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B.2.1 Introduction to orderings
SINGULAR offers a great variety of monomial orderings which provide
an enormous functionality, if used diligently. However, this
flexibility might also be confusing for the novice user. Therefore, we
recommend to those not familiar with monomial orderings to generally use
the ordering dp for computations in the polynomial ring
![$K[x_1,\ldots,x_n]$](sing_62.png){kind=small}
,resp. ds for computations in the localization
![$\hbox{Loc}_{(x)}K[x_1,\ldots,x_n]$](sing_494.png){kind=small}
.
For inhomogeneous input ideals, standard (resp. groebner) bases
computations are generally faster
with the orderings
(resp.
)if the input is quasihomogenous w.r.t. the weights
, 
, 
of 
, , 
.
If the output needs to be "triangular" (resp. "block-triangular"), the
lexicographical ordering lp (resp. lexicographical
block-orderings) need to be used. However, these orderings usually
result in much less efficient computations.