Outline

Motivation

Operations

Representations

Vectorization

Rank

Conclusions

Conclusions

• Vectorized monomial operations: significant speedups

• Rank-based monomial operations: slow-down

• dense vs. sparse vs. enumerated exponent vectors:
  Answer: "vectorized" dense

• Results are system-independent in their nature:
  Should apply similarly to other GB implementations;
  Apply also to applications of GB computations (resolutions, syzygies, ...)

• Investigation of implementational aspects of GB computations can be fruitful

Future Work

• Extension of vectorized operations to general orderings

• Unique vs. duplicate exponent vectors

• array vs. linked list polynomial representation