Algorithms for primary decomposition in SINGULAR. (English) Zbl 1369.13037

Schonemann, Hans

Araújo dos Santos, Raimundo Nonato (ed.) et al., School on real and complex singularities in São Carlos, Brazil, July 16–21, 2012 and 12th international workshop on real and complex singularities, São Carlos, Brazil, July 22–27, 2012. Lecture notes. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-030-3/hbk). Advanced Studies in Pure Mathematics 68, 171-190 (2016).

Summary: Gröbner bases are the main computational tool available for algebraic geometry. Building on top of Gröbner bases algorithms for ideal theoretical operations (intersection, quotient, saturation, free resolution,\(\dots\)) will be presented. Combining these algorithms with (multivariate) factorization leads to several algorithms for primary decomposition of ideals.
For the entire collection see [Zbl 1353.00009].

MSC:

13P10	Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
14Q99	Computational aspects in algebraic geometry
68W30	Symbolic computation and algebraic computation
13-04	Software, source code, etc. for problems pertaining to commutative algebra

Software:

SINGULAR