage: x*x
+            2*e(0, 0) + 2*e(0, 1) + 2*e(0, 2) + 2*e(2, 0) + 2*e(2, 1)
+
+        """
+        factor = i[0]
+        assert(j[0] == i[0])
+        n = self.cartesian_factors()[factor].dimension()
+
+        # The superclass method indexes into a matrix, so we have to
+        # turn the tuples i and j into integers. This is easy enough
+        # given that the first coordinate of i and j corresponds to
+        # the factor, and the second coordinate corresponds to the
+        # index of the generator within that factor. And of course
+        # we should never be multiplying two elements from different
+        # factors.
+        l = n*factor + i[1]
+        m = n*factor + j[1]
+        super().product_on_basis(l, m)
+
     def matrix_space(self):
         r"""
         Return the space that our matrix basis lives in as a Cartesian