Rank - based Monomial Operations

Rank of a monomial:

Enumeration number which is compatible with ordering

$\begin{displaymath}r_{dp}(\alpha):=\sum_{i=1}^n{\sum_{j=1}^i {\alpha_j+i-1}\choose i}. \end{displaymath}$

Advantage:

Compact exponent vector representations

Fast comparisons

Disadvantage:

rank not compatible with addition

divisiblity tests

Only for degree orderings

Solution:

Hybrid representation

Use degree entry to store rank