| ### 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)

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