- sage: actual = (alpha*x).quadratic_representation()
- sage: expected = (alpha^2)*x.quadratic_representation()
- sage: actual == expected
+ sage: (alpha*x).quadratic_representation() == (alpha^2)*Qx
+ True
+
+ Property 3:
+
+ sage: not x.is_invertible() or (
+ ....: Qx*x.inverse().vector() == x.vector() )
+ True
+
+ sage: not x.is_invertible() or (
+ ....: Qx.inverse()
+ ....: ==
+ ....: x.inverse().quadratic_representation() )
+ True
+
+ sage: Qxy*(J.one().vector()) == (x*y).vector()
+ True
+
+ Property 4:
+
+ sage: not x.is_invertible() or (
+ ....: x.quadratic_representation(x.inverse())*Qx
+ ....: == Qx*x.quadratic_representation(x.inverse()) )
+ True
+
+ sage: not x.is_invertible() or (
+ ....: x.quadratic_representation(x.inverse())*Qx
+ ....: ==
+ ....: 2*x.operator_matrix()*Qex - Qx )
+ True
+
+ sage: 2*x.operator_matrix()*Qex - Qx == Lxx