#compilation.maple # Contains data from Spring 1997 search for reality of # feedback laws. interface(quiet=true): # # This Maple script contains the data from a search done to # attempt to determine how common it is for a # `transfer function to be not controllable by real data' # # It is written up more fully in Search.description # # In short, we generated many (500) different transfer functions # with integral polynomial entries for the m=2, p=4 case, and for # each, determined the number of real and complex feedback laws for # a number (25 or 50) of different 8-tuples of real (integral) poles. # In all 15,000 tests were made. # # This was accomplished by computing an elimination Gr\"obner basis # for each of the resulting 15,000 polynomial systems. Then, for # each eliminant, the real root routine of Maple determined the # number of real roots, hence the number of real feedback laws. # # The results are displayed below in 8-tuples whose (i+1)st component # is the frequency of the systems with 2*i real feedback laws. # # Total # [23, 804, 3370, 5345, 3854, 1325, 272, 7] # # Frequency, (%) # # [.15, 5.4, 22.5, 35.6, 25.7, 8.8, 1.8, .047] # # # We may conclude from this that it is quite unlikely to find # a system that is not controllable by real data, or one for which # all feedback laws are real. # # - Frank Sottile # MSRI # 26 May, 1997. # ######################################################################### with(linalg): Total:=vector([0,0,0,0,0,0,0,0]): ################################################### # # First 50 transfer functions x 25 pole sets # ################################################### numroots:= matrix([ [4,6,10,6,12,6,6,4,4,4,8,10,4,6,6,8,4,4,4,6,4,8,6,10,4], [6,8,10,10,6,8,4,10,6,4,6,6,10,10,8,6,6,8,6,10,10,10,10,6,6], [2,2,4,2,2,4,6,8,8,4,8,2,6,2,6,4,8,2,6,8,6,4,4,2,4], [10,8,8,4,8,4,10,8,6,8,8,4,8,6,4,8,12,10,6,6,8,8,4,8,6], [4,8,2,8,8,8,8,8,10,4,8,8,8,8,8,2,6,8,8,8,8,4,6,6,10], [4,4,8,6,4,4,8,6,6,4,4,4,4,4,4,4,4,2,6,6,4,4,4,6,4], [8,14,6,8,10,6,6,8,6,8,6,6,6,12,6,6,6,10,6,6,6,8,6,8,8], [4,8,6,6,8,8,4,8,4,4,6,6,6,6,8,6,6,8,4,8,6,6,6,6,6], [8,4,6,8,8,10,6,8,10,6,8,4,8,10,6,4,12,12,4,6,6,6,8,10,10], [4,8,4,4,4,6,4,4,4,4,4,4,4,6,4,6,6,4,6,4,6,4,4,6,4], [4,4,2,6,4,6,2,6,4,6,6,4,4,2,2,2,6,4,4,2,4,6,4,2,6], [6,4,6,6,6,8,6,6,6,6,6,6,6,6,6,8,8,6,6,6,6,6,8,6,6], [8,4,8,12,6,6,8,8,10,8,8,8,10,10,6,8,4,8,8,8,8,8,8,8,6], [4,6,8,4,4,4,6,6,4,6,4,4,6,6,4,6,12,4,4,6,6,4,4,6,6], [4,6,2,4,6,4,2,8,4,4,6,2,2,6,6,2,6,4,8,6,2,4,8,4,8], [6,6,8,8,8,6,6,6,8,6,6,8,6,6,6,6,8,6,6,6,6,6,6,10,6], [6,8,8,8,8,6,6,8,6,8,8,4,6,8,6,8,10,8,8,8,6,8,6,6,6], [10,8,14,6,8,8,8,8,8,10,8,10,8,8,8,8,8,10,8,8,10,6,8,8,6], [4,6,2,4,6,4,2,8,4,4,6,2,2,6,6,2,6,4,8,6,2,4,8,4,8], [6,10,6,6,8,6,6,10,6,8,8,4,6,6,8,4,6,6,6,8,8,6,6,6,6], [4,6,4,6,4,4,4,6,6,8,6,8,4,4,2,4,4,6,6,6,4,4,4,6,2], [4,6,4,6,4,4,4,6,6,8,6,8,4,4,2,4,4,6,6,6,4,4,4,6,2], [8,8,12,8,6,8,6,8,6,2,10,8,4,4,8,8,6,10,8,6,10,6,8,4,4], [6,4,4,4,6,2,4,4,6,8,6,6,4,6,4,4,4,6,4,6,4,6,6,4,8], [4,4,10,10,6,6,6,8,8,8,4,8,6,6,8,4,8,8,6,8,8,6,8,4,6], [8,8,8,8,6,10,8,8,6,4,8,6,4,6,12,8,6,6,8,6,10,6,10,6,6], [4,2,6,6,4,6,8,4,8,6,4,6,8,6,8,6,4,4,6,8,8,10,2,8,6], [4,6,4,6,4,6,4,4,6,6,4,4,4,4,4,6,4,4,6,6,6,4,6,6,6], [8,8,10,10,10,8,6,8,8,8,10,8,8,8,10,10,10,10,8,8,12,8,10,12,10], [8,8,6,10,8,6,6,10,10,8,8,8,6,8,10,6,6,6,8,8,12,6,6,10,6], [6,4,4,4,4,6,4,6,6,6,6,4,4,4,6,4,6,6,6,6,4,4,6,8,6], [6,4,6,8,6,10,8,6,4,8,6,8,6,10,8,6,6,6,8,4,8,8,8,8,6], [8,8,6,6,6,6,6,6,4,6,4,4,2,6,2,4,6,6,4,4,6,6,6,6,6], [6,6,6,6,6,6,6,6,8,8,8,8,6,8,8,4,6,4,8,6,8,6,6,6,6], [10,8,8,6,6,8,6,6,4,6,10,6,4,8,8,6,8,4,4,4,6,8,8,8,8], [8,6,10,8,8,6,10,10,8,8,8,8,10,10,10,6,4,8,8,8,6,8,8,8,10], [6,8,10,10,8,8,10,6,10,12,8,6,6,8,8,10,6,8,8,6,8,8,10,8,8], [4,2,4,2,4,6,4,4,4,4,4,4,2,4,4,4,4,6,2,4,4,4,4,2,4], [8,8,8,10,8,8,6,8,6,6,6,8,8,6,8,6,6,6,6,6,6,8,10,8,8], [10,6,10,6,4,8,4,4,6,6,6,8,6,4,4,10,6,6,4,10,4,8,8,8,2], [6,6,8,8,6,8,6,8,6,6,8,6,6,10,6,4,6,6,6,10,8,10,8,8,8], [6,6,6,6,6,6,8,6,6,6,6,6,6,8,8,10,6,6,6,6,6,6,8,10,8], [8,4,4,8,10,8,10,10,6,8,10,8,6,10,8,8,10,6,4,14,10,10,12,6,10], [6,6,6,4,4,6,6,4,6,6,6,6,4,6,6,6,6,6,6,8,6,6,6,8,4], [4,6,2,6,4,6,6,6,4,8,4,6,8,4,8,4,4,6,4,6,8,6,6,4,6], [8,8,4,6,8,6,6,6,6,6,6,8,6,8,6,6,6,6,6,6,6,8,10,8,6], [8,4,6,8,10,10,4,4,6,8,4,10,6,10,10,10,6,10,8,6,4,10,8,8,10], [8,4,8,10,10,6,8,12,10,2,8,4,6,4,6,6,12,8,6,6,2,12,8,8,6], [6,4,2,6,8,2,4,6,8,6,4,8,4,4,6,6,8,6,4,6,8,6,10,6,8], [6,6,8,8,6,6,12,10,8,6,10,6,6,10,8,8,6,10,6,6,6,8,6,8,8] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: #print(evalm(num)); Total:= matadd(Total,num): ############################################################ # # Second 50 transfer functions x 25 pole sets # ############################################################ numroots:= matrix([ [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], [6,6,4,6,6,6,6,6,6,6,6,6,6,6,6,8,6,6,6,6,8,6,6,8,6], [8,6,6,6,8,8,6,8,6,6,8,6,6,6,8,6,8,4,8,6,4,8,6,6,8], [4,4,4,4,4,4,6,6,4,4,6,6,6,6,4,4,4,6,4,4,4,4,6,4,4], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [8,8,8,8,10,8,10,6,8,8,8,8,8,8,6,8,10,10,8,8,10,8,6,6,6], [4,4,6,6,4,4,4,4,4,4,4,4,4,4,6,4,4,4,4,6,4,4,4,4,4], [8,8,8,8,8,6,8,8,6,8,8,8,8,8,6,6,8,8,8,8,8,6,6,8,8], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], [10,12,10,12,10,12,10,12,10,10,12,10,12,12,12,12,10,12,12,10,10,12,12,12,10], [6,6,6,8,6,6,8,6,6,8,4,8,6,8,6,8,6,6,8,8,6,4,6,6,4], [10,8,8,8,8,12,10,8,10,10,8,8,8,8,12,8,10,8,10,8,8,10,8,10,10], [8,8,8,8,8,8,8,10,10,8,8,8,8,10,8,10,10,8,8,8,8,8,8,8,8], [8,10,8,10,8,8,10,10,10,8,8,10,10,8,8,8,10,10,8,10,8,12,8,8,10], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,4,6,6,6,6,4], [8,4,4,4,4,8,4,8,4,4,8,4,8,8,6,4,4,4,4,8,8,8,6,4,4], [4,4,6,4,4,4,4,4,4,4,4,4,4,4,4,4,6,4,4,4,4,4,4,4,4], [8,8,6,8,8,8,6,8,8,8,6,8,8,8,8,8,6,8,8,8,8,8,8,8,8], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], [8,8,8,10,10,12,8,10,8,10,8,12,8,8,10,8,8,10,10,8,12,12,10,8,10], [6,6,6,6,8,6,6,6,6,6,8,6,8,6,6,6,6,8,8,8,8,6,8,8,6], [6,6,6,8,8,6,6,6,6,4,10,6,10,6,6,10,6,8,10,6,8,6,6,2,6], [6,6,4,8,6,8,6,6,8,8,8,8,8,8,6,6,6,8,6,6,6,8,8,6,6], [8,6,8,6,6,6,8,6,6,6,8,6,6,8,6,8,8,6,6,6,6,6,8,6,8], [10,10,8,8,10,10,8,10,10,12,8,6,10,8,10,10,8,8,8,8,10,10,8,10,6], [6,4,4,6,4,6,6,6,4,6,6,6,4,6,6,4,4,4,4,4,4,4,4,6,4], [10,8,10,8,8,6,8,8,10,8,6,8,10,6,8,8,8,10,10,8,8,8,6,8,8], [6,4,6,6,6,6,6,6,6,6,6,6,4,6,6,6,6,6,6,6,4,6,6,6,6], [6,8,6,8,8,8,8,8,8,8,8,8,8,8,10,8,10,8,6,8,8,6,8,10,6], [6,6,4,4,4,4,4,4,4,4,4,4,4,6,4,4,4,8,4,8,4,4,6,4,4], [6,6,6,8,4,6,6,6,4,4,4,4,6,4,6,8,4,10,4,8,6,4,6,6,4], [6,6,6,6,4,6,6,6,6,6,6,6,6,6,6,4,4,6,6,6,6,4,6,6,6], [2,2,2,4,2,2,4,6,2,6,2,6,4,4,2,2,2,4,4,2,2,4,2,6,2], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,8,6,6,6,8,6,6,6,6,6,8,6,6,6,6,6,6,6,6,6,6,6], [8,6,8,8,6,8,8,6,8,6,8,6,8,6,8,6,8,8,8,8,6,8,6,8,8], [8,8,8,8,12,8,8,8,8,8,8,8,8,6,10,12,8,8,8,8,8,10,10,8,8], [4,6,4,4,6,4,6,6,6,6,4,6,4,6,6,4,4,4,6,6,6,4,4,4,4], [10,10,10,8,10,10,10,10,10,8,10,8,10,10,10,10,10,10,10,10,10,8,10,10,10], [8,4,8,4,6,6,6,8,4,6,4,6,6,6,8,6,4,4,6,6,6,6,6,6,6], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], [4,4,6,4,6,4,4,4,4,4,4,4,6,4,6,4,4,4,4,4,4,4,4,4,4], [2,2,2,2,2,2,2,2,2,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [6,4,6,4,2,4,4,4,4,6,6,2,4,6,4,4,4,4,4,4,4,6,4,4,4], [8,8,14,8,10,8,10,10,10,10,10,8,10,6,8,6,6,10,10,6,14,10,10,14,10], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [8,8,6,8,6,8,8,6,8,8,8,8,8,8,8,8,6,6,6,8,6,8,6,8,8], [4,6,4,6,6,4,6,6,4,6,4,6,4,6,4,6,4,4,6,6,4,6,4,4,4] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: #print(evalm(num)); Total:= matadd(Total,num): ############################################################ # # Third 50 transfer functions x 25 pole sets # ############################################################ numroots:= matrix([ [8,8,8,6,8,6,10,8,8,8,10,8,8,10,6,8,8,10,8,8,8,8,10,6,12], [8,4,8,8,8,8,8,8,8,10,8,4,8,8,4,4,2,8,8,8,8,4,8,6,4], [6,4,6,4,6,4,4,4,2,4,4,4,4,4,4,4,6,2,2,4,4,4,4,4,6], [4,2,4,2,4,2,4,4,2,4,2,6,2,4,6,6,4,2,6,2,2,4,2,6,2], [8,6,6,6,4,6,6,6,6,4,4,4,6,6,6,8,4,4,4,6,6,6,4,4,4], [6,2,6,4,4,4,2,8,2,2,4,6,8,2,4,6,4,4,2,4,2,2,6,4,2], [4,4,6,4,6,4,4,4,4,6,4,6,4,4,8,6,6,4,4,2,6,6,6,6,6], [8,4,8,4,4,8,10,6,4,6,4,4,6,4,6,8,8,4,4,8,6,4,4,6,4], [6,6,10,6,6,6,6,6,6,6,8,6,8,6,8,8,8,8,6,6,6,6,8,6,6], [10,10,10,10,10,10,8,8,10,10,10,6,8,6,6,6,10,10,10,8,10,10,10,4,10], [8,8,8,6,6,8,6,10,4,6,8,8,8,8,8,6,6,6,6,8,8,8,6,6,8], [6,6,6,6,6,6,6,6,6,6,2,6,6,6,6,2,6,6,6,6,6,6,6,6,6], [8,10,8,8,8,8,8,8,8,8,10,8,10,8,8,10,12,12,6,12,6,8,8,8,8], [8,6,8,4,8,8,8,4,8,8,6,6,4,6,8,4,8,6,6,8,4,8,8,6,8], [8,8,8,8,8,8,8,10,8,6,6,8,8,8,8,8,6,8,6,8,8,8,8,8,10], [6,6,4,4,6,6,4,6,6,6,4,6,6,4,4,8,6,6,6,6,4,4,6,4,4], [10,8,8,8,6,6,8,8,10,6,10,10,8,8,10,6,10,10,8,8,10,8,10,8,8], [4,6,6,6,8,6,6,6,6,6,4,6,6,6,6,6,6,6,6,6,6,6,6,4,6], [6,8,8,10,4,6,8,8,8,6,8,10,6,6,6,4,8,8,10,6,6,8,6,8,8], [2,8,2,6,10,4,6,6,6,6,2,2,6,4,6,10,6,4,4,6,2,6,4,6,6], [6,4,4,4,4,4,4,2,4,6,4,4,6,4,4,4,4,4,4,8,6,4,4,4,8], [6,6,6,4,6,4,8,4,6,6,6,6,6,6,6,6,6,4,6,4,6,6,6,6,6], [8,8,10,8,8,8,10,8,8,8,10,10,6,4,8,10,4,8,10,8,8,6,8,10,6], [6,6,6,6,6,6,6,4,4,4,6,4,6,6,6,6,6,6,6,6,4,6,6,6,6], [4,6,6,6,6,4,8,8,4,6,10,4,4,6,4,4,6,6,8,4,6,8,6,6,6], [6,6,4,6,4,6,6,8,6,4,6,6,4,6,8,6,6,6,6,6,4,6,6,6,8], [8,6,6,4,6,8,4,4,8,8,6,4,2,8,8,10,6,6,6,4,8,6,2,4,6], [6,8,6,8,6,6,8,10,10,6,6,6,6,8,8,8,4,8,6,8,10,6,10,8,8], [6,6,8,6,8,8,10,10,6,6,6,8,6,6,6,10,10,6,8,6,8,8,8,8,6], [4,4,4,4,4,6,4,6,6,4,6,6,8,6,4,6,6,6,4,8,6,6,6,8,6], [6,6,6,4,8,8,8,6,8,8,6,10,6,8,4,6,8,8,6,6,6,6,6,8,8], [8,10,8,8,6,6,10,6,8,10,8,6,4,8,4,4,8,6,6,8,2,6,6,6,8], [4,6,8,8,4,2,8,4,4,6,8,8,6,6,2,8,4,6,8,6,6,6,8,8,8], [10,8,10,10,10,10,10,10,10,8,8,8,8,8,10,10,10,10,8,8,8,8,10,8,6], [6,6,8,8,10,8,10,8,12,8,10,8,8,8,10,6,6,10,8,6,8,8,8,8,6], [10,4,10,10,6,10,6,6,6,8,6,10,6,6,6,8,8,4,8,6,6,6,4,6,6], [4,4,8,4,8,10,6,4,6,8,6,8,8,4,6,8,6,6,6,6,6,6,6,12,8], [8,8,8,8,6,8,8,8,8,8,8,6,6,4,4,8,6,8,8,8,8,6,8,8,6], [8, 