The Theory of Involutive Divisions and an Application to Hilbert Function Computations

@article{Apel1998TheTO,
  title={The Theory of Involutive Divisions and an Application to Hilbert Function Computations},
  author={Joachim Apel},
  journal={J. Symb. Comput.},
  year={1998},
  volume={25},
  pages={683-704}
}
Generalising the divisibility relation of terms we introduce the lattice of so-called involutive divisions and de ne the admissibility of such an involutive division for a given set of terms. Based on this theory we present a new approach for building up a general theory of involutive bases of polynomial ideals. In particular, we give algorithms for checking the involutive basis property and for completing an arbitrary basis to an involutive one. It turns out that our theory is more… CONTINUE READING