# Singular

### 4.5.4 ideal related functions

`char_series`
irreducible characteristic series (see char_series)
`coeffs`
matrix of coefficients (see coeffs)
`contract`
contraction by an ideal (see contract)
`diff`
partial derivative (see diff)
`degree`
multiplicity, dimension and codimension of the ideal of leading terms (see degree)
`dim`
Krull dimension of basering modulo the ideal of leading terms (see dim)
`eliminate`
elimination of variables (see eliminate)
`facstd`
factorizing Groebner basis algorithm (see facstd)
`factorize`
ideal of factors of a polynomial (see factorize)
`fglm`
Groebner basis computation from a Groebner basis w.r.t. a different ordering (see fglm)
`finduni`
computation of univariate polynomials lying in a zero dimensional ideal (see finduni)
`fres`
free resolution of a standard basis (see fres)
`groebner`
Groebner basis computation (a wrapper around `std,stdhilb,stdfglm`,...) (see groebner)
`highcorner`
the smallest monomial not contained in the ideal. The ideal has to be zero-dimensional. (see highcorner)
`homog`
homogenization with respect to a variable (see homog)
`hilb`
Hilbert series of a standard basis (see hilb)
`indepSet`
sets of independent variables of an ideal (see indepSet)
`interred`
interreduction of an ideal (see interred)
`intersect`
ideal intersection (see intersect)
`jacob`
ideal of all partial derivatives resp. jacobian matrix (see jacob)
`jet`
Taylor series up to a given order (see jet)
`kbase`
vector space basis of basering modulo ideal of leading terms (see kbase)
`koszul`
Koszul matrix (see koszul)
`lead`
`lift`
lift-matrix (see lift)
`liftstd`
standard basis and transformation matrix computation (see liftstd)
`lres`
free resolution for homogeneous ideals (see lres)
`maxideal`
power of the maximal ideal at 0 (see maxideal)
`minbase`
minimal generating set of a homogeneous ideal, resp. module, or an ideal, resp. module, in a local ring (see minbase)
`minor`
set of minors of a matrix (see minor)
`modulo`
representation of (see modulo)
`mres`
minimal free resolution of an ideal resp. module w.r.t. a minimal set of generators of the given ideal resp. module (see mres)
`mstd`
standard basis and minimal generating set of an ideal (see mstd)
`mult`
multiplicity, resp. degree, of the ideal of leading terms (see mult)
`ncols`
number of columns (see ncols)
`nres`
a free resolution of an ideal resp. module M which is minimized from the second free module on (see nres)
`preimage`
preimage under a ring map (see preimage)
`qhweight`
quasihomogeneous weights of an ideal (see qhweight)
`quotient`
ideal quotient (see quotient)
`reduce`
normalform with respect to a standard basis (see reduce)
`res`
free resolution of an ideal resp. module but not changing the given ideal resp. module (see res)
`simplify`
simplification of a set of polynomials (see simplify)
`size`
number of non-zero generators (see size)
`slimgb`
Groebner basis computation with slim technique (see slimgb)
`sortvec`
permutation for sorting ideals resp. modules (see sortvec)
`sres`
free resolution of a standard basis (see sres)
`std`
standard basis computation (see std)
`stdfglm`
standard basis computation with fglm technique (see stdfglm)
`stdhilb`
Hilbert driven standard basis computation (see stdhilb)
`subst`
substitution of a ring variable (see subst)
`syz`
computation of the first syzygy module (see syz)
`vdim`
vector space dimension of basering modulo ideal of leading terms (see vdim)
`weight`
optimal weights (see weight)

### Misc 