eja: add apply_univariate_polynomial() for elements and use it in a test.

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index c4b085089462c87be5db2ef8301583193c000770..da1145d1851c91cf1f7faef014ba8a519d5d3fcf 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -315,6 +315,49 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 return A( (self.operator_matrix()**(n-1))*self.vector() )
 
 
+        def apply_univariate_polynomial(self, p):
+            """
+            Apply the univariate polynomial ``p`` to this element.
+
+            A priori, SageMath won't allow us to apply a univariate
+            polynomial to an element of an EJA, because we don't know
+            that EJAs are rings (they are usually not associative). Of
+            course, we know that EJAs are power-associative, so the
+            operation is ultimately kosher. This function sidesteps
+            the CAS to get the answer we want and expect.
+
+            EXAMPLES::
+
+                sage: R = PolynomialRing(QQ, 't')
+                sage: t = R.gen(0)
+                sage: p = t^4 - t^3 + 5*t - 2
+                sage: J = RealCartesianProductEJA(5)
+                sage: J.one().apply_univariate_polynomial(p) == 3*J.one()
+                True
+
+            TESTS:
+
+            We should always get back an element of the algebra::
+
+                sage: set_random_seed()
+                sage: p = PolynomialRing(QQ, 't').random_element()
+                sage: J = random_eja()
+                sage: x = J.random_element()
+                sage: x.apply_univariate_polynomial(p) in J
+                True
+
+            """
+            if len(p.variables()) > 1:
+                raise ValueError("not a univariate polynomial")
+            P = self.parent()
+            R = P.base_ring()
+            # Convert the coeficcients to the parent's base ring,
+            # because a priori they might live in an (unnecessarily)
+            # larger ring for which P.sum() would fail below.
+            cs = [ R(c) for c in p.coefficients(sparse=False) ]
+            return P.sum( cs[k]*(self**k) for k in range(len(cs)) )
+
+
         def characteristic_polynomial(self):
             """
             Return my characteristic polynomial (if I'm a regular
@@ -724,6 +767,14 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: bool(actual == expected)
                 True
 
+            The minimal polynomial should always kill its element::
+
+                sage: set_random_seed()
+                sage: x = random_eja().random_element()
+                sage: p = x.minimal_polynomial()
+                sage: x.apply_univariate_polynomial(p)
+                0
+
             """
             V = self.span_of_powers()
             assoc_subalg = self.subalgebra_generated_by()