/usr/share/octave/packages/symbolic-2.2.4/vpasolve.m is in octave-symbolic 2.2.4-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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%%
%% This file is part of OctSymPy.
%%
%% OctSymPy 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 software 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 software; see the file COPYING.
%% If not, see <http://www.gnu.org/licenses/>.
%% -*- texinfo -*-
%% @documentencoding UTF-8
%% @deftypefn {Function File} {@var{y} =} vpasolve (@var{e})
%% @deftypefnx {Function File} {@var{y} =} vpasolve (@var{e}, @var{x})
%% @deftypefnx {Function File} {@var{y} =} vpasolve (@var{e}, @var{x}, @var{x0})
%% Numerical solution of a symbolic equation.
%%
%% Variable-precision numerical solution of the equation @var{e}
%% for variable @var{x} using initial guess of @var{x0}.
%%
%% Example:
%% @example
%% @group
%% >> syms x
%% >> eqn = exp(x) == x + 2;
%% >> vpasolve(eqn, x, 0.1)
%% @result{} (sym) 1.1461932206205825852370610285214
%% @end group
%% @end example
%%
%% @seealso{vpa}
%% @end deftypefn
%% Author: Colin B. Macdonald
%% Keywords: symbolic
function r = vpasolve(e, x, x0)
if (nargin < 3)
x0 = sym(0);
end
if (nargin < 2)
x = symvar(e, 1);
end
n = digits();
% nsolve gives back mpf object: https://github.com/sympy/sympy/issues/6092
% In SymPy >= 0.7.7, mpmath is not bundled so we import mpmath.
% In older versions it is usually bundled except on Fedora, hence
% the try, except bit.
cmd = {
'(e, x, x0, n) = _ins'
'if sympy.__version__ == "0.7.5" or sympy.__version__.startswith("0.7.6"):'
' try:'
' sympy.mpmath.mp.dps = n'
' findroot = sympy.mpmath.findroot'
' except AttributeError:'
' import mpmath'
' mpmath.mp.dps = n'
' findroot = mpmath.findroot'
'else:'
' import mpmath'
' mpmath.mp.dps = n'
' findroot = mpmath.findroot'
'#r = nsolve(e, x, x0)' % https://github.com/sympy/sympy/issues/8564
'#r = sympy.N(r, n)' % deal with mpf
'if isinstance(e, Equality):'
' e = e.lhs - e.rhs'
'e = e.evalf(n)'
'f = lambda meh: e.subs(x, meh)'
'r = findroot(f, x0)'
'r = sympy.N(r, n)' % deal with mpf
'return r,' };
r = python_cmd (cmd, sym(e), x, x0, n);
end
%!test
%! syms x
%! vpi = vpa(sym(pi), 64);
%! e = tan(x/4) == 1;
%! q = vpasolve(e, x, 3.0);
%! w = q - vpi ;
%! assert (double(w) < 1e-30)
%!test
%! syms x
%! vpi = vpa(sym(pi), 64);
%! e = tan(x/4) == 1;
%! q = vpasolve(e, x);
%! w = q - vpi;
%! assert (double(w) < 1e-30)
%! q = vpasolve(e);
%! w = q - vpi;
%! assert (double(w) < 1e-30)
%!test
%! % very accurate pi
%! syms x
%! e = tan(x/4) == 1;
%! m = digits(256);
%! q = vpasolve(e, x, 3);
%! assert (double(abs(sin(q))) < 1e-256)
%! digits(m);
%!test
%! % very accurate sqrt 2
%! syms x
%! e = x*x == 2;
%! m = digits(256);
%! q = vpasolve(e, x, 1.5);
%! assert (double(abs(q*q - 2)) < 1e-256)
%! digits(m);
%!test
%! % very accurate sqrt pi
%! % fails: https://github.com/sympy/sympy/issues/8564
%! syms x
%! e = x*x == sym(pi);
%! m = digits(256);
%! q = vpasolve(e, x, 3);
%! assert (double(abs(sin(q*q))) < 1e-256)
%! digits(m);
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