Changeset 475f8b in git for doc/usercard.tex

Jun 18, 1998, 10:27:38 PM (25 years ago)
Jens Schmidt <schmidt@…>
(u'spielwiese', 'ec94ef7a30b928574c0c3daf41f6804dff5f6b69')
	* usercard.tex (Computation of Invariants, Resolutions): new
	  minor fixes throughout the whole card

git-svn-id: file:///usr/local/Singular/svn/trunk@2204 2c84dea3-7e68-4137-9b89-c4e89433aadc
1 edited


  • doc/usercard.tex

    rf7bdb8 r475f8b  
    1 % $Id: usercard.tex,v 1.5 1998-06-18 15:46:17 schmidt Exp $
     1% $Id: usercard.tex,v 1.6 1998-06-18 20:27:38 schmidt Exp $
    6161\sec Names and objects()
     63Names (= identifiers) have to be declared before they are used:\cr
    6265\longentry {\it type\/} {\it name\/} \opt{= {\it expression\/}};&
    63                                 declare variable {\it name}.  All names (=
    64                                 identifiers) have to be declared before
    65                                 they are used.\cr
     66                                declare variable {\it name}\cr
    6667kill({\it name\/})&             delete variable {\it name}\cr
    370371\longentry fetch({\it ringname}, {\it name\/})&
    371                                 map object {\it name\/} from ring {\it
    372                                 ringname\/} to current base\-ring.  The rings
    373                                 have to be ``almost'' identical.\cr
     372                                map from ring {\it ringname\/} to current
     373                                base\-ring.  The rings have to be identical up
     374                                to names of ring variables\cr
    374375\longentry imap({\it ringname}, {\it name\/})&
    375                                 map object {\it name\/} from subring {\it
    376                                 ringname\/} to current basering\cr
     376                                map from subring {\it ringname\/} to current
     377                                basering\cr
    377378\longentry subst({\it expression}, {\it ringvar}, {\it monomial\/})&
    378379                                substitute {\it ringvar\/} by {\it monomial\/}
    382383\sec Miscellany(1.5cm)
    383 \longentry setring({\it name\/})&
    384                                 make {\it name\/} the current basering\cr
     384\longentry setring({\it ringname\/})&
     385                                make {\it ringname\/} the current basering\cr
    385386\subsec{Data on polynomials}
    386387\longentry ord({\it poly\/\alt vector\/})&
    395396                                (2) number of monomials; (3) length\cr
    396397\longentry lead({\it expression\/})&
    397                                 return initial term(s) of {\it expression}\cr
     398                                return initial term(s)\cr
    398399\subsec{Operations on polynomials}
    399400\longentry gcd({\it $\hbox{poly}_1$}, {\it $\hbox{poly}_2$\/})&
    400                                 return greatest common divisor of {\it
    401                                 $\hbox{poly}_1$\/} and {\it $\hbox{poly}_2$}\cr
     401                                return greatest common divisor\cr
    402402\longentry factorize({\it poly\/}\opt{, {\it int\/}})&
    403                                 return irreducible factors of {\it poly}.  A
    404                                 constant factor and multiplicities are returned
    405                                 in dependency on {\it int}.\cr
     403                                return irreducible factors.  Return constant
     404                                factor and multiplicities in dependency on {\it
     405                                int}.\cr
    410410diff({\it expression}, {\it ringvar\/})\par
    411411diff({\it $\hbox{ideal}_1$}, {\it $\hbox{ideal}_2$\/})&
    412                                 (1) return partial deriv.\ of {\it expression\/}
    413                                 by {\it ringvar\/}; (2) differentiate each elt.\
    414                                 of {\it $\hbox{ideal}_2$\/} by the differential
    415                                 operators corresponding to the elements of {\it
     412                                (1) return partial derivation by {\it
     413                                ringvar\/}; (2) differentiate each elt.\ of {\it
     414                                $\hbox{ideal}_2$\/} by the differential
     415                                operators corres\-pon\-ding to the elements of {\it
    416416                                $\hbox{ideal}_1$}\cr
    417417\longentry jacob({\it poly\/\alt ideal\/})&
    418                                 return the jacobi ideal or matrix, resp.\cr
     418                                return jacobi ideal or matrix, resp.\cr
    419419\longentry jet({\it expression}, {\it int\/}\opt{, {\it intvec\/}})&
    420                                 return the {\it int\/}-jet of {\it expression}.
     420                                return {\it int\/}-jet of {\it expression}.
    421421                                Return weighted {\it int\/}-jet if {\it
    422422                                intvec\/} is specifified.\cr
    425427\sec Standard bases(1.5cm)
    435437\longentry stdfglm({\it ideal\/}\opt{, {\it string\/}})&
    436438                                use FGLM algorithm to compute a SB from a SB
    437                                 w.r.t.\ a ``simple'' ordering {\it string\/}
     439                                w.r.t.\ the ``simpler'' ordering {\it string\/}
    438440                                (de\-faults to {\tt dp})\cr
    439441\longentry stdhilb({\it ideal\/}\opt{, {\it intvec\/}})&
    453 \sec Invariants of ideals and modules(1.5cm)
     455\sec Computation of invariants(1.5cm)
     457Most of the results are meaningful only if the input ideal or module is
     458represented by a standard basis.\cr
     459\longentry degree({\it ideal\/\alt module\/})&
     460                                display (Krull) dimension, codimension and
     461                                multiplicity\cr
     462\longentry dim({\it ideal\/\alt module\/})&
     463                                return (Krull) dimension\cr
    454464\longentry hilb({\it ideal\/\alt module\/}\opt{, {\it int\/}})&
    455465                                display first and second Hilbert series with one
    456                                 argument.\cr
     466                                argument.  Return {\it int}-th Hilber series
     467                                otherwise (${\it \hbox{int}} = 1,2$).\cr
     468\longentry mult({\it ideal\/\alt module\/})&
     469                                return multiplicity\cr
     470\longentry vdim({\it ideal\/\alt module\/})&
     471                                return vector space dimension of current
     472                                basering modulo {\it ideal\/} or {\it module},
     473                                resp.\cr
     476\sec Resolutions(1.5cm)
     478An integer argument {\it length\/} in the following descriptions specifies the
     479length of the resolution to compute.  If {\it length\/} equals zero, the whole
     480resolution is computed.\cr
     481\longentry res({\it ideal\/\alt module}, {\it length\/}\opt{, {\it int\/}})&
     482                                compute a free resolution (FR) of {\it ideal\/}
     483                                resp.\ {\it module\/} using a heuristically
     484                                chosen method.  Compute a minimal resolution if
     485                                a third argument is given.\cr
     486\longentry mres({\it ideal\/\alt module}, {\it length\/})&
     487                                compute a minimal FR using the standard basis
     488                                method\cr
     489\longentry lres({\it ideal\/\alt module}, {\it length\/})&
     490                                compute a FR using LaSacala's method\cr
     491\longentry sres({\it ideal\/\alt module}, {\it length\/})&
     492                                compute a FR using Schreyer's method\cr
     493\longentry syz({\it ideal\/\alt module\/})&
     494                                compute the first syzygy\cr
     495\longentry minres({\it resolution\/\alt list\/})&
     496                                minimize a free resolution\cr
     497\longentry betty({\it resolution\/\alt list\/})&
     498                                compute the graded Betti numbers of a module
     499                                represented by a resolution\cr
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