Reed-Muller bar-product recursion (source code)

= Reed-Muller bar-product recursion
{c}

For $0<r<d$,
$$
\operatorname{RM}(d,r)
=\operatorname{RM}(d-1,r)
\mid\operatorname{RM}(d-1,r-1).
$$
Consequently
$$
\dim\operatorname{RM}(d,r)=\sum_{j=0}^r\binom dj.
$$