########################################################################## #72.maple # # This MAPLE code is designed to set up and run a single instance # # of Shapiro's conjecture concerning real enumerative goemetry. # # # # It treats the enumerative problem of 12 codimension 1 Schubert # # hypersurfaces in G_{2,6}, each defined by a codimension 2-plane. # # There are 132 2-planes meeting 12 codimension 2 linear subspaces # # of C^8. # # # # Computing drl Gr\"obner basis (SINGULAR) 8175 seconds # # # ########################################################################## interface(quiet=true): with(linalg): L := s -> matrix([ [s^8, 8*s^7,28*s^6,56*s^5,70*s^4,56*s^3,28*s^2, m , n ], [s^7, 7*s^6,21*s^5,35*s^4,35*s^3,21*s^2, 7*s , k , l ], [s^6, 6*s^5,15*s^4,20*s^3,15*s^2, 6*s , 1 , i , j ], [s^5, 5*s^4,10*s^3,10*s^2, 5*s , 1 , 0 , g , h ], [s^4, 4*s^3, 6*s^2, 4*s , 1 , 0 , 0 , e , f ], [s^3, 3*s^2, 3*s , 1 , 0 , 0 , 0 , c , d ], [s^2, 2*s , 1 , 0 , 0 , 0 , 0 , a , b ], [s , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 1 ], [1 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 ]]): lprint(`int t=timer;`); lprint(`ring R = 0,(a,b,c,d,e,f,g,h,i,j,k,l,m,n), (dp(14));`); Index:={1,2,3,4,5,6,7,8,9,10,11,12,13,14}: equations:= {}: for ii in Index do equations:= equations union {det(L(ii))}: od: lprint(`print("interface(quiet=true):");`); lprint(`print("with(linalg):");`); lprint(`print("readlib(realroot):");`); lprint(`print("");`); lprint(`ideal I =`); for ee in equations do lprint(eval(ee),`,`);od; lprint(`0;`); lprint(`ideal G = std(I);`); lprint(`dim(G);`); lprint(`mult(G);`); lprint(`timer-t;`); lprint(`print(G);`); lprint(`quit;`); quit;