# 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))
`lead`
`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)
`vdim`
vector space dimension of basering modulo the leading ideal (see vdim (plural))