### D.12.4 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.12.4.1 ecart |  | ecart of f
> D.12.4.2 tail |  | tail of f
> D.12.4.3 sameComponent |  | test for same module component of lead(f) and lead(g)
> D.12.4.4 leadmonomial |  | leading monomial as polynomial (also for vectors)
> D.12.4.5 monomialLcm |  | lcm of monomials m and n as polynomial (also for vectors)
> D.12.4.6 spoly |  | s-polynomial of f [symmetric form]
> D.12.4.7 minEcart |  | element g from T of minimal ecart s.t. LM(g)|LM(h)
> D.12.4.8 NFMora |  | normal form of i w.r.t Mora algorithm
> D.12.4.9 prodcrit |  | test for product criterion
> D.12.4.10 chaincrit |  | test for chain criterion
> D.12.4.11 pairset |  | pairs form G neither satisfying prodcrit nor chaincrit
> D.12.4.12 updatePairs |  | pairset P enlarded by not useless pairs (h,f), f in S
> D.12.4.13 standard |  | standard basis of ideal/module
> D.12.4.14 localstd |  | local standard basis of id using Lazard's method

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