##########################################################################
#24.maple                                                                #
#                                                                        #
#	This MAPLE code creates a Singular file which computes a         #
#	Degree reverse Lexicographic Groebner basis.                     #
#                                                                        #
#	It treats the enumerative problem of 8 codimension 1 Schubert    #
#	hypersurfaces in Grass(4,6), each defined by a 2-plane.          #
#	There are 14 4-planes meeting 8 fixed 2-planes in C^6.           #
#                                                                        #
#					                seconds          #
#	Computing a drl Gr\"obner basis  (SINGULAR)       .02            #
#	                                                                 #
##########################################################################
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],
              [1,0, 0 ,  0  ,  a  ,  b   ],
              [0,1, 0 ,  0  ,  c  ,  d   ],
              [0,0, 1 ,  0  ,  e  ,  f   ],
              [0,0, 0 ,  1  ,  g  ,  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<24.sing`);
lprint(`//`);
lprint(`//ring R= 0, (a,b,c,d,e,f,g,h), dp;`);
lprint(`//`);
lprint(`//ring R= 0, (b,a,d,f,c,e,h,g), wp(5,4,4,3,3,2,2,1);`);
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;