On Wed, Dec 13, 2023 at 10:55 AM Enrique Artal <enriquear...@gmail.com> wrote:
>
> I have the toy example belowto compare the direct use of smith_form and the
> combination of hermite_form and smith_form.
>
> Last execution (there are random inputs) gave:
> CPU times: user 2.22 s, sys: 5.93 ms, total: 2.23 s Wall time: 2.23 s CPU
> times: user 454 ms, sys: 990 µs, total: 455 ms Wall time: 456 ms
>
> %%%%%%%%%%%%%%%%%%%%%
> R.<t> = QQ[]
> n = 3
> m = 5
> ds = (n, m)
> M = MatrixSpace(R, n, m)
> V = random_vector(R, n)
> A0 = Matrix(R, n, m)
> A0[0, 0] = R.random_element()
> for j in range(1, n):
> A0[j, j] = A0[j -1, j - 1] * R.random_element()
> def par(n):
> i1 = ZZ.random_element(0,n)
> j1 = i1
> while j1 == i1:
> j1 = ZZ.random_element(0,n)
> return (i1, j1)
> def smith_hermite(A):
> D1, U1 = A.hermite_form(transformation=True)
> D, U2, V = D1.smith_form()
> U = U2 * U1
> return D, U, V
> P = {j: identity_matrix(R, ds[j]) for j in range(2)}
> s = 20
> for k in range(2):
> for a in range(s):
> i, j = par(n)
> f = R.random_element()
> P[k].add_multiple_of_row(i, j ,f)
> i, j = par(n)
> P[k].swap_rows(i, j)
> i, j = par(n)
> f = R.random_element()
> P[k].add_multiple_of_column(i, j ,f)
> i, j = par(n)
> P[0].swap_columns(i, j)
> A = P[0] * A0 * P[1]
> %time D, U, V = A.smith_form()
> %time D1, U1, V1 = smith_hermite(A)
hmm, what's Smith form of a matrix over Q ?
Q is not a PID.
>
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