//(GMG/BM, last modified 22.06.96)
///////////////////////////////////////////////////////////////////////////////
version="$Id: ringgb.lib,v 1.16 2001/01/16 13:48:40 Singular Exp $";
category="Beta Testing";
info="
LIBRARY:  ringgb.lib     Examples and tests for ringgb development

PROCEDURES:
 findZeroPoly(f);        finds a zero polynomial for reducing f
 zeroReduce(f);          normal form of f concerning the ideal of zero polynomials
 zeroReduceProt(f);          normal form of f concerning the ideal of zero polynomials
";

LIB "general.lib";
///////////////////////////////////////////////////////////////////////////////

proc findZeroPoly (poly f)
"USAGE:   findZeroPoly(f); f - a polynomial
RETURN:  zero polynomial with the same leading term as f if exists, otherwise 0
NOTE:    just a wrapper
EXAMPLE: example findZeroPoly; shows an example
"
{
   return(system("findZeroPoly", f));
}
example
{ "EXAMPLE:"; echo = 2;
  option(teach);
  ring r = 65536, (y,x), dp;
  poly f = 1024*x^8*y^2+11264*x^8*y+28672*x^8+45056*x^7*y^2+36864*x^7*y+16384*x^7+40960*x^6*y^2+57344*x^6*y+32768*x^6+30720*x^5*y^2+10240*x^5*y+8192*x^5+35840*x^4*y^2+1024*x^4*y+20480*x^4+30720*x^3*y^2+10240*x^3*y+8192*x^3+4096*x^2*y^2+45056*x^2*y+49152*x^2+40960*x*y^2+57344*x*y+32768*x;
  findZeroPoly(f);
}

proc zeroReduceExt (poly f , int i)
"USAGE:   zeroReduceExt(f, i); f - a polynomial, i - noisy level
RETURN:  reduced normal form of f modulo zero polynomials
EXAMPLE: example zeroReduceExt; shows an example
"
{
   poly h = f;
   poly n = 0;
   poly g = findZeroPoly(h);
   while ( h <> 0 ) {
      while ( g <> 0 ) {
         h = h - g;
         if (i == 1) {
            printf("reduce with: %s", g);
            printf("to: %s", h);
         }
         g = findZeroPoly(h);
      }
      n = lead(h) + n;
      h = h - lead(h);
      g = findZeroPoly(h);
   }
   return(n);
}
example
{ "EXAMPLE:"; echo = 2;
  option(teach);
  ring r = 65536, (y,x), dp;
  poly f = 1024*x^8*y^2+11264*x^8*y+28672*x^8+45056*x^7*y^2+36864*x^7*y+16384*x^7+40960*x^6*y^2+57344*x^6*y+32768*x^6+30720*x^5*y^2+10240*x^5*y+8192*x^5+35840*x^4*y^2+1024*x^4*y+20480*x^4+30720*x^3*y^2+10240*x^3*y+8192*x^3+4096*x^2*y^2+45056*x^2*y+49152*x^2+40960*x*y^2+57344*x*y+32768*x;
  zeroReduceExt(f,0);
  zeroReduceExt(f,1);
}

proc zeroReduce (poly f)
"USAGE:   zeroReduce(f); f - a polynomial
RETURN:  reduced normal form of f modulo zero polynomials
EXAMPLE: example zeroReduce; shows an example
"
{
   return(zeroReduceExt(f, 0));
}
example
{ "EXAMPLE:"; echo = 2;
  option(teach);
  ring r = 65536, (y,x), dp;
  poly f = 1024*x^8*y^2+11264*x^8*y+28672*x^8+45056*x^7*y^2+36864*x^7*y+16384*x^7+40960*x^6*y^2+57344*x^6*y+32768*x^6+30720*x^5*y^2+10240*x^5*y+8192*x^5+35840*x^4*y^2+1024*x^4*y+20480*x^4+30720*x^3*y^2+10240*x^3*y+8192*x^3+4096*x^2*y^2+45056*x^2*y+49152*x^2+40960*x*y^2+57344*x*y+32768*x;
  zeroReduce(f);
}

proc zeroReduceProt (poly f)
"USAGE:   zeroReduceProt(f); f - a polynomial
RETURN:  reduced normal form of f modulo zero polynomials and describes the way *g*
EXAMPLE: example zeroReduceProt; shows an example
"
{
   return(zeroReduceExt(f, 1));
}
example
{ "EXAMPLE:"; echo = 2;
  option(teach);
  ring r = 65536, (y,x), dp;
  poly f = 1024*x^8*y^2+11264*x^8*y+28672*x^8+45056*x^7*y^2+36864*x^7*y+16384*x^7+40960*x^6*y^2+57344*x^6*y+32768*x^6+30720*x^5*y^2+10240*x^5*y+8192*x^5+35840*x^4*y^2+1024*x^4*y+20480*x^4+30720*x^3*y^2+10240*x^3*y+8192*x^3+4096*x^2*y^2+45056*x^2*y+49152*x^2+40960*x*y^2+57344*x*y+32768*x;
  zeroReduceProt(f);
}