Changeset 789d6f in git


Ignore:
Timestamp:
Dec 19, 2013, 2:52:39 PM (10 years ago)
Author:
Oleksandr Motsak <motsak@…>
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'b52fc4b2495505785981d640dcf7eb3e456778ef')
Children:
b1645e52df1f9ba737d354f5a3f4bebff0aac7cd
Parents:
4821a301f6cf9983952236a781877498075ab2e9
git-author:
Oleksandr Motsak <motsak@mathematik.uni-kl.de>2013-12-19 14:52:39+01:00
git-committer:
Oleksandr Motsak <motsak@mathematik.uni-kl.de>2013-12-19 17:09:18+01:00
Message:
More formatting for schreyer.lib
File:
1 edited

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  • Singular/LIB/schreyer.lib

    r4821a3 r789d6f  
    33category="General purpose";
    44info="
    5 LIBRARY: schreyer.lib     Helpers for computing a Schreyer resolution in derham.lib
     5LIBRARY: schreyer.lib     Helpers for computing a Schreyer resolution in @code{derham.lib}
    66AUTHOR:  Oleksandr Motsak <U@D>, where U={motsak}, D={mathematik.uni-kl.de}
     7KEYWORDS: Schreyer ordering; Schreyer resolution; syzygy
    78
    89PROCEDURES:
    9  Sres(M,len)      compute Schreyer resolution of module M of maximal length len
    10  Ssyz(M)          compute Schreyer resolution of module M of length 1
    11  Scontinue(len)   extend currently active resolution by (at most) len syszygies
    12 
    13 KEYWORDS: Schreyer ordering; Schreyer resolution; syzygy
     10Sres(M,len)     compute Schreyer resolution of module M of maximal length len
     11Ssyz(M)         compute Schreyer resolution of module M of length 1
     12Scontinue(len)  extend currently active resolution by (at most) len syszygies
     13
    1414NOTE:  requires the dynamic or built-in module: syzextra
    1515";
     
    394394"USAGE:  Sres(module M, int len)
    395395RETURN:  ring, containing a Schreyer resolution
    396 PURPOSE: computes a Schreyer resolution of (basering^rank(M))/M with at most len syzygy modules,
    397          computed with respect to a Schreyer (induced) ordering.
    398 NOTE:    Input is a set of vectors M over a basering. basering may be non-commutative.
    399 NOTE:    Schreyer resolution is represented by a list of modules RES and a module MRES
     396PURPOSE: computes a Schreyer resolution of (basering^rank(M))/M with at most len syzygy modules
     397NOTE:    input is a set of vectors M over a basering. The ring basering may be non-commutative.
     398@*       If given len is zero then nvars(basering) + 1 is used instead.
     399@*       Schreyer resolution is represented by a list of modules RES and a module MRES
    400400         belonging to a specially constructed ring, which is endowed with a Schreyer ordering.
    401          The list of modules RES contains the images of maps (also called syzygies) subsituting the
     401@*       The list of modules RES contains the images of maps (also called syzygies) subsituting the
    402402         computed beginning of a Schreyer free resolution of (baseRing^rank(M))/M.
    403          The leading zero map RES[1] with rank(M) zero generators indicates that the image of
     403@*       The leading zero map RES[1] with rank(M) zero generators indicates that the image of
    404404         the first differential map is zero. The second map RES[2] is given by M, which indicates that
    405405         the resolution is of (baseRing^rank(M))/M is being computed.
    406          The module MRES is a direct sum of modules from RES and comprises all computed differential maps.
    407          Syzygies are shifted so that gen(i) is mapped to MRES[i] under the differential.
    408          Syzygies are given by Groebner bases with respect to corresponding Schreyer orderings.
    409 NOTE:    Schreyer ordering extends an arbitrary starting module ordeing (defined by basering)
     406@*       The module MRES is a direct sum of modules from RES and comprises all computed differential maps.
     407@*       Syzygies are shifted so that gen(i) is mapped to MRES[i] under the differential.
     408@*       Schreyer ordering extends an arbitrary starting module ordeing (defined by basering)
    410409         and is extended to higher syzygt modules using the following definition:
    411          a < b if and only if (d(a) < d(b)) OR ( (d(a) = d(b) AND (comp(a) < comp(b)) ),
    412          where d(a) is the image of a under the differential (given by MRES),
     410@*       a < b if and only if (d(a) < d(b)) OR ( (d(a) = d(b) AND (comp(a) < comp(b)) ),
     411@*       where d(a) is the image of a under the differential (given by MRES),
    413412         and comp(a) is the mod. component, for any module terms a and b.
    414 NOTE:    If len == 0 then len is set to be nvars(basering) + 1
     413@*       Syzygies are given by Groebner bases with respect to corresponding Schreyer orderings.
    415414EXAMPLE: example Sres; shows an example
    416415"
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