/usr/share/octave/packages/interval-3.1.0/@infsupdec/nthroot.m is in octave-interval 3.1.0-5.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | ## Copyright 2015-2016 Oliver Heimlich
## Copyright 2017 Joel Dahne
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @documentencoding UTF-8
## @defmethod {@@infsupdec} nthroot (@var{X}, @var{N})
##
## Compute the real n-th root of @var{X}.
##
## Accuracy: The result is a valid enclosure. The result is a tight
## enclosure for @var{n} ≥ -2. The result also is a tight enclosure if the
## reciprocal of @var{n} can be computed exactly in double-precision.
## @seealso{@@infsupdec/pown, @@infsupdec/pownrev, @@infsupdec/realsqrt, @@infsupdec/cbrt}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2015-02-20
function result = nthroot (x, n)
if (nargin ~= 2)
print_usage ();
return
endif
if (not (isa (x, "infsupdec")))
x = infsupdec (x);
endif
result = newdec (nthroot (intervalpart (x), n));
## nthroot is continuous everywhere, but not defined everywhere
even = mod (n, 2) == 0;
defined = (not (even) & (n > 0 | inf (x) > 0 | sup (x) < 0)) ...
| (even & ((n > 0 & inf (x) >= 0)| (n < 0 & inf (x) > 0)));
result.dec(not (defined)) = _trv ();
result.dec = min (result.dec, x.dec);
endfunction
%!assert (isequal (nthroot (infsupdec (25, 36), 2), infsupdec (5, 6)));
%!assert (isequal (nthroot (infsupdec (-1, 1), 2), infsupdec (0, 1, "trv")));
%!assert (isequal (nthroot (infsupdec (-1, 1), 3), infsupdec (-1, 1)));
%!assert (isequal (nthroot (infsupdec (-1, 1), -2), infsupdec (1, inf, "trv")));
%!assert (isequal (nthroot (infsupdec (-1, 1), -3), infsupdec (-inf, inf, "trv")));
|