answer.sage

A.<u,v,w>=QuaternionAlgebra(2,3)


Id=identity_matrix(2)
U=matrix([[sqrt(2),0],[0,-sqrt(2)]])
V=matrix([[0,1],[3,0]])
W=U*V

E0=Id
E1=U
E2=(1/2)*Id+(1/2)*U+(1/2)*V
E3=(1/2)*U+(1/2)*W
B=[E0,E1,E2,E3]

# Robust way to generate the list of matrices
maxm = 5 #set the range
L = []
for i in range(-max,max):
    for j in range(-max,max):
        for k in range(-max,max):
            for l in range(-max,max):
                temp = i*B[0] + j*B[1] + k*B[2] + l*B[3]
                if temp.determinant() == 1:
                    L.append(temp)


print(str(len(L)) + " matrices are selected in L")

#S.<a,b>=QQ[]

#P = matrix([[a,b],[b,1-a]])

#INEQS=[(g.transpose()*P*g-P).trace() for g in L]

def coeff(F):
    C=[]
    C.append((F.coefficient({a:0,b:0})))
    C.append((F.coefficient({a:1,b:0})))
    C.append((F.coefficient({a:0,b:1})))
    return C

ineqs=[]

for F in INEQS:
    ineqs.append(coeff(F))

poly=Polyhedron(ieqs=ineqs,base_ring=AA)
# Format printing
print(poly)
print("\n Vertices are:")
for j in poly.Vrepresentation():
    print("(" + str(j[0].radical_expression()) + " , " + str(j[1].radical_expression()) + ")")