ore_algebra.examples.stdfun¶
Elementary and special functions
sage: from ore_algebra.examples import stdfun
sage: stdfun.airy_ai.dop(airy_ai(x))
0
sage: stdfun.airy_ai.dop.numerical_solution(
....: stdfun.airy_ai.ini, [stdfun.airy_ai.pt, 1])
[0.135292416312881...]
sage: stdfun.airy_bi.dop(airy_bi(x))
0
sage: stdfun.airy_bi.dop.numerical_solution(
....: stdfun.airy_bi.ini, [stdfun.airy_bi.pt, 1])
[1.207423594952871...]
sage: stdfun.arctan.dop(arctan(x))
0
sage: stdfun.arctan.dop.numerical_solution(
....: stdfun.arctan.ini, [stdfun.arctan.pt, 1])
[0.7853981633974483...]
sage: stdfun.cos.dop(cos(x))
0
sage: stdfun.cos.dop.numerical_solution(
....: stdfun.cos.ini, [stdfun.cos.pt, pi/3])
[0.500000000000000...]
sage: stdfun.dawson.dop.numerical_solution(
....: stdfun.dawson.ini, [stdfun.dawson.pt, 1])
[0.538079506912768...]
sage: stdfun.erf.dop(erf(x))
0
sage: stdfun.erf.dop.numerical_solution(
....: stdfun.erf.ini, [stdfun.erf.pt, 1])
[0.842700792949714...]
sage: stdfun.erfi.dop(erfi(x))
0
sage: stdfun.erfi.dop.numerical_solution(
....: stdfun.erfi.ini, [stdfun.erfi.pt, 1])
[1.65042575879754...]
sage: stdfun.exp.dop(exp(x))
0
sage: stdfun.exp.dop.numerical_solution(
....: stdfun.exp.ini, [stdfun.exp.pt, 1])
[2.71828182845904...]
sage: stdfun.log.dop(log(x))
0
sage: stdfun.log.dop.numerical_solution(
....: stdfun.log.ini, [stdfun.log.pt, 2])
[0.69314718055994...]
sage: e1 = stdfun.mittag_leffler_e(1)
sage: e1.dop(exp(x))
0
sage: e1.dop.numerical_solution(
....: e1.ini, [e1.pt, 1])
[2.71828182845904...]
sage: e2 = stdfun.mittag_leffler_e(2)
sage: e2.dop(cosh(sqrt(x))).simplify_full()
0
sage: e2.dop.numerical_solution(e2.ini, [e2.pt, 2])
[2.17818355660857...]
sage: eh = stdfun.mittag_leffler_e(1/2)
sage: eh.dop(exp(x^2)*(1+erf(x))).simplify_full()
0
sage: eh.dop.numerical_solution(eh.ini, [eh.pt, 2])
[108.940904389977...]
sage: ea = stdfun.mittag_leffler_e(7/3, 1/2)
sage: ea.dop.numerical_solution(ea.ini, [ea.pt, 1])
[1.17691287735093...]
sage: stdfun.sin.dop(sin(x))
0
sage: stdfun.sin.dop.numerical_solution(
....: stdfun.sin.ini, [stdfun.sin.pt, pi/3])
[0.86602540378443...]
Functions
mittag_leffler_e(alpha[, beta]) |
Classes
IVP(pt, dop, ini) |