#Defining polynomial for the field of definition of the Gram-matrix: mpapmm2 := delta^4-18*delta^3+583/5*delta^2-1658/5*delta+9101/25; #Among its real roots the ones in the following postions #(roots in increasing order) #yield the relevant real Gram-matrices: rootapmm2:=[1, 2]; #(Warning: Use at least 10 digits) #Minimal polynomial of trace of Gram-matrix: Trapmm2 := lambda^4-18*lambda^3+583/5*lambda^2-1658/5*lambda+9101/25; #Numerical approximations of Eigenvalues of relevant Gram-matrices: EVGapmm21 := [1.38196601117927, 1.38196601117927, 1.96383495167324]; EVGapmm22 := [1.38196601117927, 1.38196601117927, 4.63879617186167]; #Formal Gram-matrix: Gapmm2 := Matrix(12,12,[ [-35/5442*delta^3+985/10884*delta^2-683/1814*delta+9445/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-13823/3628], [-35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+9445/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-13823/3628, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884], [-35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+9445/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-13823/3628, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628], [-35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+9445/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-13823/3628, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884], [-35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+9445/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-13823/3628, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628], [35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, 175/5442*delta^3-4925/10884*delta^2+2161/907*delta-47225/10884, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, -175/5442*delta^3+4925/10884*delta^2-2161/907*delta+47225/10884, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721], [105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-13823/3628, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+9445/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884], [-35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, -175/5442*delta^3+4925/10884*delta^2-2161/907*delta+47225/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, 175/5442*delta^3-4925/10884*delta^2+2161/907*delta-47225/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721], [105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-13823/3628, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+9445/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884], [-385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-13823/3628, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+9445/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884], [-385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-13823/3628, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+9445/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884], [105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-13823/3628, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -385/5442*delta^3+10835/10884*delta^2-7513/1814*delta+54917/10884, 105/1814*delta^3-2955/3628*delta^2+6147/1814*delta-15637/3628, -35/2721*delta^3+985/5442*delta^2-3639/3628*delta+6083/2721, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, 35/2721*delta^3-985/5442*delta^2+3639/3628*delta-6083/2721, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+4003/10884, -35/5442*delta^3+985/10884*delta^2-683/1814*delta+9445/10884] ]):