Points 3.6 is a software package for symbolic computations on points developed in the framework of Project Points (started in 1999) aimed at creating and implementing novel algorithms to solve problems in Algebraic Geometry. The Points software includes packages for the computation of the Hilbert function and of minimal generators of the ideal of a finite set of points (the points can be also fat) or of rational varieties or of elliptic curves over finite fields of type Z_p. The release Points3.6 (2004) extends the application of the above packages, except that for elliptic curves, to the field Q of rational numbers. All the algorithms implemented in Points have polynomial computational cost and are programmed in the object-oriented language C++. The features are: -1- Computations on zero-dimensional schemes: simple points: -1.1- Hilbert function of ideals of projective points. -1.2- Minimal generators of ideals of projective points. -1.3- Conductor of projective points. -1.4- Checking the Ideal Generation Conjecture (on Z_p). fat points: -1.5- Hilbert function of ideals of fat projective points. -1.6- Hilbert function of ideals of the projective closure of affine fat points. -1.7- Minimal generators of ideals of fat projective points. -1.8- Maximal rank and minimally generation of ideals of fat points. -2- Minimal generators of ideals of parametric rational curves. -3- Minimal generators of ideals of parametric varieties up to a given degree. -4- Hilbert function and minimal generators of ideals of elliptic curves computed as birational images of plane elliptic curves (only on Z_p). In some particular cases it is also possible to compute minimal generators of the first linear syzygies. The release Points3.7 (2006) fixes some minor bugs and is the last public release.

Points 3.6 (software for computations on points) / Orecchia, F.; Cioffi, Francesca; Ramella, I.. - (2004).

Points 3.6 (software for computations on points)

CIOFFI, FRANCESCA;
2004

Abstract

Points 3.6 is a software package for symbolic computations on points developed in the framework of Project Points (started in 1999) aimed at creating and implementing novel algorithms to solve problems in Algebraic Geometry. The Points software includes packages for the computation of the Hilbert function and of minimal generators of the ideal of a finite set of points (the points can be also fat) or of rational varieties or of elliptic curves over finite fields of type Z_p. The release Points3.6 (2004) extends the application of the above packages, except that for elliptic curves, to the field Q of rational numbers. All the algorithms implemented in Points have polynomial computational cost and are programmed in the object-oriented language C++. The features are: -1- Computations on zero-dimensional schemes: simple points: -1.1- Hilbert function of ideals of projective points. -1.2- Minimal generators of ideals of projective points. -1.3- Conductor of projective points. -1.4- Checking the Ideal Generation Conjecture (on Z_p). fat points: -1.5- Hilbert function of ideals of fat projective points. -1.6- Hilbert function of ideals of the projective closure of affine fat points. -1.7- Minimal generators of ideals of fat projective points. -1.8- Maximal rank and minimally generation of ideals of fat points. -2- Minimal generators of ideals of parametric rational curves. -3- Minimal generators of ideals of parametric varieties up to a given degree. -4- Hilbert function and minimal generators of ideals of elliptic curves computed as birational images of plane elliptic curves (only on Z_p). In some particular cases it is also possible to compute minimal generators of the first linear syzygies. The release Points3.7 (2006) fixes some minor bugs and is the last public release.
2004
Points 3.6 (software for computations on points) / Orecchia, F.; Cioffi, Francesca; Ramella, I.. - (2004).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/417511
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