Let E be a set of distinct nonzero evaluation points. The polynomial phi(T)=product over s in E of (1-T/s) equals one at zero and zero at every point in E. Its degree is |E|; when E is empty, phi=1. If a term uses an outside-group coordinate only at those points, multiplying it by phi removes those unwanted dependencies while leaving its value at zero unchanged. Example: E={2,3} gives (1-T/2)(1-T/3), a degree-two multiplier. Many incompatible points mean high degree, so the construction must first ensure that each term has only a few of them.