Outline

Motivation

Operations

Representations

Vectorization

Rank

Conclusions

Monomial Operations

Monomials in this talk:

Monomial operations:
  • Divisibility: $\alpha \vert \beta \Leftrightarrow \forall i \in \{1..n\}: \alpha_i \le \beta_i$
  • Addition: $ \gamma := \alpha + \beta \mbox{ with }\forall i \in \{1..n\}: \gamma_i=\alpha_i + \beta_i$
  • Comparison w.r.t. a monomial ordering

GB computations over small finite fields:
  • most time spent in monomial operations (Singular average: appr. 70%)
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