??situation where ideal carving out subspace is "automatically" principal ?? ... ??for some good reason ..... ???vs contrasting situations .... ??? ....

???"characteristic function" .... ???? ... (??"boolean" case ??? ...) ... ??"normalization" ??? ...

???pun on "character..." here ???? .... ????? .....

?? any interesting case of combining this (...) situation with situation where subspace carved out is subgroup ??? ..... ????? .... ??? "fourier analysis" ???? .... ????? ....

???"root of unity" .... ????

"x^n" .... ???? ?? vs "x^n-1" ... ??? ... ???? toric ????? .... ????....

??? "log(x^n)" ... ????? ..... = x*n ... ????....