Changeset dd73043 in git for Singular/LIB/rinvar.lib


Ignore:
Timestamp:
Jul 18, 2006, 5:22:16 PM (18 years ago)
Author:
Hans Schönemann <hannes@…>
Branches:
(u'spielwiese', '2a584933abf2a2d3082034c7586d38bb6de1a30a')
Children:
731e67e500fa1748d36cc7e4c72bb40cf2ab3b02
Parents:
27b3cfc2e355210dca9a4d1c4b1a6feaed10aca3
Message:
*hannes: format, typos in docu


git-svn-id: file:///usr/local/Singular/svn/trunk@9315 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

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  • Singular/LIB/rinvar.lib

    r27b3cf rdd73043  
    11// Last change 10.12.2000 (TB)
    22///////////////////////////////////////////////////////////////////////////////
    3 version="$Id: rinvar.lib,v 1.15 2006-07-18 11:59:45 Singular Exp $";
     3version="$Id: rinvar.lib,v 1.16 2006-07-18 15:22:15 Singular Exp $";
    44category="Invariant theory";
    55info="
    … …  
    77AUTHOR:   Thomas Bayer,   tbayer@in.tum.de
    88          http://wwwmayr.informatik.tu-muenchen.de/personen/bayert/
    9           Current Adress: Institut fuer Informatik, TU Muenchen
     9          Current Address: Institut fuer Informatik, TU Muenchen
    1010OVERVIEW:
    11  Implementation based on Derksen's algorithm. Written in the frame of the
     11 Implementation based on Derksen's algorithm. Written in the scope of the
    1212 diploma thesis (advisor: Prof. Gert-Martin Greuel) 'Computations of moduli
    1313 spaces of semiquasihomogenous singularities and an implementation in Singular'
    … …  
    219219proc HilbertSeries(ideal I, wt)
    220220"USAGE:   HilbertSeries(I, w); ideal I, intvec wt
    221 PURPOSE: compute the polynomial p of the Hilbert Series,represented by p/q, of
     221PURPOSE: compute the polynomial p of the Hilbert Series, represented by p/q, of
    222222         the ring K[t_1,...,t_m,y_1,...,y_r]/I1 where 'w' are the weights of
    223223         the variables, computed, e.g., by 'HilbertWeights', 'I1' is of the
    … …  
    225225RETURN:  intvec
    226226NOTE:    the leading 0 of the result does not belong to p, but is needed in
    227          the hilbert-driven 'std'.
     227         the Hilbert driven 'std'.
    228228"
    229229{
    … …  
    507507proc LinearActionQ(Gaction, int nrs)
    508508"USAGE:   LinearActionQ(action,nrs); ideal action, int nrs
    509 PURPOSE: check if the action defined by 'action' is linear w.r.t. the variables
    510          var(nrs + 1...nvars(basering)).
     509PURPOSE: check whether the action defined by 'action' is linear w.r.t. the
     510         variables var(nrs + 1...nvars(basering)).
    511511RETURN:  0 action not linear
    512512         1 action is linear
    … …  
    550550proc LinearCombinationQ(ideal I, poly f)
    551551"USAGE:   LinearCombination(I, f); ideal I, poly f
    552 PURPOSE: test if f can be written as a linear combination of the generators of I.
     552PURPOSE: test whether f can be written as a linear combination of the generators of I.
    553553RETURN:  0 f is not a linear combination
    554554         1 f is a linear combination
    … …  
    732732proc InvariantQ(poly f, ideal G, action)
    733733"USAGE:   InvariantQ(f, G, action); poly f; ideal G, action
    734 PURPOSE: check if the polynomial f is invariant w.r.t. G where G acts via
     734PURPOSE: check whether the polynomial f is invariant w.r.t. G, where G acts via
    735735         'action' on K^m.
    736736ASSUME:  basering = K[s_1,...,s_m,t_1,...,t_m] where K = Q of K = Q(a) and
    … …  
    858858         'action' is a linear group action of G on K^n (n = ncols(action))
    859859RETURN:  ideal of the nullcone of G.
    860 NOTE:    the generators of the nullcone are homogenous, but i.g. not invariant
     860NOTE:    the generators of the nullcone are homogenous, but in general not invariant
    861861EXAMPLE: example NullCone; shows an example
    862862"
    … …  
    928928proc ReynoldsOperator(ideal Grp, ideal Gaction, list #)
    929929"USAGE:   ReynoldsOperator(G, action [, opt]); ideal G, action; int opt
    930 PURPOSE: compute the Reynolds operator of the group G which act via 'action'
     930PURPOSE: compute the Reynolds operator of the group G which acts via 'action'
    931931RETURN:  polynomial ring R over a simple extension of the ground field of the
    932932         basering (the extension might be trivial), containing a list
    … …  
    10031003proc ReynoldsImage(list reynoldsOp, poly f)
    10041004"USAGE:   ReynoldsImage(RO, f); list RO, poly f
    1005 PURPOSE: compute the Reynolds image of the polynomial f where RO represents
     1005PURPOSE: compute the Reynolds image of the polynomial f, where RO represents
    10061006         the Reynolds operator
    10071007RETURN:  poly
    … …  
    10641064RETURN: list
    10651065  _[1] ideal I'
    1066   _[2] ideal representing a map phi to a ring with probably less vars. s.t.
     1066  _[2] ideal representing a map phi to a ring with probably less vars. s.th.
    10671067       phi(I) = I'
    10681068  _[3] list of variables
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