source: git/Singular/LIB/lejeune.lib @ 4c4b1e

//-*- mode:C++;-*-
// $Id: lejeune.lib,v 1.3 2005-06-20 10:18:00 cremer Exp $

info="
LIBRARY: lejeune1.4.lib  Arc space computations
AUTHOR:  Nadine Cremer,    nadine.cremer@gmx.de
[SEE ALSO: <comma-separated words of cross references>]
[KEYWORDS: <semicolon-separated phrases of index keys>]
PROCEDURES:
    variables(k,i);      creates k*i new var. t,a(1),..,a(i),..,x(1),..,x(i)
    a_z(k);            returns kth letter of the alphabet
    tpolys(k,i);        creates polyn. a(1)*t+..+a(n)*t^n
  ";


LIB "ring.lib";
LIB "general.lib";


proc plugin_coeffs (int i,poly f)
{
  def r=basering;
  int k=nvars(r);
  string str=variables(k,i);
  
  def R=changevar(""+varstr(r)+",t,"+variables(k,i)+"");
  setring R;
  ideal I=tpolys(i,k);
  poly g=imap(r,f);
  map h=r,I;
  ideal J=h(f);
  matrix output=coeffs(J[1],t);
  keepring R;
  return(output);
}








proc variables (int k,int i)
{
  list l;
  int s,u;                              // loop variables
  string str;               
  for (u=1;u<=k;u++) 
   {
     for (s=1;s<=i;s++)
     {
       str=""+a_z(u)+"("+string(s)+")";     
       l[(u-1)*i+s]=str;
     }
   } 
  //l=insert(l,"t");
  string str1=string(l);
  return(str1);
}


proc a_z (int n)                      // returns nth letter of the alphabet
{ 
  if((n<1)||(n>26))                     // input admissible?
   { 
     "n must range between 1 and 26!";
      return(0); 
   } 
  string s="ring r=0,("+A_Z("a",n)+"),ds;"; 
  execute(s); 
  return (string(var(n))); 
} 



proc tpolys (int i,int k)             // constructs polynomials a(1)*t+... 
{                                     // has to be called from tpolys
  int s,t;                             // loop variables
  int v;           
  poly sum; 
  ideal I; 
  for(t=1;t<=k;t++) 
   {  
     v=(t-1)*i; 
     for(s=1;s<=i;s++) 
      { 
        sum=sum+var(1+k+v+s)*var(k+1)^s;    // clumsy: working with "var(1)"
      } 
     I[t]=sum; 
     sum=0; 
   }   
  return(I); 
}