4.12.4 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)

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

initial module (see 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)