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4.14.4 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
- 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)
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