# Why could the error term be sampled coefficient wise?

In SEAL homomorphic encryption library, it implements the BFV and CKKS. We know the error $$e\in R_q$$ which is a Guassian distribution. When sampling an error term $$e = \sum_{i=0}^{n-1} e_ix^i$$, it just samples $$e_i$$ from some discrete Guassain distribution over the integers.

However, it seems that the discrete Guassian distribution over high dimension lattice could not be sampled coefficient wise. What goes wrong ?