12,6,6,6,10,10,6,6,6,6,12,6,8,4,6,8,10,12,4,6,6,6,6,10], [8,4,4,6,6,8,8,8,6,6,6,6,4,6,4,6,8,6,4,6,6,6,4,6,6], [8,8,8,2,8,6,8,6,6,4,6,6,6,4,2,2,4,6,6,6,4,2,6,6,2], [6,4,4,4,4,2,6,6,4,6,4,2,6,6,6,6,4,6,4,6,6,4,6,6,4], [12,12,8,8,12,10,12,8,8,10,8,8,12,10,8,10,8,10,12,8,12,8,8,10,10], [8,10,6,8,8,6,6,10,6,8,2,6,8,10,10,8,6,8,6,10,10,6,10,10,6], [8,8,6,10,10,2,6,6,8,6,6,4,4,4,4,4,8,10,4,8,10,4,4,10,4], [6,8,8,8,8,6,4,6,6,6,6,4,8,8,8,8,6,8,6,6,8,8,6,8,8], [2,2,2,2,4,4,8,2,8,4,4,2,2,4,4,2,2,4,4,2,2,6,4,6,8], [8,6,4,8,8,8,4,4,6,8,4,4,4,6,8,6,4,8,8,6,6,8,8,10,8], [4,8,6,6,6,6,6,4,8,6,4,6,6,4,6,8,6,6,6,6,6,6,6,4,6], [6,6,6,4,6,4,4,6,6,6,6,6,6,6,6,6,4,6,6,6,4,6,6,6,6] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: #print(evalm(num)); Total:= matadd(Total,num): ########################################################## # # Fourth 50 transfer functions x 25 pole sets # ########################################################## numroots:= matrix([ [6,6,6,2,6,4,2,6,2,2,6,6,6,2,4,2,4,6,6,4,2,2,4,6,4], [8,8,8,6,4,8,8,8,6,6,8,8,6,8,4,8,8,8,8,8,8,8,8,6,8], [4,4,4,2,4,4,4,2,4,6,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,4,4], [8,8,8,6,6,10,10,6,6,8,8,6,8,8,6,8,6,8,10,8,8,8,8,8,8], [6,6,4,6,4,8,8,4,6,4,8,6,8,6,6,6,8,4,4,6,6,6,6,8,6], [4,4,4,6,6,4,4,4,6,6,4,4,6,4,6,6,4,4,4,4,4,4,4,4,4], [6,6,6,6,6,8,6,6,6,6,8,6,6,6,6,6,4,6,6,6,8,6,6,6,6], [6,6,6,6,4,6,4,4,4,6,6,4,6,6,6,6,6,6,4,6,6,4,6,6,4], [2,8,4,6,6,6,6,6,6,2,4,4,4,4,8,2,4,6,6,2,4,4,8,6,6], [2,6,6,2,6,4,6,4,4,6,8,8,6,4,8,6,4,6,4,4,2,4,6,4,6], [6,4,6,6,10,8,4,6,6,10,6,4,10,10,10,6,10,6,8,10,8,10,6,10,6], [4,6,6,6,6,4,4,6,6,6,8,6,4,6,4,6,6,6,6,4,6,6,6,6,6], [4,6,4,6,4,6,4,6,6,6,8,4,4,4,6,4,4,4,6,6,6,6,4,4,6], [4,4,6,4,4,8,4,6,8,2,6,6,6,6,4,4,4,4,4,4,4,4,6,6,6], [4,4,6,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,4,4,4,4,6,4,4], [6,6,6,6,6,4,4,4,6,6,4,6,6,4,4,4,6,8,4,2,4,8,4,4,6], [4,4,2,8,2,4,8,2,2,4,2,4,4,6,2,4,8,2,4,2,6,6,2,2,2], [4,6,6,6,6,6,6,6,4,6,6,6,8,6,6,6,6,6,6,4,6,6,6,6,6], [8,6,8,8,8,6,8,6,6,6,8,6,4,6,8,6,8,6,6,8,6,6,8,8,6], [6,6,6,6,8,8,6,8,6,8,6,6,6,8,6,8,8,8,6,6,8,6,6,8,6], [4,6,6,6,4,6,4,4,6,4,6,6,4,6,6,6,6,4,6,6,4,4,4,4,6], [10,10,8,10,12,12,12,10,12,10,10,12,12,10,10,12,10,12,10,12,10,12,10,10,10], [2,6,6,6,6,6,4,8,2,6,8,4,6,6,6,6,6,6,6,6,2,6,4,2,4], [6,6,6,8,8,8,8,8,8,8,6,10,8,8,8,6,8,6,8,8,8,6,8,6,6], [4,6,8,4,4,4,6,8,4,4,8,4,4,4,8,8,8,8,8,10,4,6,8,8,6], [4,2,4,4,4,4,2,2,2,4,2,4,4,4,4,4,4,4,4,4,2,2,2,6,2], [8,8,10,6,10,10,8,8,8,10,8,10,8,6,8,10,8,8,8,10,10,10,8,8,10], [8,4,4,6,2,8,4,4,8,2,2,4,8,8,4,2,8,4,6,8,2,8,6,2,6], [10,2,2,4,8,2,2,2,2,4,4,2,4,10,2,2,2,4,2,4,4,4,4,4,2], [6,6,6,4,4,4,4,6,6,6,10,6,6,4,4,4,4,6,4,4,6,4,4,8,4], [6,4,6,6,6,6,6,6,4,6,6,6,6,6,4,4,6,6,6,6,4,4,4,6,4], [8,6,6,8,8,8,6,6,6,8,8,6,8,6,6,8,6,8,6,6,8,8,8,6,8], [6,6,8,8,8,8,6,6,8,6,6,6,8,8,6,8,8,8,6,8,6,6,6,8,8], [6,8,6,6,12,12,4,6,6,4,10,10,6,10,6,6,6,6,8,8,8,8,8,12,8], [4,6,4,6,6,6,8,4,6,6,4,4,4,6,4,6,4,4,4,4,4,6,6,6,6], [6,8,8,6,4,6,6,6,8,4,6,6,6,8,6,6,6,8,6,6,8,6,4,6,6], [6,8,8,8,8,6,6,8,10,4,10,8,6,10,8,6,6,8,6,6,10,8,4,6,8], [8,4,6,6,6,4,6,6,6,4,4,6,6,6,6,4,8,6,6,4,6,6,6,6,8], [4,6,4,6,4,4,4,6,4,6,4,4,4,6,4,4,6,6,4,4,4,4,4,4,4], [8,8,10,6,8,8,8,8,8,8,8,8,8,6,8,10,8,8,8,8,4,8,6,6,8], [6,8,8,8,6,6,6,6,4,8,6,6,6,6,6,6,6,6,6,8,6,8,8,8,6], [4,2,2,2,6,6,4,6,6,2,4,2,6,6,6,2,4,4,4,2,2,4,4,2,2], [0,4,2,0,2,6,2,4,0,6,2,2,2,2,6,0,2,2,2,0,2,2,2,6,2], [8,10,8,8,6,8,8,8,8,8,8,10,8,8,8,10,8,8,8,6,8,8,6,10,8], [4,4,6,6,4,4,4,4,6,6,6,4,4,6,6,6,8,4,6,8,6,6,4,6,6], [6,6,8,4,6,6,8,6,6,6,6,8,8,6,6,8,6,6,8,6,6,6,6,8,6], [2,2,2,2,6,2,2,4,2,4,4,2,2,0,2,4,4,4,4,2,4,2,4,2,4], [8,4,2,4,6,8,4,4,6,6,6,8,6,6,2,4,8,8,4,8,6,8,8,8,8], [2,4,6,0,6,6,6,0,0,0,4,0,4,4,4,0,0,6,0,6,8,8,8,8,0] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: #print(evalm(num)); Total:= matadd(Total,num): ############################################################# # # Fifth 50 transfer functions x 25 pole sets # ############################################################# numroots:= matrix([ [8,8,4,6,8,6,10,8,10,4,6,6,6,6,6,8,6,6,6,10,4,8,8,6,4], [4,6,2,4,6,4,2,4,4,2,4,6,2,6,4,4,6,4,4,4,6,2,4,4,4], [8,8,8,8,8,4,4,6,4,4,10,8,4,4,10,8,8,10,8,8,4,10,8,6,6], [6,4,6,4,6,4,4,6,4,6,4,6,4,6,6,6,6,4,4,6,4,4,4,4,4], [6,8,8,8,8,4,4,8,8,4,4,6,8,6,6,6,8,4,8,2,8,4,6,8,8], [8,8,6,8,6,10,8,6,8,8,10,8,6,8,8,8,8,8,4,8,8,8,8,8,10], [4,4,4,6,4,4,4,4,6,4,6,4,4,4,4,4,6,6,4,4,6,6,4,6,6], [6,6,6,6,4,6,6,4,6,4,6,4,8,4,4,4,6,6,4,4,2,4,4,4,4], [8,8,10,8,8,8,8,6,10,8,12,6,10,10,8,6,8,8,4,6,10,10,10,6,10], [6,8,6,6,8,6,6,6,10,6,8,8,6,8,6,6,10,6,8,6,6,10,6,6,10], [4,2,4,2,4,2,4,6,4,4,4,2,6,2,4,2,4,4,4,4,2,4,6,4,4], [6,4,6,6,6,6,6,4,8,8,6,4,8,6,6,8,6,4,6,8,4,6,6,6,6], [10,8,8,8,8,8,10,8,8,8,8,8,8,8,8,8,8,10,8,10,8,8,8,8,8], [4,8,4,8,8,10,6,6,4,6,4,6,8,6,6,8,6,8,8,6,8,6,4,6,4], [8,6,6,8,8,10,8,6,8,6,6,8,8,6,6,6,10,8,4,6,6,8,6,8,8], [4,4,6,6,4,8,8,8,6,4,4,8,8,8,4,4,6,4,4,6,4,4,4,8,6], [4,6,6,6,4,8,8,8,6,6,6,6,6,6,6,8,6,6,6,6,6,8,6,6,8], [4,4,4,4,4,4,4,4,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], [6,8,6,8,6,10,8,8,8,10,8,8,8,8,6,8,8,8,8,10,8,8,6,6,8], [6,4,4,6,6,6,4,4,4,6,4,4,4,6,4,8,4,6,6,4,4,4,2,4,4], [2,6,4,6,6,4,6,6,4,6,6,6,4,4,6,6,6,6,4,4,4,4,6,6,8], [6,6,8,4,8,6,8,4,8,8,8,8,4,6,10,8,6,4,6,10,6,6,8,8,8], [4,8,4,8,4,6,8,4,8,4,4,8,8,8,4,8,4,8,8,6,6,4,6,6,4], [8,10,6,10,8,8,8,6,10,8,6,6,8,8,10,10,8,8,8,8,8,8,8,6,10], [8,6,8,6,6,6,6,6,10,8,6,8,6,6,8,8,8,6,6,8,6,4,8,8,8], [6,6,8,4,6,4,8,4,6,6,6,8,6,4,6,6,8,6,4,6,6,4,4,4,6], [4,4,4,6,6,4,4,4,6,6,4,6,6,6,6,6,6,6,4,4,6,6,4,6,4], [6,8,8,8,6,6,8,8,6,8,6,6,6,4,4,8,8,6,8,6,8,4,8,6,6], [4,4,4,6,8,4,6,8,8,10,8,6,4,8,4,8,6,8,6,4,8,6,8,8,6], [10,6,8,6,6,8,6,6,8,6,6,6,6,6,6,8,4,8,8,8,6,8,8,8,8], [10,6,6,6,6,10,8,8,12,6,10,4,8,8,6,6,6,6,6,6,6,6,8,8,6], [6,2,4,4,2,4,2,4,4,6,4,4,4,6,4,2,8,2,6,6,6,6,6,6,4], [4,6,4,4,4,6,6,4,4,4,8,4,6,4,4,4,6,4,6,8,4,6,6,4,4], [6,8,4,4,8,4,8,2,8,6,4,6,2,4,2,2,2,6,4,2,10,2,6,6,2], [4,2,2,2,8,6,2,4,2,2,2,6,4,2,4,2,8,2,6,4,6,2,4,4,2], [2,4,6,6,6,4,6,8,4,4,10,6,6,4,4,8,8,8,6,4,4,6,4,6,4], [4,4,2,6,2,2,2,6,6,2,6,6,6,4,6,6,2,6,2,6,6,10,4,4,6], [8,8,4,4,2,4,4,4,4,2,6,6,4,4,4,4,4,6,4,6,4,4,6,6,6], [4,6,6,6,6,6,4,6,6,4,4,6,6,4,4,6,4,6,4,6,4,6,4,6,6], [4,4,2,2,4,2,8,2,2,2,6,2,6,4,4,2,2,2,6,4,4,6,6,6,4], [6,8,10,6,6,8,8,8,8,8,8,6,6,6,8,8,8,8,12,8,6,10,10,8,8], [8,2,4,4,8,4,6,4,2,8,4,6,4,8,6,4,4,4,2,6,4,8,4,8,4], [10,10,8,10,10,8,8,8,6,10,8,10,10,10,8,8,8,8,8,10,10,10,8,10,8], [4,6,4,2,2,6,2,2,4,8,6,8,6,4,4,6,10,8,4,4,2,8,2,6,6], [4,4,6,4,2,2,2,4,2,2,2,6,2,4,4,2,6,4,8,4,4,2,2,4,2], [4,2,4,2,6,6,2,2,2,4,2,4,4,2,2,2,2,2,2,4,2,2,4,2,2], [6,8,6,6,6,6,4,6,8,6,6,4,8,4,6,6,6,6,8,8,4,4,6,6,4], [2,6,6,4,4,2,4,0,0,8,6,4,8,4,0,6,8,4,4,8,4,8,6,0,4], [8,6,6,8,4,8,6,6,6,4,6,6,6,4,8,6,8,6,6,8,6,8,6,8,8], [6,6,8,6,8,6,4,6,6,10,6,8,6,6,6,6,8,8,8,6,6,6,4,6,6] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: #print(evalm(num)); Total:= matadd(Total,num): ############################################################# # # sixth 50 transfer functions x 25 pole sets # ############################################################# numroots:= matrix([ [6,6,4,6,6,6,8,8,6,8,6,6,4,6,6,6,8,6,8,6,6,8,6,6,6], [10,10,10,8,8,8,10,8,8,10,10,10,10,6,10,10,6,6,10,6,8,10,8,10,6], [4,2,8,4,8,6,6,10,2,6,6,2,4,6,2,2,6,4,4,4,2,4,8,2,8], [6,6,6,6,6,6,4,4,6,4,6,4,6,8,8,4,6,6,6,4,4,6,6,6,6], [6,6,6,6,6,6,6,6,6,4,6,6,6,6,8,6,6,4,6,6,6,6,6,8,4], [8,8,6,6,8,6,6,8,10,6,6,6,6,8,8,6,6,8,6,6,6,6,8,8,8], [4,6,4,4,4,6,4,4,6,6,2,6,8,6,6,4,4,6,6,6,4,6,2,6,8], [2,2,6,6,6,6,2,6,2,2,6,6,2,2,6,2,4,2,6,6,8,6,6,2,6], [6,4,8,4,8,6,4,4,4,4,4,4,4,8,6,6,4,6,10,4,6,8,8,6,4], [6,8,6,8,8,4,4,8,6,8,10,8,2,8,4,2,8,0,8,8,10,8,2,8,8], [6,8,8,8,8,8,8,6,12,8,10,8,8,8,8,8,10,8,8,8,8,10,8,8,8], [12,6,6,10,12,4,10,10,10,12,8,12,12,12,10,10,12,10,12,12,12,12,12,8,8], [6,6,6,6,6,8,8,6,6,10,8,8,6,6,6,8,6,8,6,8,6,6,6,6,4], [4,4,4,4,4,4,4,4,4,6,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6], [2,6,6,6,4,2,2,6,6,2,2,2,6,2,6,2,2,2,2,2,6,4,2,2,2], [6,6,4,6,2,6,2,6,6,8,6,6,6,6,4,4,6,6,4,4,4,6,4,4,4], [4,6,4,6,6,6,6,8,6,6,8,4,4,4,6,6,6,6,8,6,4,4,8,4,6], [4,2,2,4,4,2,4,4,6,4,4,2,0,4,2,4,4,4,4,4,2,4,4,4,2], [6,6,8,6,6,4,2,6,6,6,8,8,6,6,8,8,10,8,6,4,8,6,6,6,8], [4,4,4,4,4,6,4,4,6,6,6,6,6,6,6,4,6,4,6,4,6,4,4,6,6], [6,4,4,6,6,6,6,4,6,4,4,4,4,4,4,4,4,4,4,6,4,4,4,4,4], [4,4,8,4,10,4,4,4,8,4,6,8,4,8,4,4,4,8,10,4,4,4,4,4,4], [8,8,8,6,8,8,6,6,8,8,10,8,6,8,8,8,8,8,8,8,8,8,6,8,8], [6,8,8,8,8,6,8,8,6,8,6,6,6,6,10,8,8,6,8,4,8,6,6,10,6], [8,8,8,10,10,6,10,12,8,4,10,6,10,6,10,6,8,12,8,10,6,10,4,10,4], [2,4,6,6,6,4,4,6,6,4,6,4,4,8,2,8,6,2,6,4,2,4,4,6,6], [8,6,6,6,6,6,6,6,6,6,10,6,6,6,6,8,8,6,6,6,6,6,6,6,6], [6,4,4,4,6,4,6,8,4,4,4,8,6,4,6,6,8,4,10,4,4,4,4,4,4], [4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,2,6,4,2,4,4,4,4,6,6], [6,6,6,4,6,6,4,6,6,6,4,6,6,6,4,6,6,6,6,6,6,6,8,6,6], [4,6,4,4,4,4,6,4,4,4,4,6,4,8,6,6,4,6,6,6,4,4,4,4,8], [6,6,6,6,8,6,6,8,6,8,6,8,6,8,6,6,4,6,6,4,4,6,6,6,6], [6,6,8,6,6,6,6,6,6,6,6,8,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,8,8,6,8,8,8,8,10,10,6,6,6,6,8,6,8,8,8,6,6,6,6,8], [6,6,6,6,6,6,6,4,6,6,4,4,6,6,6,6,6,6,8,6,6,6,6,6,6], [6,8,6,6,4,4,8,4,6,6,8,8,6,6,4,6,8,4,4,6,6,6,6,8,6], [8,8,6,8,4,6,6,8,8,6,6,8,6,6,6,4,6,6,8,4,4,4,6,8,8], [4,4,4,4,4,6,6,4,4,4,4,4,8,4,4,4,4,2,4,4,4,4,4,4,4], [6,4,8,6,6,8,6,8,4,4,8,6,6,6,6,4,8,4,8,8,8,4,6,6,6], [4,6,4,6,4,2,4,4,6,4,6,4,4,4,4,2,4,4,6,4,4,6,4,4,6], [8,4,8,10,8,8,10,4,4,4,6,4,8,4,4,4,8,4,4,4,8,8,8,8,8], [8,10,8,10,10,10,10,8,10,8,10,10,8,8,10,10,10,10,8,10,10,8,8,10,10], [4,2,6,8,6,8,8,2,8,4,8,8,6,4,2,8,4,8,2,10,8,8,8,8,8], [4,4,6,6,4,4,6,4,6,6,6,6,8,6,4,4,8,4,8,6,10,8,4,6,6], [4,4,4,4,6,4,4,6,4,4,4,6,6,8,4,4,4,6,4,6,4,8,4,4,4], [6,6,6,8,6,8,8,10,8,6,4,6,6,6,8,6,8,8,8,8,6,8,6,10,8], [8,6,6,8,8,6,8,8,6,8,6,6,6,8,6,4,6,6,6,6,6,6,4,6,6], [8,8,8,8,8,8,8,6,10,10,8,8,8,8,8,8,8,8,8,8,10,8,10,10,8], [8,4,8,6,8,10,8,10,8,8,6,4,8,4,8,8,8,6,6,8,4,6,6,8,8], [6,4,6,6,4,6,6,2,6,4,4,6,8,6,2,4,4,6,4,6,6,6,2,6,6] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: #print(evalm(num)); Total:= matadd(Total,num): ########################################################### # # Seventh 50 transfer functions x 25 pole sets # ######################################################## numroots:= matrix([ [8,8,8,8,8,8,8,8,8,6,8,8,8,8,8,6,8,8,8,8,8,8,8,8,8], [10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10], [4,6,2,6,4,6,4,4,4,4,4,4,6,4,4,6,4,4,4,6,4,6,4,6,6], [8,10,4,8,10,6,8,4,4,8,8,4,8,10,8,10,4,8,6,4,4,8,4,10,8], [6,6,6,6,6,6,4,4,4,4,6,4,6,6,6,6,6,6,6,6,6,6,6,4,4], [4,4,4,10,6,4,4,4,6,4,8,4,6,4,4,6,4,4,4,4,4,6,4,6,6], [6,6,6,6,6,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,6,8,10,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,6,8,8,8,8,8,8,8,8,6,8,8,8,8,8,8,8,8], [6,8,8,6,6,6,6,8,6,8,8,6,6,8,8,6,6,6,8,6,6,8,8,6,8], [6,6,8,6,6,6,6,6,8,6,8,8,6,6,6,8,8,6,4,6,6,6,8,8,6], [8,6,8,8,6,6,8,4,8,6,8,8,6,6,6,8,6,8,8,4,8,6,8,6,8], [2,4,4,2,4,4,4,4,4,2,4,4,4,4,4,2,4,4,2,4,4,2,2,2,4], [6,6,6,6,6,8,6,8,8,6,8,8,6,6,6,6,6,6,6,6,6,8,6,6,6], [4,4,6,4,4,4,4,4,4,4,4,4,6,4,4,4,6,4,6,4,4,4,4,4,4], [2,4,4,4,2,2,2,4,2,4,4,4,4,4,4,4,4,2,2,4,2,2,4,4,4], [6,6,4,6,6,6,6,6,4,6,6,6,4,6,6,6,6,6,6,6,6,6,6,6,6], [6,8,8,8,10,8,6,8,8,8,10,8,8,8,8,8,8,10,6,8,8,10,8,8,8], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,4,4,4,4,4,4], [6,6,6,6,6,6,6,8,6,6,6,6,8,8,6,6,6,8,6,6,6,6,8,8,8], [6,4,8,8,6,6,8,6,8,6,6,8,8,6,8,6,4,6,8,8,8,4,4,8,6], [6,6,8,6,8,6,10,8,6,6,8,8,8,8,6,8,8,8,8,8,6,6,8,6,8], [8,8,8,8,8,6,8,8,8,8,6,8,6,6,8,8,8,8,8,8,8,6,6,8,8], [6,6,6,6,4,4,6,4,4,6,2,4,6,4,6,6,6,6,4,6,4,6,6,6,4], [6,2,6,4,4,6,4,6,4,4,6,4,6,6,4,6,6,2,2,4,4,4,4,4,6], [4,8,4,8,8,8,4,6,8,8,4,6,6,2,6,4,4,4,4,8,8,2,6,4,4], [4,2,2,2,4,4,2,4,4,2,2,4,4,4,4,2,2,2,4,4,2,2,4,4,4], [10,10,10,10,10,8,10,10,10,10,8,8,8,10,10,8,8,10,8,10,10,10,10,10,10], [10,8,10,10,10,10,10,10,10,6,6,6,8,10,10,10,6,10,10,10,8,8,8,10,10], [4,4,2,4,4,4,4,4,6,4,4,6,2,4,4,4,2,4,4,4,2,2,2,4,4], [2,2,4,2,4,2,2,2,2,2,2,4,4,2,2,2,4,2,2,2,2,2,2,4,2], [6,8,6,8,6,8,6,8,6,6,6,8,6,6,8,6,6,6,8,6,8,6,6,6,8], [4,4,4,8,8,10,8,4,4,2,8,8,4,10,4,8,4,4,4,8,8,8,8,4,10], [10,10,10,10,12,10,10,10,10,10,8,10,10,8,8,10,10,10,10,10,10,8,10,12,10], [2,6,6,4,2,6,6,6,2,6,6,6,6,6,4,2,6,4,2,6,2,6,2,2,6], [8,4,8,8,4,8,8,8,4,8,8,4,8,8,4,4,4,4,4,4,8,4,4,4,8], [6,6,6,6,6,6,8,6,6,6,6,6,6,6,6,6,6,6,6,6,8,6,6,6,6], [2,2,2,2,2,2,2,2,2,2,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2], [6,8,6,6,6,6,8,6,6,8,6,4,6,6,4,8,8,8,8,6,8,4,6,4,4], [6,6,6,6,6,8,6,6,6,6,6,6,8,8,8,6,6,8,8,6,6,8,6,6,6], [6,2,6,4,6,2,6,4,2,4,6,6,6,6,6,6,6,4,4,6,6,6,6,4,2], [6,4,4,6,4,4,6,4,4,4,6,6,6,4,4,4,4,6,6,4,4,4,4,6,6], [4,4,6,4,4,4,6,6,4,6,4,4,4,4,6,4,4,4,4,4,4,4,4,6,4], [6,8,8,10,10,8,8,6,8,8,8,10,8,8,8,8,8,10,10,10,10,8,8,6,8], [8,8,6,8,6,6,6,8,4,6,2,6,8,4,4,6,8,6,4,6,8,6,4,4,4], [8,6,8,10,8,8,8,6,8,8,4,6,8,4,6,10,6,8,6,6,6,6,10,8,6], [6,4,6,6,6,4,4,8,8,4,6,4,8,4,6,6,8,6,8,8,4,8,2,6,8], [10,10,8,10,6,10,8,6,10,6,10,8,6,10,6,8,10,10,10,10,8,10,10,8,10], [8,8,8,4,8,8,4,4,8,8,8,8,4,8,8,8,10,4,4,8,8,8,10,8,4], [8,6,10,4,8,6,4,2,10,6,2,10,10,2,10,6,10,8,10,4,10,8,4,10,10] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: #print(evalm(num)); Total:= matadd(Total,num): ########################################################## # # Eigth 50 transfer functions x 25 pole sets # ######################################################### numroots:= matrix([ [4,4,4,8,4,8,4,8,6,4,4,4,4,4,8,4,8,8,8,6,4,6,4,4,4], [8,8,6,8,10,6,8,6,8,8,8,6,8,6,8,6,8,8,8,6,8,8,8,8,8], [12,10,10,12,12,10,10,10,10,10,12,10,12,12,10,12,10, 10,10,10,10,10,12,10,10], [10,8,10,10,10,10,8,8,10,10,10,8,10,10,8,8,8,8,8,12,12,10,8,8,10], [8,4,8,6,4,8,4,8,8,8,8,6,8,4,8,8,8,6,4,8,6,8,6,8,4], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,2,4,6,6,2,2,6,6,2,6,4,2,2,6,2,4,6,2,4,6,2,6,6], [12,8,12,8,6,10,12,8,10,12,12,10,8,12,8,10,10,8,8,12,8,8,6,8,8], [4,4,6,6,6,6,4,6,6,6,6,6,6,6,6,6,4,4,6,6,6,8,6,6,4], [6,6,6,6,4,2,8,6,6,6,6,6,6,8,6,4,4,6,6,4,6,8,8,6,2], [6,6,4,8,2,4,6,4,4,2,6,6,6,4,6,4,4,6,4,4,4,6,2,4,6], [4,4,4,4,6,4,4,4,4,6,4,4,4,4,6,4,4,4,4,4,4,4,4,4,4], [4,4,4,4,4,6,4,4,4,6,4,4,4,4,4,4,6,6,6,4,4,6,4,4,4], [4,4,6,4,6,4,6,6,4,4,6,6,6,6,6,4,6,4,4,4,6,4,4,4,6], [10,10,8,8,8,10,8,8,8,8,10,8,8,8,8,8,8,10,8,10,10,8,10,10,8], [6,6,6,6,2,4,4,6,4,6,6,6,4,6,4,6,6,4,6,6,6,6,4,2,4], [6,8,6,6,8,6,6,6,6,6,6,6,8,6,6,6,6,8,6,6,6,6,6,6,6], [8,4,6,6,10,6,10,6,4,6,10,6,6,6,6,6,6,6,8,6,6,6,4,6,6], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], # All 