Next:
2.1 Definition
Up:
Algorithms in Singular
Previous:
1.2 Examples for monomial
2. Standard bases
Definition 2..1
We define
to be the localization of
with respect to the multiplicative closed set
or
and
.
Remark 2..2
1)
, where
denotes the localization of
with respect to the maximal ideal
. In particular,
is noetherian, Loc
is
flat and
is Loc
flat.
2)
If < is a wellordering then
x
^{0}
= 1 is the smallest monomial and Loc
. If 1 >
x
_{i}
for all
i
, then Loc
.
3)
If, in general,
and
then
hence
2.1 Definition
2.2 Standard bases for submodules of free modules
2.3 Basic properties
2.3.1 Ideal membership
2.3.2 Elimination
2.3.3 Hilbert series
2.4 Applications
2.4.1 Submodule
2.4.2 Euclidian algorithm
2.4.3 Gaussian algorithm
2.4.4 Kernel of a ring homomorphism
2.4.5 Radical membership
2.4.6 Principal ideal
2.4.7 Trivial ideal
2.4.8 Module intersection 1

ZCA Home

Reports
