Changeset 839b04d in git for Singular/LIB/finvar.lib
 Timestamp:
 Aug 4, 1997, 4:46:51 PM (26 years ago)
 Branches:
 (u'spielwiese', 'a719bcf0b8dbc648b128303a49777a094b57592c')
 Children:
 2d18815165593b7beda491c982a1f635a1b4048e
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 bb0968599ad062a86ceb2420fea0c6cac6244052
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 1 edited
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Singular/LIB/finvar.lib
rbb0968 r839b04d 1 // $Header: /exports/cvsroot2/cvsroot/Singular/LIB/finvar.lib,v 1. 2 19970703 15:49:54Singular Exp $1 // $Header: /exports/cvsroot2/cvsroot/Singular/LIB/finvar.lib,v 1.3 19970804 14:46:49 Singular Exp $ 2 2 //////////////////////////////////////////////////////////////////////////////// 3 3 // send bugs and comments to agnes@math.unisb.de … … 10 10 part_mol(M,n[,p]); n terms of partial expansion of Molien series M 11 11 eval_rey(RO,p); evaluate poly p under Reynolds operator RO 12 rad_con(p,I); check radical containment of poly p in ideal I13 12 inv_basis(deg,G1,G2,...); basis of space of homogeneous invariants of 14 13 degree deg under the finite matrix group … … 40 39 LIB "elim.lib"; 41 40 LIB "general.lib"; 41 LIB "poly.lib"; 42 42 //////////////////////////////////////////////////////////////////////////////// 43 43 … … 681 681 682 682 //////////////////////////////////////////////////////////////////////////////// 683 // Input: <ideal>=<f1,f2,...,fm> and <polynomial> g684 // Question: Does g lie in the radical of <ideal>?685 // Solution: Compute a standard basis G for <f1,f2,...,fm,gz1> where z is a new686 // variable. Then g is contained in the radical of <ideal> <=> 1 is687 // generator in G.688 ////////////////////////////////////////////////////////////////////////////////689 proc rad_con (poly g,ideal I)690 USAGE: rad_con(<poly>,<ideal>);691 RETURNS: 1 (TRUE) (type <int>) if <poly> is contained in the radical of692 <ideal>, 0 (FALSE) (type <int>) otherwise693 EXAMPLE: example rad_con; shows an example694 { def br=basering;695 int n=nvars(br);696 int dB=degBound;697 degBound=0;698 string mp=string(minpoly);699 execute "ring R=("+charstr(br)+"),(x(1..n),z),dp;";700 execute "minpoly=number("+mp+");";701 ideal irrel=x(1..n);702 map f=br,irrel;703 poly p=f(g);704 ideal J=f(I)+ideal(p*z1);705 J=std(J);706 degBound=dB;707 if (J[1]==1)708 { return(1);709 }710 else711 { return(0);712 }713 }714 example715 { " EXAMPLE: Sturmfels: Algorithms in Invariant Theory 2.3.7.";716 echo=2;717 ring R=0,(x,y,z),dp;718 ideal I=x2+y2,z2;719 poly f=x4+y4;720 rad_con(f,I);721 ideal J=x2+y2,z2,x4+y4;722 poly g=z;723 rad_con(g,I);724 }725 726 ////////////////////////////////////////////////////////////////////////////////727 683 // This procedure generates a basis of invariant polynomials in degree g. The 728 684 // way this works, is that we look how the generators act on a general
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