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

leading terms of a set of generators (see 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)