# Singular

### 4.13.4 module related functions

`coeffs`
matrix of coefficients (see coeffs)
`degree`
multiplicity, dimension and codimension of the module of leading terms (see degree)
`diff`
partial derivative (see diff)
`dim`
Krull dimension of free module over the basering modulo the module of leading terms (see dim)
`eliminate`
elimination of variables (see eliminate)
`freemodule`
the free module of given rank (see freemodule)
`fres`
free resolution of a standard basis (see fres)
`groebner`
Groebner basis computation (a wrapper around `std,stdhilb,stdfglm`,...) (see groebner)
`hilb`
Hilbert function of a standard basis (see hilb)
`homog`
homogenization with respect to a variable (see homog)
`interred`
interreduction of a module (see interred)
`intersect`
module intersection (see intersect)
`jet`
Taylor series up to a given order (see jet)
`kbase`
vector space basis of free module over the basering modulo the module of leading terms (see kbase)
`lead`
`lift`
lift-matrix (see lift)
`liftstd`
standard basis and transformation matrix computation (see liftstd)
`lres`
free resolution (see lres)
`minbase`
minimal generating set of a homogeneous ideal, resp. module, or an ideal, resp. module, over a local ring
`modulo`
represents (see modulo)
`mres`
minimal free resolution of an ideal resp. module w.r.t. a minimal set of generators of the given module (see mres)
`mult`
multiplicity, resp. degree, of the module of leading terms (see mult)
`nres`
computation of a free resolution of an ideal resp. module M which is minimized from the second free module on (see nres)
`ncols`
number of columns (see ncols)
`nrows`
number of rows (see nrows)
`print`
nice print format (see print)
`prune`
minimization of the embedding into a free module (see prune)
`qhweight`
quasihomogeneous weights of an ideal, resp. module (see qhweight)
`quotient`
module 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 vectors (see simplify)
`size`
number of non-zero generators (see size)
`sortvec`
permutation for sorting ideals/modules (see sortvec)
`sres`
free resolution of a standard basis (see sres)
`std`
standard basis computation (see std, liftstd)
`subst`
substitution of a ring variable (see subst)
`syz`
computation of the first syzygy module (see syz)
`vdim`
vector space dimension of free module over the basering modulo module of leading terms (see vdim)
`weight`
"optimal" weights (see weight)