Changeset 50cbdc in git for Singular/LIB/brnoeth.lib


Ignore:
Timestamp:
Aug 27, 2001, 4:48:02 PM (23 years ago)
Author:
Hans Schönemann <hannes@…>
Branches:
(u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
Children:
2567b5a6cb7109be5a83e53eb94abb1c38fb9945
Parents:
3de58c9ca0aeaafdf5cb29f986967bffa405b542
Message:
*hannes: merge-2-0-2


git-svn-id: file:///usr/local/Singular/svn/trunk@5619 2c84dea3-7e68-4137-9b89-c4e89433aadc
File:
1 edited

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  • Singular/LIB/brnoeth.lib

    r3de58c r50cbdc  
    1 version="$Id: brnoeth.lib,v 1.11 2001-02-09 13:11:35 lossen Exp $";
     1version="$Id: brnoeth.lib,v 1.12 2001-08-27 14:47:46 Singular Exp $";
     2category="Miscellaneous";
    23info="
    34LIBRARY:   brnoeth.lib  Brill-Noether Algorithm, Weierstrass-SG and AG-codes
    … …  
    19811982          In the intvec L[4] (conductor) the i-th entry corresponds to the
    19821983          i-th entry in the list of places L[3].
    1983          
     1984
    19841985          With no optional arguments, the conductor is computed by
    19851986          local invariants of the singularities; otherwise it is computed
    … …  
    19891990          of the places above P in the list of closed places L[3]. @*
    19901991          If the point is at infinity, P[1] is a homogeneous irreducible
    1991           polynomial in two variables. 
    1992 
    1993           If @code{printlevel>=0} additional comments are displayed (default: 
    1994           @code{printlevel=0}). 
     1992          polynomial in two variables.
     1993
     1994          If @code{printlevel>=0} additional comments are displayed (default:
     1995          @code{printlevel=0}).
    19951996KEYWORDS: Hamburger-Noether expansions; adjunction divisor
    19961997SEE ALSO: closed_points, NSplaces
    … …  
    21262127  Aff_SLocus;             // ideal of the affine singular locus
    21272128  Aff_SPoints[1];         // 1st affine singular point: (1:1:1), no.1
    2128   Inf_Points[1];          // singular point(s) at infinity: (1:0:0), no.4 
     2129  Inf_Points[1];          // singular point(s) at infinity: (1:0:0), no.4
    21292130  Inf_Points[2];          // list of non-singular points at infinity
    21302131  //
    … …  
    21392140  //
    21402141  pause("press RETURN");
    2141   // we look at the place(s) of degree 2 by changing to the ring 
     2142  // we look at the place(s) of degree 2 by changing to the ring
    21422143  C[5][2][1];
    2143   def S(2)=C[5][2][1];         
     2144  def S(2)=C[5][2][1];
    21442145  setring S(2);
    21452146  POINTS;                // base point(s) of place(s) of degree 2: (1:a:1)
    … …  
    21642165          See @ref{Adj_div} for a description of the entries in L.
    21652166NOTE:     The list_expression should be the output of the procedure Adj_div.@*
    2166           If @code{printlevel>=0} additional comments are displayed (default: 
    2167           @code{printlevel=0}). 
     2167          If @code{printlevel>=0} additional comments are displayed (default:
     2168          @code{printlevel=0}).
    21682169SEE ALSO: closed_points, Adj_div
    21692170EXAMPLE:  example NSplaces; shows an example
    … …  
    33693370  list C=Adj_div(x3y+y3+x);
    33703371  C=NSplaces(3,C);
    3371   // the first 3 Places in C[3] are of degree 1. 
     3372  // the first 3 Places in C[3] are of degree 1.
    33723373  // we define the rational divisor G = 4*C[3][1]+4*C[3][3] (of degree 8):
    33733374  intvec G=4,0,4;
    … …  
    34013402  // programm
    34023403  poly auxp=gcd(F[1],F[2]);
    3403   return(ideal(division(auxp,F)[1]));
     3404  return(ideal(division(F,auxp)[1]));
    34043405}
    34053406///////////////////////////////////////////////////////////////////////////////
    … …  
    35223523NOTE:     The procedure must be called from the ring CURVE[1][2],
    35233524          where CURVE is the output of the procedure @code{NSplaces}.
    3524 @*        i represents the place CURVE[3][i]. 
     3525@*        i represents the place CURVE[3][i].
    35253526@*        Rational functions are represented by numerator/denominator
    35263527          in form of ideals with two homogeneous generators.
    … …  
    39153916  def ER=HC[1][4];
    39163917  setring ER;
    3917   intvec G=5;      // the rational divisor G = 5*HC[3][1] 
     3918  intvec G=5;      // the rational divisor G = 5*HC[3][1]
    39183919  intvec D=2..9;   // D = sum of the rational places no. 2..9 over F_4
    39193920  // let us construct the corresponding evaluation AG code :
    … …  
    39623963  def ER=HC[1][4];
    39633964  setring ER;
    3964   intvec G=5;      // the rational divisor G = 5*HC[3][1] 
     3965  intvec G=5;      // the rational divisor G = 5*HC[3][1]
    39653966  intvec D=2..9;   // D = sum of the rational places no. 2..9 over F_4
    39663967  // let us construct the corresponding residual AG code :
    … …  
    43664367  def ER=HC[1][4];
    43674368  setring ER;
    4368   intvec G=5;      // the rational divisor G = 5*HC[3][1] 
     4369  intvec G=5;      // the rational divisor G = 5*HC[3][1]
    43694370  intvec D=2..9;   // D = sum of the rational places no. 2..9 over F_4
    43704371  // construct the corresp. residual AG code of type [8,3,>=5] over F_4:
    43714372  matrix C=AGcode_Omega(G,D,HC);
    4372   // we can correct 1 error and the genus is 1, thus F must have degree 2 
     4373  // we can correct 1 error and the genus is 1, thus F must have degree 2
    43734374  // and support disjoint from that of D;
    43744375  intvec F=2;
    … …  
    45164517  def ER=HC[1][4];
    45174518  setring ER;
    4518   intvec G=5;      // the rational divisor G = 5*HC[3][1] 
     4519  intvec G=5;      // the rational divisor G = 5*HC[3][1]
    45194520  intvec D=2..9;   // D = sum of the rational places no. 2..9 over F_4
    45204521  // construct the corresp. residual AG code of type [8,3,>=5] over F_4:
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