Home Online Manual
Back: cantormult
Forward: ecart
Up: Singular Manual
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.12.5 teachstd_lib

Procedures for teaching standard bases
G.-M. Greuel, greuel@mathematik.uni-kl.de

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).


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