# 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)
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)