Truncated normal forms for solving polynomial systems: Generalized and efficient algorithms

We consider the problem of finding isolated common roots a set polynomial functions defining zero-dimensional ideal I in ring R polynomials over C. Normal form algorithms provide an algebraic approach to solve this problem. The framework presented Telen et al. (2018) uses truncated normal forms (TNFs) compute algebra structure R/I and solutions I. This allows for use much more general bases than standard monomials R/I. is exploited paper introduce two special (non-monomial) types basis with nice properties. us, instance, adapt expected location also propose efficient computation TNFs generalization construction case non-generic systems. potential TNF method usefulness new results are exposed by many experiments.