############################################################################
#42.maple                                                                  #
#                                                                          #
#   This MAPLE code sets up a Singular file which computes a              #
#   Degree reverse Lexicographic Groebner basis.                           #
#                                                                          #
#   It treats the enumerative problem of 8 codimension 1 Schubert          #
#   hypersurfaces in Grass(2,6), each defined by a codimension 2-plane.    # 
#   There are 14 2-planes meeting 8 codimension 2 linear subspaces         # 
#   of C^6.                                                                #
#                                                                          #
#   				                    seconds                #
#   Computing a drl Gr\"obner basis  (SINGULAR)       .04                  #
#   				                                           #
############################################################################
interface(quiet=true):

Eq := s -> simplify(linalg[det](linalg[matrix]([
              [1,s,s^2, s^3 , s^4 ,   s^5],
              [0,1,2*s,3*s^2,4*s^3, 5*s^4],
              [0,0, 1 , 3*s ,6*s^2,10*s^3],
              [0,0, 0 ,  1  ,4*s  ,10*s^2],
              [1,0, a ,  c  ,  e  ,  g   ],
              [0,1, b ,  d  ,  f  ,  h   ]]))):

eqs:=[]:
for i from 1 to 8 do eqs:=[eqs[],Eq(9-i)]: od:

lprint(`//Execute this with:`);
lprint(`//Singular --ticks-per-sec=100<42.sing`);
lprint(`//`);
lprint(`timer=1;`);
lprint(`//`);
lprint(`ring R= 0 , (a,b,c,d,e,f,g,h),dp;`);
lprint(`ideal I=`);
for i from 1 to 8 do  
lprint(eqs[i],`,`);  od:
lprint(`0;`);
lprint(`int t=timer;`);
lprint(`ideal G;`);
lprint(`G= std(I);G= std(I);G= std(I);G= std(I);G= std(I);`);
lprint(`G= std(I);G= std(I);G= std(I);G= std(I);G= std(I);`);
lprint(`G= std(I);G= std(I);G= std(I);G= std(I);G= std(I);`);
lprint(`G= std(I);G= std(I);G= std(I);G= std(I);G= std(I);`);
lprint(`G= std(I);G= std(I);G= std(I);G= std(I);G= std(I);`);
lprint(`G= std(I);G= std(I);G= std(I);G= std(I);G= std(I);`);
lprint(`G= std(I);G= std(I);G= std(I);G= std(I);G= std(I);`);
lprint(`G= std(I);G= std(I);G= std(I);G= std(I);G= std(I);`);
lprint(`G= std(I);G= std(I);G= std(I);G= std(I);G= std(I);`);
lprint(`G= std(I);G= std(I);G= std(I);G= std(I);G= std(I);`);
lprint(`int s=timer-t;`);

lprint(`print("Time to compute 50 drl Groebner bases: "); `);
lprint(`s;`);
lprint(`print("Time units, counts per second:");`);
lprint(`system("--ticks-per-sec");`);
lprint(`degree(G);`);
lprint(`ncols(G);`);
lprint(`print(G);`);

lprint(`quit;`);

quit;