4's!!!!!! [8,8,6,8,8,8,8,8,10,8,8,8,6,8,6,6,8,8,6,8,8,8,8,8,8], [10,4,4,4,4,4,8,4,10,10,4,8,4,4,4,4,10,8,8,6,8,4,8,4,4], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [2,6,2,6,2,6,2,6,2,2,2,6,2,6,2,2,2,6,6,2,6,6,6,2,2], [4,4,6,8,4,6,4,4,4,4,4,4,4,4,4,4,4,4,4,6,8,4,4,4,4], [8,4,6,6,4,6,8,8,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [8,4,4,4,4,4,4,8,4,8,4,4,8,8,4,4,4,4,4,4,4,6,4,4,4], [8,8,8,8,8,8,8,6,8,8,8,8,6,8,6,8,10,8,6,8,8,8,8,6,8], [4,6,6,6,4,4,6,4,4,4,4,4,4,4,4,4,4,4,6,4,4,4,4,4,4], [8,8,10,8,8,8,10,8,8,8,10,8,8,8,10,8,8,8,10,8,10,8,8,8,10], [4,2,2,4,2,4,2,4,4,2,4,6,6,2,4,6,2,6,2,2,4,2,2,4,4], [6,2,6,8,2,2,8,2,6,8,8,8,4,8,4,6,6,8,2,8,8,4,2,4,8], [6,4,6,6,4,6,6,6,6,6,4,6,6,6,6,4,4,4,4,6,6,6,6,4,6], [8,8,8,2,8,2,8,4,8,4,8,4,4,4,4,4,4,4,8,4,8,4,8,8,2], [6,6,6,2,2,2,2,2,2,2,6,6,2,6,6,6,2,2,6,2,2,2,2,6,6], [4,4,4,6,4,8,6,6,4,6,6,4,4,4,6,6,6,6,4,6,4,4,6,4,4], [4,10,10,4,10,10,10,4,10,8,10,10,8,10,10,10,10,10,10,10,4,4,10,10,10], [6,6,6,6,4,2,6,6,6,6,6,6,4,6,6,6,6,6,4,6,6,6,4,2,6], [8,8,4,8,4,8,8,6,6,4,8,8,4,4,8,6,4,8,8,8,8,8,4,8,6], [8,10,8,10,10,6,10,10,10,10,8,10,10,10,10,10,8,10,10,8,10,10,8,10,10], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,4,4,4,4,4,4,4,4,6], [4,4,4,4,4,4,6,4,6,6,6,4,4,6,4,6,6,6,6,6,6,6,6,6,6], [8,6,8,8,10,8,8,8,8,8,8,8,6,8,8,8,8,8,8,8,8,8,8,8,10], [8,8,8,8,8,8,8,8,8,10,10,8,10,8,10,10,10,8,8,10,10,8,8,10,10], [8,6,6,4,4,6,6,8,8,8,8,6,4,4,8,8,8,6,4,4,8,6,8,4,4], [10,10,8,8,8,12,10,8,6,6,8,8,8,8,8,10,8,8,8,8,8,10,6,8,12], # # An example not controllable by real feedback. # [2,2,2,2,2,0,2,2,2,0,2,2,2,2,2,2,2,2,2,2,2,2,4,2,4], # [6,6,6,6,8,6,6,6,6,8,6,6,6,8,6,6,6,6,8,8,6,8,8,8,6], [6,4,4,4,6,4,4,4,4,4,4,2,4,4,4,2,6,2,4,4,2,6,6,4,4], [6,8,4,4,8,4,4,4,4,4,4,8,4,6,4,4,4,4,4,8,4,4,4,4,4], [6,6,6,6,6,6,6,6,6,6,6,6,6,8,6,8,6,6,8,8,6,6,6,6,8] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: #print(evalm(num)); Total:= matadd(Total,num): ########################################################### # # Ninth 25 transfer functions x 50 pole sets # ########################################################### numroots:= matrix([ [4,6,8,6,4,4,4,6,6,4,6,4,6,6,4,6,6,6,6,6,6,4,4,4,6], [4,4,6,4,6,4,4,4,4,6,4,8,6,6,6,6,6,6,6,4,6,6,4,6,4], [8,2,8,6,8,8,2,8,8,8,2,2,8,8,2,8,6,6,8,2,6,2,6,6,8], [6,8,6,2,6,6,6,8,6,8,6,8,6,8,8,6,2,6,2,8,6,2,6,8,8], [4,6,4,4,6,6,6,4,4,6,4,6,4,6,6,6,6,4,4,6,6,6,6,6,4], [6,4,4,6,4,6,4,4,6,6,4,6,6,6,6,4,4,6,6,6,6,4,4,6,6], [10,8,8,6,10,8,6,10,8,8,10,8,10,6,10,8,10,6,8,6,6,10,10,6,10], [10,10,6,10,10,8,6,6,6,6,10,10,6,6,10,6,6,8,10,10,10,10,6,6,6], [6,4,6,6,4,6,6,4,4,6,6,6,6,4,4,6,6,6,6,6,6,6,4,6,6], [4,4,6,4,6,6,4,6,6,4,6,6,4,4,4,4,6,4,4,4,4,6,4,8,6], [4,4,4,6,4,4,4,6,4,4,4,6,4,6,4,6,4,6,4,4,4,4,4,4,4], [4,4,4,4,4,4,4,6,6,4,4,4,4,4,4,4,4,4,4,4,6,6,4,4,6], [6,4,6,4,6,4,6,4,8,6,6,6,6,4,4,8,4,6,6,8,8,4,4,6,6], [6,6,6,6,4,4,6,4,6,6,6,4,8,8,6,4,6,4,6,4,4,6,4,6,6], [6,6,6,6,4,4,4,6,4,6,4,6,4,6,4,6,4,4,4,6,4,6,4,4,4], [6,4,4,4,6,4,6,4,6,4,4,4,4,6,4,6,6,4,4,6,4,6,6,4,4], [8,8,8,10,10,8,8,10,10,10,10,8,8,8,10,8,10,10,8,8,10,10,10,8,12], [10,8,8,8,8,8,10,8,10,10,10,8,10,8,8,8,8,8,6,8,10,8,8,10,8], [8,10,8,6,6,6,6,10,10,6,6,6,8,6,8,8,10,6,10,6,8,8,8,6,6], [6,8,6,6,6,6,6,8,6,6,8,10,6,8,6,6,6,8,6,6,8,6,6,6,6], [6,6,4,4,4,6,4,4,6,6,6,6,6,6,4,4,4,6,6,6,6,6,6,6,6], [8,6,6,8,6,6,4,8,6,4,4,4,4,6,6,6,6,4,4,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,6,4,6,6,6,6,6,8,8,6,6,10,6,8,10,10,6,10,8,6,6,4], [6,8,6,6,6,6,6,8,6,8,6,6,6,6,8,6,6,8,4,6,8,4,6,6,6], [4,8,8,8,8,8,8,4,4,8,4,8,4,4,8,8,8,6,4,4,8,8,6,8,4], [8,8,4,4,4,8,8,4,4,8,4,4,6,8,4,4,8,8,4,4,4,8,8,6,4], [4,4,4,4,6,4,4,6,6,4,4,4,4,4,4,6,6,4,4,4,4,6,4,4,4], [4,6,4,4,4,6,4,4,6,4,4,4,6,4,4,4,4,4,6,4,4,4,6,4,4], [8,12,12,12,10,10,10,10,8,12,10,10,10,12,8,10,12,10,6,10,12,12,12,12,6], [10,10,12,12,10,8,12,10,10,10,10,12,8,12,10,12,10,10,10,10,10,10,8,8,10], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,8,8,8,8,6,8,8,8,8,8,8,8,8,8,6,8,8,8,8,8,10,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,6,8,8,8,8,8,8,8,8,8], [4,8,4,6,8,4,8,8,4,8,8,4,6,6,10,8,4,8,6,4,4,6,4,6,6], [6,8,6,4,4,8,6,4,6,8,8,8,8,8,4,8,4,8,8,6,8,4,4,4,4], [6,4,4,2,4,4,2,4,6,2,6,2,6,6,4,4,4,4,6,4,6,6,4,6,2], [2,6,4,2,4,2,4,6,4,4,6,4,4,6,4,6,4,6,6,4,6,6,6,6,4], [4,6,8,6,6,4,4,6,4,4,4,4,4,4,6,4,4,6,4,6,4,6,4,6,4], [4,6,4,4,4,6,4,4,6,4,4,4,6,4,4,4,8,4,6,4,4,4,4,4,6], [4,2,4,2,4,2,6,4,2,4,4,6,6,2,4,2,4,4,4,4,6,4,4,4,2], [2,2,2,2,2,2,2,2,2,2,2,2,4,2,4,2,4,2,4,2,4,6,4,2,2], [6,8,8,8,8,8,6,6,8,8,8,8,6,6,6,8,8,8,8,8,4,6,6,10,8], [8,8,8,6,8,6,8,6,6,8,8,8,8,6,8,6,8,8,8,8,8,8,8,8,8], [6,4,6,6,4,6,6,6,6,6,6,6,8,6,4,8,6,6,6,8,6,6,6,6,6], [6,4,6,6,6,6,6,6,4,4,6,8,6,6,8,8,6,4,6,6,4,6,6,6,6], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: #print(evalm(num)); Total:= matadd(Total,num): ########################################################### # # tenth 25 transfer functions x 50 pole sets # ############################################################# numroots:= matrix([ [6,2,6,4,6,6,4,6,6,6,6,6,6,6,6,2,6,6,6,2,6,6,6,6,2], [2,6,6,6,6,6,2,2,6,6,6,6,2,6,2,6,2,6,6,6,6,2,6,6,6], [8,8,8,8,8,8,8,8,8,10,6,8,6,10,8,8,8,8,8,8,10,8,8,8,6], [8,6,10,8,8,8,8,8,8,8,8,8,8,8,8,8,8,10,8,6,8,8,8,6,8], [6,4,6,6,6,6,6,8,6,4,8,8,4,6,4,4,4,4,4,6,6,6,4,6,8], [6,6,4,4,6,4,6,4,6,4,8,4,4,8,4,8,6,4,6,8,6,4,4,6,6], [8,8,6,6,8,6,6,6,6,6,8,8,8,6,6,6,6,8,8,6,6,8,8,6,8], [6,6,6,6,6,6,8,8,8,8,6,10,6,8,6,6,6,6,6,8,6,6,10,6,8], [8,6,8,10,10,10,6,10,8,10,6,8,8,8,10,8,8,10,10,8,10,8,10,10,6], [6,10,10,10,8,8,8,10,6,10,10,10,6,10,10,8,10,10,8,10,8,10,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [6,6,6,6,8,8,8,6,6,8,8,6,6,8,8,8,6,8,8,8,6,6,8,8,6], [6,6,6,8,6,6,8,8,6,6,6,8,6,6,6,8,8,6,10,4,6,6,8,8,8], [6,6,8,6,6,8,4,6,8,6,8,6,8,6,6,8,8,6,8,8,6,6,6,8,6], [6,6,8,6,6,8,6,6,4,8,6,8,4,6,6,6,6,6,6,6,6,8,8,6,6], [10,8,12,8,12,10,10,10,12,8,10,10,10,10,10,10,8,8,10,8,10,8,10,8,8], [10,10,10,10,10,8,10,10,10,12,8,8,10,10,10,10,8,8,10,10,10,10,8,10,10], [4,8,4,6,6,8,6,8,6,6,6,6,6,6,8,6,4,8,6,6,6,6,4,6,8], [8,8,8,6,6,6,6,6,6,6,8,8,4,6,4,4,6,6,8,8,8,4,8,6,6], [6,4,6,4,6,6,6,6,6,6,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,6,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,4,6,4,6,6], [6,6,2,6,6,4,4,6,6,6,6,6,6,6,6,4,4,6,6,4,6,6,6,6,8], [6,6,6,6,6,6,6,6,2,8,6,6,6,6,4,6,6,6,4,4,4,8,6,4,6], [4,4,4,4,4,4,6,4,4,4,4,4,4,4,4,6,4,4,6,4,4,4,4,4,6], [4,6,4,6,4,6,6,4,4,6,4,4,4,4,6,4,4,4,4,6,4,4,6,4,4], [10,8,8,8,10,10,8,10,8,8,10,10,10,8,10,8,8,8,8,8,8,8,10,10,10], [8,8,8,8,8,8,10,10,8,8,8,8,10,8,8,8,8,10,10,10,10,10,8,8,8], [6,6,6,6,6,6,6,6,6,6,6,2,2,6,6,6,2,6,6,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,2,6,6,2,6,8,6,6,6,6,6,2,6,2,6,6], [4,6,6,6,4,4,6,6,6,4,6,6,6,6,6,6,6,6,4,6,6,6,6,6,6], [6,6,6,4,6,6,6,6,6,6,6,6,4,6,4,6,4,4,6,6,6,6,6,6,6], [8,8,8,8,8,8,10,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,6,8,6,8,8,10,6,6,6,8,6,8,6,6,6,6,6,8,6,6,6,6,8], [6,6,8,6,6,6,6,8,6,6,6,6,6,6,6,6,6,6,6,6,8,8,8,6,6], [6,6,6,6,6,6,6,6,8,6,6,6,6,6,8,6,6,6,6,6,6,6,6,6,6], [6,6,8,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,6,6,6,6,6,6,6], [8,8,10,8,10,10,10,8,8,8,8,12,8,12,10,8,12,12,8,8,10,8,8,10,12], [12,10,10,10,8,10,10,12,8,8,8,6,10,8,10,10,10,12,8,8,10,10,10,10,10], [8,8,6,6,8,6,8,6,6,6,6,6,8,6,6,6,6,6,6,8,6,6,8,6,6], [6,8,6,6,6,8,6,8,8,6,6,6,8,8,6,6,6,6,6,6,8,6,6,8,8], [6,6,8,8,6,6,6,6,6,4,6,6,8,6,6,8,6,4,8,6,6,6,6,8,8], [6,8,6,6,6,6,6,8,6,8,6,6,6,6,4,6,8,6,6,8,6,6,6,6,4], [8,8,4,6,10,10,10,10,10,4,8,6,10,8,4,10,8,4,6,4,6,6,4,4,6], [10,10,6,10,6,10,8,10,8,8,10,10,6,10,4,6,8,6,6,10,10,10,4,10,10], [4,4,4,10,4,4,4,4,10,4,4,4,4,4,4,10,4,10,10,4,10,4,4,4,4], [4,4,4,4,4,10,4,4,4,4,10,4,10,4,4,10,10,4,4,10,4,4,10,10,10], [12,12,12,12,12,12,12,12,12,10,12,12,6,12,12,12,12,12,10,12,6,12,12,12,12], [12,10,12,10,12,12,10,12,12,12,8,12,12,12,10,12,12,12,14,12,12,12,10,12,12] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: Total:= matadd(Total,num): ################################################################ # # eleventh 25 transfer functions x 50 pole sets # ################################################################## numroots:= matrix([ [8,8,8,8,8,8,8,8,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [2,2,4,2,2,2,4,4,2,4,4,4,4,2,2,2,2,4,2,4,4,4,4,2,4], [4,4,4,4,4,4,2,4,4,4,2,2,4,4,4,4,4,2,4,4,4,4,4,4,4], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [10,10,10,8,8,10,10,10,10,10,10,10,10,10,10,10,10,10,8,10,10,10,10,10,10], [10,8,10,10,10,10,10,10,10,10,10,10,10,10,10,8,10,10,10,10,10,10,10,10,10], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [4,6,6,4,6,4,6,6,4,4,4,4,6,4,4,4,4,6,6,4,6,4,6,4,4], [4,4,6,6,6,4,4,6,4,6,4,4,4,4,4,6,6,6,6,4,4,4,4,4,6], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12], [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12], [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2], [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2], [10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10], [10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4], [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2], [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2], [6,6,6,6,6,6,8,6,6,6,6,6,6,6,6,6,8,8,8,6,8,6,8,8,6], [6,6,8,8,6,8,8,8,6,6,6,8,8,6,8,6,6,8,8,6,6,8,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [8,8,8,6,6,8,6,8,8,8,6,8,8,8,6,8,8,8,8,8,8,8,8,8,8], [8,8,6,8,6,8,6,8,8,8,8,8,6,8,6,8,6,8,6,6,6,8,8,6,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: #print(evalm(num)); Total:= matadd(Total,num): ####################################################################### # # twelfth and final 50 transfer functions x 25 pole sets # ####################################################################### numroots:= matrix([ [8,8,8,6,8,8,8,8,6,8,8,8,6,8,8,8,8,6,8,6,6,6,8,8,8], [10,10,10,10,10,8,10,10,10,10,10,10,8,10,10,10,10,10,10,8,10,8,10,10,10], [6,6,6,6,6,6,6,6,6,6,6,6,8,6,6,6,6,6,6,6,8,8,6,6,6], [10,10,8,10,10,8,10,10,8,10,10,8,8,10,10,10,10,10,10,8,8,8,10,10,10], [8,8,8,8,8,8,8,8,8,8,8,6,8,8,8,8,8,8,8,6,8,8,8,8,8], [10,10,10,10,10,8,10,10,12,10,10,10,10,10,10,10,10,10,10,10,10,8,10,10,10], [8,8,4,6,8,6,8,8,4,8,8,4,6,6,8,8,8,6,6,6,6,6,6,6,8], [10,10,6,10,10,6,10,10,6,10,10,6,10,10,10,10,10,10,10,10,10,10,10,10,10], [12,12,10,12,12,10,12,12,10,12,12,10,12,12,12,12,12,12,12,12,12,12,12,12,12], [8,8,8,8,8,6,8,8,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [6,6,4,4,4,2,6,6,6,6,6,4,2,4,6,6,6,4,6,4,4,4,4,6,6], [8,8,4,8,8,4,8,8,4,8,8,4,8,8,8,8,8,8,8,6,8,8,8,8,8], [10,10,6,8,10,6,10,10,6,10,10,6,8,8,10,10,10,8,10,8,8,8,8,8,10], [6,6,4,6,6,4,6,6,4,6,6,4,6,6,6,6,6,6,6,6,6,6,6,6,6], [10,10,6,10,10,6,10,10,6,10,10,6,8,10,10,10,10,10,10,8,10,8,10,10,10], [6,6,4,8,8,4,8,6,4,8,8,4,8,8,8,8,8,8,8,10,8,8,8,8,8], [8,8,10,8,8,10,8,8,10,8,8,10,8,8,8,8,8,8,8,8,8,8,8,8,8], [6,6,6,6,6,8,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [4,4,6,4,4,6,4,4,6,4,4,6,6,4,4,4,4,6,4,8,6,6,4,4,4], [6,8,6,8,8,6,8,8,6,8,8,6,8,8,8,6,8,8,8,6,8,8,8,8,8], [6,6,2,6,6,8,6,6,2,6,6,4,6,6,6,6,6,6,6,4,6,6,6,6,6], [4,4,8,4,4,4,4,4,8,4,4,8,4,4,4,4,4,4,4,4,4,4,4,4,4], [6,6,2,6,6,2,6,6,2,6,6,2,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,4,6,6,6,6,6,4,6,6,4,6,6,6,6,6,6,6,4,6,6,6,6,6], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,6,6,4,6,6,6,6,6,6,6,6,4,4,4,6,4,4,4,2,4,4,4,4,4], [6,6,10,6,6,8,6,6,12,6,6,10,6,6,6,6,6,6,6,6,6,6,6,6,6], [10,10,8,8,10,10,10,10,8,10,10,8,10,8,10,10,10,8,10,8,8,10,8,10,10], [8,10,4,10,10,6,10,10,4,10,10,4,6,10,10,10,10,10,10,6,8,6,10,10,10], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [10,10,6,10,10,6,10,10,6,10,10,6,10,10,10,10,10,10,10,8,10,10,10,10,10], [12,12,8,12,12,8,12,12,8,12,12,8,12,12,12,12,12,12,12,12,12,12,12,12,12], [6,6,6,6,6,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [6,6,6,4,6,6,6,6,6,6,6,6,2,4,6,6,6,4,4,2,2,2,4,4,4], [8,8,8,8,8,8,8,8,8,8,8,10,10,8,8,8,8,8,8,10,10,10,8,8,8], [6,6,8,6,6,8,6,6,8,6,6,8,6,6,6,6,6,6,6,8,6,6,6,6,6], [8,8,10,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8], [6,6,6,6,6,6,6,6,8,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [8,8,6,8,8,6,8,8,6,8,8,6,8,8,8,8,8,8,8,8,8,8,8,8,8], [10,10,8,10,10,8,10,10,6,10,10,6,8,10,10,10,10,8,10,8,8,8,10,10,10], [8,8,8,10,10,6,10,8,8,8,8,8,10,10,10,8,10,10,10,10,10,10,10,10,10], [10,10,8,10,10,4,10,10,8,10,10,8,10,10,8,8,8,10,8,10,8,8,8,8,8], [4,4,6,4,4,4,4,4,4,4,4,6,4,4,4,4,4,4,4,4,4,4,4,4,4], [8,8,8,8,8,4,8,8,8,8,8,8,6,8,8,8,8,6,8,4,6,6,8,8,8], [4,4,4,4,4,6,4,4,4,4,4,4,6,4,4,4,4,6,4,6,6,6,4,4,4], [6,6,4,4,6,4,4,6,4,4,4,4,4,4,4,6,4,4,4,4,4,4,4,4,4], [4,4,6,4,4,4,4,4,6,4,4,6,6,4,4,4,4,4,4,8,4,4,4,4,4], [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6], [6,8,2,6,8,2,6,8,2,6,6,2,6,6,6,6,6,6,6,6,6,6,6,6,6] ]): num:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 50 do for jj from 1 to 25 do if numroots[ii,jj]=0 then num[1]:=num[1]+1: else if numroots[ii,jj]=2 then num[2]:=num[2]+1: else if numroots[ii,jj]=4 then num[3]:=num[3]+1: else if numroots[ii,jj]=6 then num[4]:=num[4]+1: else if numroots[ii,jj]=8 then num[5]:=num[5]+1: else if numroots[ii,jj]=10 then num[6]:=num[6]+1: else if numroots[ii,jj]=12 then num[7]:=num[7]+1: else if numroots[ii,jj]=14 then num[8]:=num[8]+1: else print(`Something Strange`,ii,jj,numroots[ii,jj]); fi; fi; fi; fi; fi; fi; fi: fi: od: od: Total:= matadd(Total,num): #################### # # End # ################### S:=0: for ii from 1 to 8 do S:= Total[ii]+S: od: Digits:=4: tot:=vector([0,0,0,0,0,0,0,0]): for ii from 1 to 8 do tot[ii]:= 100.0*Total[ii]/S: od: print(Total); print(tot); quit; ########################################################################### The 25 8-tuples used in the last run: -10,-9,-4,-3,-2,5,6,30, -10,-1,3,-4,-7,7,8,10, -7,0,3,4,5,7,8,9, -9,-4,4,5,7,-8,8,10, -9,-1,1,-3,3,-7,9,10, -6,0,-1,1,-4,4,9,10, -10,-2,4,-5,6,7,-8,10, -9,-1,2,-4,6,-8,9,10, -19,-17,-16,0,1,16,17,18, -12,-10,-8,-5,-2,2,10,13, -15,-11,-8,-2,8,12,15,19, -17,-5,0,2,3,10,11,20, -20,-16,-15,1,2,8,19,20, -30,-13,-12,-11,-3,2,3,20, -15,-14,-12,-10,-5,9,10,16, -17,-16,-15,-11,-8,-6,-5,8, -88,-87,-20,-6,23,24,56,75, -71,-70,-69,-15,2,5,15,33, -48,-43,-41,-39,23,38,40,41, 1,2,3,4,5,6,7,8, -31,-30,-29,-28,-27,2,3,5, 2,3,5,7,11,13,17,19, 23,29,31,37,41,43,47,53, 50,60,80,101,121,138,141,143, -12,-11,-10,-9,9,10,11,12