As the first part of a demonstration on eigensystems, I was surprised to
see that computing QQbar polynomial roots was way slower that computing the
roots of the same polynomial expressed as a symbolic expression, or solveing
it :
# Relative timings of QQbar.roots and solve
from time import time as stime
BR = QQbar
Dim = 3
set_random_seed(0)
pM = MatrixSpace(BR, Dim).random_element()
sM = matrix([[SR(u.radical_expression()) for u in v] for v in pM])
sl = var("sl")
slI = sl*diagonal_matrix([1]*Dim)
sCM = sM - slI
sCP = sCM.det()
t0 = stime()
SS = solve(sCP, sl)
t1 = stime()
SR = sCP.roots()
t2 = stime()
R1.<pl> = BR[]
plI = pl*diagonal_matrix([1]*Dim)
pCM = pM - plI
pCP = pCM.det()
t3 = stime()
SP = pCP.roots()
t4 = stime()
print("solve : %7.2f, roots(symbolic) : %7.2f, roots(QQbar) : %7.2f"%\
(t1 -t0, t2 - t1, t4 - t3))
gives :
solve : 2.36, roots(symbolic) : 2.04, roots(QQbar) : 600.07
a quick check on Cocalc <https://cocalc.com> showed the same behavior in
9.1 ; so if it is a problem, it is not a recent one…
Is this the expected behavior ?
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