# ore_algebra.analytic.examples.misc¶

Miscellaneous examples

An example kindly provided by Christoph Koutschan:

sage: from ore_algebra.analytic.examples.misc import koutschan1
sage: koutschan1.dop.numerical_solution(koutschan1.ini, [0, 84])
[0.011501537469552017...]


One by Bruno Salvy, where we follow a branch of the solutions of an algebraic equation:

sage: from ore_algebra.analytic.examples.misc import salvy1_pol, salvy1_dop
sage: Pols.<z> = QQ[]
sage: a = AA.polynomial_root(54*z**3+324*z**2-4265*z+432, RIF(0.1, 0.11))
sage: roots = salvy1_pol(z=a).univariate_polynomial().roots(QQbar)
sage: val = salvy1_dop.numerical_solution([0, 0, 0, 0, 0, 1/2], [0, a]) # long time (5.2 s)
sage: CBF100 = ComplexBallField(100)
sage: [r for (r, _) in roots if CBF100(r) in val]                       # long time
[0.0108963334211605...]


An example provided by Steve Melczer which used to trigger an issue with the numerical analytic continuation code:

sage: from ore_algebra.analytic.examples.misc import melczer1
sage: melczer1.numerical_transition_matrix([0, rts[1]])[0, 0]
[4.64191240683...] + [-0.01596122801...]*I
sage: melczer1.local_basis_expansions(rts[1])
[1 + (1269/32*a+3105/28)*(z + 0.086...? + 0.069...*I)^4 + ...,
(z + 0.086...? + 0.069...*I)^(1/2) + (365/96*a+13/3)*(z + 0.086...? + 0.069...*I)^(3/2) - ...,
...]


Classes

 IVP(dop, ini)
class ore_algebra.analytic.examples.misc.IVP(dop, ini)
dop

Alias for field number 0

ini

Alias for field number 1