Most packages cannot handle more than a few polynomials. The constant should be exactly 0 and the regression coefficient should be 1. This is a perfectly valid regression. The program should not complain. Cryptic error messages are unacceptable here.
Singularity is the most fundamental regression error.
The program should inform you that ZERO has no variance or it should go ahead and compute the regression and report a correlation and total sum of squares of exactly 0. There are major differences in the way least squares is implemented, however. Here are some simple examples which exploit the differences and involve widely needed features. If you cannot set these examples up with the help of the user manual, call technical suport. That is a test in itself.