#52.maple # # Frank Sottile # 27 October 1998 # Berkeley, CA # # Testing instances of Shapiro's Totally Positive conjecture # for the case of 6 2-planes in C^7 meeting 5 4-planes non-trivially. # # Number Seed Time Size # 200 1 Make systems 156.990 648194 \ # Eliminants 209 190062 > Schur # Real roots 20 / # 2800 123 Make systems 14309.18 9054899 \ # Eliminants 10087 2653975 > Schubert # Real roots 1864.130 / # # 1000 1212 Make systems 5190.539 3235288 \ # Eliminants 4106 947026 > Schubert # Real roots 644.120 / # interface(quiet=true): with(linalg): _seed:=1212: die:=rand(1..10): ELM:=proc(X,Y,Z,W,S,T) matrix([ [1,X,0,0,0,0,0], [0,1,Y,0,0,0,0], [0,0,1,Z,0,0,0], [0,0,0,1,W,0,0], [0,0,0,0,1,S,0], [0,0,0,0,0,1,T], [0,0,0,0,0,0,1]]) end: Pos:=proc(a1,b1,b2,c1,c2,c3,d1,d2,d3,d4,e1,e2,e3,e4,e5,f1,f2,f3,f4,f5,f6) multiply(ELM(a1,0,0,0,0,0),ELM(b1,b2,0,0,0,0),ELM(c1,c2,c3,0,0,0), ELM(d1,d2,d3,d4,0,0),ELM(e1,e2,e3,e4,e5,0),ELM(f1,f2,f3,f4,f5,f6)) end: Coords:=matrix([ [1,a,b,c,0,0,0], [0,0,0,1,d,e,f]]): COLS:=[[1,2,3,4,5,6],[1,2,3,4,5,7],[1,2,3,4,6,7], [1,2,3,5,6,7],[1,2,4,5,6,7],[1,3,4,5,6,7],[2,3,4,5,6,7]]: M.0:=band([1],7): ST_Nreal:="lprint(`realroots = `,NREAL,`seed = `,": ST_end:=");": ############################################################################# # # #lprint(`timer = 1;`); lprint(`option(redSB);`); lprint(`int t=timer;`); lprint(`ring R= 0, (a,b,c,d,e,f), (dp(5),dp(1));`); lprint(`ideal I;`); lprint(`ideal G;`); lprint(`print("interface(quiet=true):");`); lprint(`print("readlib(realroot):");`); for ntrials from 1 to 1000 do SEED:=_seed: for j from 1 to 3 do Params:=[]: for i from 1 to 21 do Params:=[Params[],die()]: od: M.j:=multiply(Pos(Params[]),M.(j-1)); od: lprint(`I=`); for j from 1 to 3 do M:=stackmatrix(submatrix(M.j,[1,2,3,4],[1,2,3,4,5,6,7]),Coords): for Col in COLS do lprint(det(submatrix(M,[1,2,3,4,5,6],Col)),`,`);: od: od: lprint(`0;`); lprint(`G = std(I);`); lprint(`print("POLY:=");`); lprint(`short=0;`); lprint(`G[1];`); lprint(`print(":");`); lprint(`print("NREAL:= nops(realroot(POLY, 1/100)): ");`); lprint(`print(" if NREAL<6 then");`); lprint(`print("`,convert(ST_Nreal,symbol)); lprint(convert(SEED,symbol)); lprint(convert(ST_end,symbol),` ");`); lprint(`print("fi: ");`); lprint(`print(" ");`); lprint(`print(" ");`); lprint(`print("#######################################################");`); lprint(`print("# #");`); lprint(`print("# Next One #");`); lprint(`print("# #");`); lprint(`print("#######################################################");`); lprint(`print(" ");`); od: lprint(`print("time(); ");`); lprint(`print("quit; ");`); lprint(`timer-t;`); lprint(`quit;`); time(); quit;