Forgot to add : pM.eigenvectors_right() doesn’t returns after 5 hours… And,
yes, all pM‘s elements have a radical expression :
sage: sM
[ -sqrt(2) - 1 1/4*I*sqrt(759) - 1/4 -2*sqrt(3)]
[ 1/2*I*sqrt(3) + 1/2 1/8*sqrt(33) + 1/8 -1/5*sqrt(29) + 3/5]
[ 0 1/4 1/2*I*sqrt(23) + 1/2]
HTH,
Le vendredi 11 juin 2021 à 09:51:46 UTC+2, Emmanuel Charpentier a écrit :
> 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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