#Defining polynomial for the field of definition of the Gram-matrix: mpadppm2 := delta^2-68/5*delta+1111/25; #Among its real roots the ones in the following postions #(roots in increasing order) #yield the relevant real Gram-matrices: rootadppm2:=[1, 2]; #(Warning: Use at least 10 digits) #Minimal polynomial of trace of Gram-matrix: Tradppm2 := lambda^2-68/5*lambda+1111/25; #Numerical approximations of Eigenvalues of relevant Gram-matrices: EVGadppm21 := [1.70557280903711, 1.87639320226194, 1.87639320226194]; EVGadppm22 := [2.32360679772956, 2.32360679772956, 3.49442719091877]; #Formal Gram-matrix: Gadppm2 := Matrix(12,12,[ [-5/18*delta+409/180, -1/20, -1/12*delta+3/5, -1/36*delta+2/9, -1/36*delta+2/9, -1/20, 1/6*delta-27/20, -1/36*delta+2/9, 2/9*delta-311/180, -1/36*delta+2/9, 1/6*delta-27/20, -1/12*delta+23/30], [-1/20, 5/18*delta-247/180, 7/36*delta-11/9, 1/4*delta-8/5, -1/6*delta+59/60, -5/36*delta+32/45, 7/36*delta-11/9, -1/20, -1/6*delta+59/60, -1/12*delta+23/30, -2/9*delta+49/36, -5/36*delta+32/45], [-1/12*delta+3/5, 7/36*delta-11/9, 1/9*delta-13/180, -1/4*delta+49/30, -1/4*delta+49/30, 7/36*delta-11/9, 1/9*delta-103/180, 1/6*delta-27/20, -1/4*delta+17/15, 1/6*delta-27/20, 1/9*delta-103/180, -2/9*delta+49/36], [-1/36*delta+2/9, 1/4*delta-8/5, -1/4*delta+49/30, 2/9*delta-149/180, 2/9*delta-239/180, -1/6*delta+59/60, -1/4*delta+49/30, -1/36*delta+2/9, 2/9*delta-239/180, 2/9*delta-311/180, -1/4*delta+17/15, -1/6*delta+59/60], [-1/36*delta+2/9, -1/6*delta+59/60, -1/4*delta+49/30, 2/9*delta-239/180, 2/9*delta-149/180, 1/4*delta-8/5, -1/4*delta+17/15, 2/9*delta-311/180, 2/9*delta-239/180, -1/36*delta+2/9, -1/4*delta+49/30, -1/6*delta+59/60], [-1/20, -5/36*delta+32/45, 7/36*delta-11/9, -1/6*delta+59/60, 1/4*delta-8/5, 5/18*delta-247/180, -2/9*delta+49/36, -1/12*delta+23/30, -1/6*delta+59/60, -1/20, 7/36*delta-11/9, -5/36*delta+32/45], [1/6*delta-27/20, 7/36*delta-11/9, 1/9*delta-103/180, -1/4*delta+49/30, -1/4*delta+17/15, -2/9*delta+49/36, 1/9*delta-13/180, -1/12*delta+3/5, -1/4*delta+49/30, 1/6*delta-27/20, 1/9*delta-103/180, 7/36*delta-11/9], [-1/36*delta+2/9, -1/20, 1/6*delta-27/20, -1/36*delta+2/9, 2/9*delta-311/180, -1/12*delta+23/30, -1/12*delta+3/5, -5/18*delta+409/180, -1/36*delta+2/9, -1/36*delta+2/9, 1/6*delta-27/20, -1/20], [2/9*delta-311/180, -1/6*delta+59/60, -1/4*delta+17/15, 2/9*delta-239/180, 2/9*delta-239/180, -1/6*delta+59/60, -1/4*delta+49/30, -1/36*delta+2/9, 2/9*delta-149/180, -1/36*delta+2/9, -1/4*delta+49/30, 1/4*delta-8/5], [-1/36*delta+2/9, -1/12*delta+23/30, 1/6*delta-27/20, 2/9*delta-311/180, -1/36*delta+2/9, -1/20, 1/6*delta-27/20, -1/36*delta+2/9, -1/36*delta+2/9, -5/18*delta+409/180, -1/12*delta+3/5, -1/20], [1/6*delta-27/20, -2/9*delta+49/36, 1/9*delta-103/180, -1/4*delta+17/15, -1/4*delta+49/30, 7/36*delta-11/9, 1/9*delta-103/180, 1/6*delta-27/20, -1/4*delta+49/30, -1/12*delta+3/5, 1/9*delta-13/180, 7/36*delta-11/9], [-1/12*delta+23/30, -5/36*delta+32/45, -2/9*delta+49/36, -1/6*delta+59/60, -1/6*delta+59/60, -5/36*delta+32/45, 7/36*delta-11/9, -1/20, 1/4*delta-8/5, -1/20, 7/36*delta-11/9, 5/18*delta-247/180] ]):