Changeset 972fb1 in git for Singular/LIB/rinvar.lib


Ignore:
Timestamp:
Feb 19, 2002, 1:30:16 PM (21 years ago)
Author:
Hans Schönemann <hannes@…>
Branches:
(u'spielwiese', '91fdef05f09f54b8d58d92a472e9c4a43aa4656f')
Children:
900cea1b1461e5dcef8e13aba10034edc5914c65
Parents:
ebcda0c47fce53217b409edb6303bb31e69e3ef4
Message:
*hannes: spelling


git-svn-id: file:///usr/local/Singular/svn/trunk@5898 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

Legend:

Unmodified
Added
Removed
  • Singular/LIB/rinvar.lib

    rebcda0 r972fb1  
    11// Last change 10.12.2000 (TB)
    22///////////////////////////////////////////////////////////////////////////////
    3 version="$Id: rinvar.lib,v 1.7 2001-02-02 16:34:03 mschulze Exp $";
     3version="$Id: rinvar.lib,v 1.8 2002-02-19 12:30:16 Singular Exp $";
    44category="Invariant theory";
    55info="
     
    4141proc EquationsOfEmbedding(ideal embedding, int nrs)
    4242"USAGE:   EquationsOfEmbedding(embedding, s); ideal embedding; int s;
    43 PUROPSE: compute the ideal of the variety parameterized by 'embedding' by
     43PURPOSE: compute the ideal of the variety parameterized by 'embedding' by
    4444         implicitation and change the variables to the old ones.
    4545RETURN:  ideal
     
    7171proc ImageGroup(ideal Grp, ideal Gaction)
    7272"USAGE:   ImageGroup(G, action); ideal G, action;
    73 PUROPSE: compute the ideal of the image of G in GL(m,K) induced by the linear
     73PURPOSE: compute the ideal of the image of G in GL(m,K) induced by the linear
    7474         action 'action', where G is an algebraic group and 'action' defines
    7575         an action of G on K^m (size(action) = m).
     
    199199proc HilbertWeights(ideal I, wt)
    200200"USAGE:   HilbertWeights(I, w); ideal I, intvec wt
    201 PUROPSE: compute the weights of the "slack" variables needed for the
     201PURPOSE: compute the weights of the "slack" variables needed for the
    202202         computation of the algebraic relations of the generators of 'I' s.t.
    203203         the Hilbert driven 'std' can be used.
     
    218218proc HilbertSeries(ideal I, wt)
    219219"USAGE:   HilbertSeries(I, w); ideal I, intvec wt
    220 PUROPSE: compute the polynomial p of the Hilbert Series,represented by p/q, of
     220PURPOSE: compute the polynomial p of the Hilbert Series,represented by p/q, of
    221221         the ring K[t_1,...,t_m,y_1,...,y_r]/I1 where 'w' are the weights of
    222222         the variables, computed, e.g., by 'HilbertWeights', 'I1' is of the
     
    244244proc HilbertSeries1(wt)
    245245"USAGE:   HilbertSeries1(wt); ideal I, intvec wt
    246 PUROPSE: compute the polynomial p of the Hilbert Series represented by p/q of
     246PURPOSE: compute the polynomial p of the Hilbert Series represented by p/q of
    247247         the ring K[t_1,...,t_m,y_1,...,y_r]/I where I is a complete inter-
    248248         section and the generator I[i] has degree wt[i]
     
    273273proc ImageVariety(ideal I, F, list #)
    274274"USAGE:   ImageVariety(ideal I, F [, w]);ideal I; F is a list/ideal, intvec w.
    275 PUROPSE: compute the Zariski closure of the image of the variety of I under
     275PURPOSE: compute the Zariski closure of the image of the variety of I under
    276276         the morphism F.
    277277NOTE:    if 'I' and 'F' are quasihomogenous w.r.t. 'w' then the Hilbert-driven
     
    359359proc LinearizeAction(ideal Grp, Gaction, int nrs)
    360360"USAGE:   LinearizeAction(G,action,r); ideal G, action; int r
    361 PUROPSE: linearize the group action 'action' and find an equivariant embedding
     361PURPOSE: linearize the group action 'action' and find an equivariant embedding
    362362         of K^m where m = size(action).
    363363ASSUME:  G contains only variables var(1..r) (r = nrs)
     
    504504proc LinearActionQ(Gaction, int nrs)
    505505"USAGE:   LinearActionQ(action,nrs,nrt); ideal action, int nrs
    506 PUROPSE: check if the action defined by 'action' is linear w.r.t. the variables
     506PURPOSE: check if the action defined by 'action' is linear w.r.t. the variables
    507507         var(nrs + 1...nvars(basering)).
    508508RETURN:  0 action not linear
     
