Singular

D.12.5 teachstd_lib

Library:

teachstd.lib

Purpose:

Procedures for teaching standard bases

Author:

G.-M. Greuel, [email protected]

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 satisfying 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