/*M	Groebner basis algorithm over a Galois-field	input: a list of polynomials over a Galois-fieldM*/#include <_pol3.h>main(){  single anz,met,r,p,n;  pol    P,G;  list   AL,VL,Vgfs,PL,PL1;  init(P,G,AL,VL,Vgfs,PL,PL1);  PL    = _0;  GBRHO = 0;/* Galois-field */  printf("\n characteristic p of the Galois-field GF(p^n): p = ");  p = getsi();  printf(" degree n of the Galois-field GF(p^n): n = ");  n = getsi();  printf(" polynomial generating the Galois-field: G(a) = ");  Vgfs = list1(list1('a'));  /* <-- variable list belonging to				    the Galois-field elements */  G    = getpms(1,p,Vgfs);  AL   = gfsalgen(p,n,G);/* list of variables occuring in the polynomials */  printf("\n Enter the variable list for the polynomials");  printf(" (e.g. in the form \"x y z #\").\n");  printf(" Please do NOT use the variable 'a'!  ");  VL = getvl();  r  = llength(VL);/* term order */  printf("\n The following term orders are possible:\n");  printf("          - lexicographical                      ( EVORD = 1 ),\n");  printf("          - graduated lexicographical            ( EVORD = 2 ),\n");  printf("          - total degree ordering\n");  printf("            (Buchberger's total degree ordering) ( EVORD = 3 ),\n");  printf("          - lexicographical with inverse\n");  printf("            exponent vector                      ( EVORD = 4 ).\n");  printf(" EVORD = ");  EVORD = getsi();/* list of polynomials over the specified Galois-field */  printf("\n Enter a list of polynomials over the");  printf(" specified Galois-field in the form\n");  printf("         { p1 ... pm }\n");  printf(" where each polynomial pi ends with a '#'.\n ");  PL = getdipgfsl(r,p,AL,VL,Vgfs);/* computation of the Groebner basis */  printf("\n normal / recursive method ?  1 / 0 : ");  met = getsi();  if ( met == 1 )  PL1 = dipgfsgb(r,p,AL,PL);  /*  <---- normale Groebner basis algorithm ---- */  else  PL1 = dipgfsgbr(r,p,AL,PL);            /*  <---- recursive Groebner basis algorithm ---- *//* output */  printf("\n Groebner basis:");  putdipgfsl(r,p,AL,PL1,VL,Vgfs);}