
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 zerodimensional.
(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
 leading terms of a set of generators (see lead)
lift
 liftmatrix (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 nonzero 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)
