# Singular

#### 7.2.1.4 ideal related functions (plural)

dim
Gelfand-Kirillov dimension of basering modulo the ideal of leading terms (see dim (plural))
eliminate
elimination of variables (see eliminate (plural))
intersect
ideal intersection (see intersect (plural))
kbase
vector space basis of basering modulo the leading ideal (see kbase (plural))
lift
lift-matrix (see lift (plural))
liftstd
left Groebner basis and transformation matrix computation (see liftstd (plural))
maxideal
generators of a power of the maximal ideal at 0 (see maxideal)
modulo
represents (see modulo (plural))
mres
minimal free resolution of an ideal and a minimal set of generators of the given ideal (see mres (plural))
ncols
number of columns (see ncols)
nres
computes a free resolution of an ideal resp. module M which is minimized from the second free module on (see nres (plural))
oppose
creates an opposite ideal of a given ideal from the given ring into a basering (see oppose)
preimage
preimage under a ring map (see preimage (plural))
quotient
ideal quotient (see quotient (plural))
reduce
left normal form with respect to a left Groebner basis (see reduce (plural))
simplify
simplify a set of polynomials (see simplify)
size
number of non-zero generators (see size)
slimgb
left Groebner basis computation with slim technique (see slimgb (plural))
std
left Groebner basis computation (see std (plural))
subst
substitute a ring variable (see subst (plural))
syz
computation of the first syzygy module (see syz (plural))
twostd
two-sided Groebner basis computation (see twostd (plural))
vdim
vector space dimension of basering modulo the leading ideal (see vdim (plural))