A New Algorithm for Discussing Gröbner Bases with Parameters

@article{Montes2002ANA,
  title={A New Algorithm for Discussing Gr{\"o}bner Bases with Parameters},
  author={Antonio Montes},
  journal={J. Symb. Comput.},
  year={2002},
  volume={33},
  pages={183-208}
}
In many practical applications it is necessary to determine a Gröbner basis of an ideal of polynomials whose coefficients depend on some parameters. The main problem in this context is to obtain the distinct reduced Gröbner basis for all possible values of the parameters. Examples of this situation can be found, for instance, in constructive algebraic geometry when determining conditions for a family of curves to have singular points (see Section 11.2); in robotics, in order to determine… CONTINUE READING

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