    542542proc LinearCombinationQ(ideal I, poly f)
    543543"USAGE:   LinearCombination(I, f); ideal I, poly f
    544 PUROPSE: test if f can be written as a linear combination of the generators of I.
     544PURPOSE: test if f can be written as a linear combination of the generators of I.
    545545RETURN:  0 f is not a linear combination
    546546         1 f is a linear combination
     
    584584proc InvariantRing(ideal G, ideal action, list #)
    585585"USAGE:   InvariantRing(G, Gact [, opt]); ideal G, Gact; int opt
    586 PUROPSE: compute generators of the invariant ring of G w.r.t. the action 'Gact'
     586PURPOSE: compute generators of the invariant ring of G w.r.t. the action 'Gact'
    587587ASSUME:  G is a finite group and 'Gact' is a linear action.
    588588RETURN:  polynomial ring over a simple extension of the groundfield of the
     
    706706proc InvariantQ(poly f, ideal G, action)
    707707"USAGE:   InvariantQ(f, G, action); poly f; ideal G, action
    708 PUROPSE: check if the polynomial f is invariant w.r.t. G where G acts via
     708PURPOSE: check if the polynomial f is invariant w.r.t. G where G acts via
    709709         'action' on K^m.
    710710ASSUME:  basering = K[s_1,...,s_m,t_1,...,t_m] where K = Q of K = Q(a) and
     
    731731proc MinimalDecomposition(poly f, int nrs, int nrt)
    732732"USAGE:   MinimalDecomposition(f,a,b); poly f; int a, b.
    733 PUROPSE: decompose f as a sum M[1,1]*M[2,1] + ... + M[1,r]*M[2,r] where M[1,i]
     733PURPOSE: decompose f as a sum M[1,1]*M[2,1] + ... + M[1,r]*M[2,r] where M[1,i]
    734734         contains only s(1..a), M[2,i] contains only t(1...b) s.t. r is minimal
    735735ASSUME:  f polynomial in K[s(1..a),t(1..b)], K = Q or K = Q(a) and minpoly != 0
     
    827827proc NullCone(ideal G, action)
    828828"USAGE:   NullCone(G, action); ideal G, action
    829 PUROPSE: compute the ideal of the nullcone of the linear action of G on K^n,
     829PURPOSE: compute the ideal of the nullcone of the linear action of G on K^n,
    830830         given by 'action', by means of Deksen's algorithm
    831831ASSUME:  basering = K[s(1..r),t(1..n)], K = Q or K = Q(a) and minpoly != 0,
     
    902902proc ReynoldsOperator(ideal Grp, ideal Gaction, list #)
    903903"USAGE:   ReynoldsOperator(G, action [, opt); ideal G, action; int opt
    904 PUROPSE: compute the Reynolds operator of the group G which act via 'action'
     904PURPOSE: compute the Reynolds operator of the group G which act via 'action'
    905905RETURN:  polynomial ring R over a simple extension of the groundfield of the
    906906         basering (the extension might be trivial), containing a list
     
    961961proc ReynoldsImage(list reynoldsOp, poly f)
    962962"USAGE:   ReynoldsImage(RO, f); list RO, poly f
    963 PUROPSE: compute the Reynolds image of the polynomial f where RO represents
     963PURPOSE: compute the Reynolds image of the polynomial f where RO represents
    964964         the Reynolds operator
    965965RETURN:  poly
     
    980980static proc SimplifyCoefficientMatrix(matrix coefMatrix)
    981981"USAGE:   SimplifyCoefficientMatrix(M); M matrix coming from coef(...)
    982 PUROPSE: simplify the matrix, i.e. find linear dependencies among the columns
     982PURPOSE: simplify the matrix, i.e. find linear dependencies among the columns
    983983RETURN:  matrix M, f = M[1,1]*M[2,1] + ... + M[1,n]*M[2,n]
    984984"
     
    10651065static proc TransferIdeal(R, string name, poly newA)
    10661066" USAGE:  TransferIdeal(R, name, newA); ring R, string name, poly newA
    1067 PUROPSE: Maps an ideal with name 'name' in R to the basering, s.t. all
     1067PURPOSE: Maps an ideal with name 'name' in R to the basering, s.t. all
    10681068         variables are fixed but par(1) is replaced by 'newA'.
    10691069RETURN:  ideal
Note: See TracChangeset for help on using the changeset viewer.