Janet-Like Monomial Division

  • Vladimir P. Gerdt
  • Yuri A. Blinkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3718)


In this paper we introduce a new type of monomial division called Janet-like, since its properties are similar to those of Janet division. We show that the former division improves the latter one. This means that a Janet divisor is always a Janet-like divisor but the converse is generally not true. Though Janet-like division is not involutive, it preserves all algorithmic merits of Janet division, including Noetherianity, continuity and constructivity. Due to superiority of Janet-like division over Janet division, the algorithm for constructing Gröbner bases based on the new division is more efficient than its Janet division counterpart.


Polynomial Ideal Monomial Ideal Toric Ideal Monomial Order Involutive Algorithm 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Vladimir P. Gerdt
    • 1
  • Yuri A. Blinkov
    • 2
  1. 1.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchDubnaRussia
  2. 2.Department of Mathematics and MechanicsSaratov UniversitySaratovRussia

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