### 4.6.4 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)

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