ore_algebra.analytic.ui

Some convenience functions for features not yet easily accessible from methods of differential operators.

Functions

multi_eval_diffeq(dop, ini, path[, eps])	Evaluate a solution at several points along a path.
transition_matrices(dop, path[, eps])	Compute several transition matrices at once.

ore_algebra.analytic.ui.multi_eval_diffeq(dop, ini, path, eps=1e-16)

Evaluate a solution at several points along a path.

EXAMPLES:

sage: from ore_algebra.analytic.ui import *
sage: Dops, x, Dx = DifferentialOperators()
sage: QQi.<i> = QuadraticField(-1, 'I')

sage: dop = (x^2 + 1)*Dx^2 + 2*x*Dx
sage: multi_eval_diffeq(dop, [0, 1], [k/5 for k in range(5)], 1e-10)
[(0, 0),
(1/5, [0.197395559...]),
(2/5, [0.380506377...]),
(3/5, [0.540419500...]),
(4/5, [0.674740942...])]

The logarithm:

sage: multi_eval_diffeq(Dx*x*Dx, ini=[0, 1], path=[1, i, -1])
[(1,  0),
 (i,  [...] + [1.57079632679489...]*I),
 (-1, [...] + [3.14159265358979...]*I)]

XXX: make similar examples work with points in RLF/CLF (bug with binsplit?)

TESTS:

sage: multi_eval_diffeq(Dx - 1, ini=[42], path=[1])
[(1, 42.000...)]

ore_algebra.analytic.ui.transition_matrices(dop, path, eps=1e-16)

Compute several transition matrices at once.

EXAMPLES:

sage: from ore_algebra.analytic.ui import *
sage: Dops, x, Dx = DifferentialOperators()

sage: dop = (x^2 + 1)*Dx^2 + 2*x*Dx
sage: tms = transition_matrices(dop, [k/5 for k in range(5)], 1e-10)
sage: tms[2]
(
     [ [1.00...] [0.3805063771...]]
2/5, [ [+/- ...] [0.8620689655...]]
)

sage: transition_matrices(Dx - 1, [i/5 for i in range(6)], 1e-10)
[(0,   [1.000000000...]),
 (1/5, [[1.221402758...]]),
 (2/5, [[1.491824697...]]),
 (3/5, [[1.822118800...]]),
 (4/5, [[2.225540928...]]),
 (1,   [[2.718281828...]])]