#########################################################################
#25.maple                                                               #
#                                                                       #
#   This MAPLE code sets up[ a Singular file which computes a           #
#   Degree reverse Lexicographic Groebner basis.                        #
#                                                                       #
#   It treats the enumerative problem of 10 Schubert                    #
#   hypersurfaces in G(5,2), each defined by a 2-plane.                 # 
#   There are 42 5-planes meeting 10 fixed 2-planes in C^7.             #
#                                                                       #
#   Computing drl Gr\"obner basis  (SINGULAR)   3.69   seconds          #
#	                                                                #
#########################################################################

interface(quiet=true):


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



eqs:=[]:
for i from 1 to 10 do eqs:=[eqs[],Eq(i)]: od:

lprint(`//Execute this with:`);
lprint(`//Singular --ticks-per-sec=100<25.sing`);
lprint(`//`);
lprint(`//ring R= 0, (a,b,c,d,e,f,g,h,x,y), dp;`);
lprint(`//`);
lprint(`timer=1;`);
lprint(`//`);
lprint(`ring R= 0, (a,b,c,d,e,f,g,h,x,y), dp;`);
lprint(`ideal I=`);
for i from 1 to 10 do  
lprint(eqs[i],`,`);  od:
lprint(`0;`);
lprint(`int t=timer;`);
lprint(`ideal G = std(I);`);
lprint(`int s=timer-t;`);
lprint(`print("Time to compute one 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;