Editing Symmetric algebra (section)

==Symmetric algebra of an affine space==
One can analogously construct the symmetric algebra on an [[affine space]]. The key difference is that the symmetric algebra of an affine space is not a graded algebra, but a [[filtered algebra]]: one can determine the degree of a polynomial on an affine space, but not its homogeneous parts.

For instance, given a linear polynomial on a vector space, one can determine its constant part by evaluating at 0. On an affine space, there is no distinguished point, so one cannot do this (choosing a point turns an affine space into a vector space).