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D.12.5 teachstd_lib
- Library:
- teachstd.lib
- Purpose:
- Procedures for teaching standard bases
- Author:
- G.-M. Greuel, greuel@mathematik.uni-kl.de
- Note:
- The library is intended to be used for teaching purposes, but not
for serious computations. Sufficiently high printlevel allows to
control each step, thus illustrating the algorithms at work.
The procedures are implemented exactly as described in the book
'A SINGULAR Introduction to Commutative Algebra' by G.-M. Greuel and
G. Pfister (Springer 2002).
Procedures:
D.12.5.1 ecart ecart of f D.12.5.2 tail tail of f D.12.5.3 sameComponent test for same module component of lead(f) and lead(g) D.12.5.4 leadmonomial leading monomial as polynomial (also for vectors) D.12.5.5 monomialLcm lcm of monomials m and n as polynomial (also for vectors) D.12.5.6 spoly s-polynomial of f [symmetric form] D.12.5.7 minEcart element g from T of minimal ecart s.t. LM(g)|LM(h) D.12.5.8 NFMora normal form of i w.r.t Mora algorithm D.12.5.9 prodcrit test for product criterion D.12.5.10 chaincrit test for chain criterion D.12.5.11 pairset pairs form G neither satifying prodcrit nor chaincrit D.12.5.12 updatePairs pairset P enlarded by not useless pairs (h,f), f in S D.12.5.13 standard standard basis of ideal/module D.12.5.14 localstd local standard basis of id using Lazard's method