+def is_full_space(K):
+ r"""
+ Return whether or not this cone is equal to its ambient vector space.
+
+ OUTPUT:
+
+ ``True`` if this cone is the entire vector space and ``False``
+ otherwise.
+
+ EXAMPLES:
+
+ A ray in two dimensions is not equal to the entire space::
+
+ sage: K = Cone([(1,0)])
+ sage: is_full_space(K)
+ False
+
+ Neither is the nonnegative orthant::
+
+ sage: K = Cone([(1,0),(0,1)])
+ sage: is_full_space(K)
+ False
+
+ The right half-space contains a vector subspace, but it is still not
+ equal to the entire plane::
+
+ sage: K = Cone([(1,0),(-1,0),(0,1)])
+ sage: is_full_space(K)
+ False
+
+ But if we include nonnegative sums from both axes, then the resulting
+ cone is the entire two-dimensional space::
+
+ sage: K = Cone([(1,0),(-1,0),(0,1),(0,-1)])
+ sage: is_full_space(K)
+ True
+
+ """
+ return K.linear_subspace() == K.lattice().vector_space()
+
+