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inst/@sym/ainterval.m

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+%% Copyright (C) 2017 Lagu
+%%
+%% 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
+%% @defmethod @@sym ainterval (@var{x})
+%% Return the union of intervals of x when, @var{x} is in rectangular form
+%% or the union of intervals of r when self is in polar form.
+%%
+%% Example:
+%% @example
+%% @group
+%% a = interval (sym (2), 3);
+%% b = interval (sym (4), 5);
+%% ainterval (complexregion (a * b))
+%%   @result{} ans = (sym) [2, 3]
+%% @end group
+%% @end example
+%%
+%% @example
+%% @group
+%% c = interval (sym (1), 7);
+%% ainterval (complexregion (a * b + b * c))
+%%   @result{} ans = (sym) [2, 3] ∪ [4, 5]
+%% @end group
+%% @end example
+%%
+%% @end defmethod
+
+
+function y = ainterval(x)
+  if (nargin ~= 1)
+    print_usage ();
+  end
+  y = elementwise_op ('lambda x: x.a_interval', sym (x));
+end
+
+
+%!test
+%! a = interval (sym (1), 2);
+%! b = interval (sym (4), 5);
+%! k = ainterval (complexregion (a * b));
+%! assert (isequal (k, a))
+
+%!test
+%! a = interval (sym (1), 2);
+%! b = interval (sym (4), 5);
+%! c = interval (sym (-3), 2);
+%! k = ainterval (complexregion (a * b + b * c));
+%! assert (isequal (k, a + b))

inst/@sym/binterval.m

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+%% Copyright (C) 2017 Lagu
+%%
+%% 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
+%% @defmethod @@sym binterval (@var{x})
+%% Return the union of intervals of y when, @var{x} is in rectangular form
+%% or the union of intervals of theta when self is in polar form.
+%%
+%% Example:
+%% @example
+%% @group
+%% a = interval (sym (2), 3);
+%% b = interval (sym (4), 5);
+%% binterval (complexregion (a * b))
+%%   @result{} ans = (sym) [4, 5]
+%% @end group
+%% @end example
+%%
+%% @example
+%% @group
+%% c = interval (sym (1), 7);
+%% binterval (complexregion (a * b + b * c))
+%%   @result{} ans = (sym) [1, 7]
+%% @end group
+%% @end example
+%%
+%% @end defmethod
+
+
+function y = binterval(x)
+  if (nargin ~= 1)
+    print_usage ();
+  end
+  y = elementwise_op ('lambda x: x.b_interval', sym (x));
+end
+
+
+%!test
+%! a = interval (sym (1), 2);
+%! b = interval (sym (4), 5);
+%! k = binterval (complexregion (a * b));
+%! assert (isequal (k, b))
+
+%!test
+%! a = interval (sym (1), 2);
+%! b = interval (sym (4), 5);
+%! c = interval (sym (-3), 2);
+%! k = binterval (complexregion (a * b + b * c));
+%! assert (isequal (k, b + c))

inst/@sym/boundary.m

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+%% Copyright (C) 2017 Lagu
+%%
+%% 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
+%% @defmethod @@sym boundary (@var{x})
+%% The boundary or frontier of a set.
+%%
+%% Example:
+%% @example
+%% @group
+%% a = interval (sym (1), 2);
+%% b = interval (sym (5), 8);
+%% boundary (a + b)
+%%   @result{} ans = (sym) @{1, 2, 5, 8@}
+%% @end group
+%% @end example
+%%
+%% @end defmethod
+
+
+function y = boundary(x)
+  if (nargin ~= 1)
+    print_usage ();
+  end
+  y = elementwise_op ('lambda x: x.boundary', sym (x));
+end
+
+
+%!test
+%! a = interval (sym (0), 1);
+%! b = interval (sym (0), 1, true, false);
+%! assert( isequal( boundary (a), boundary (b)))

inst/@sym/complement.m

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+%% Copyright (C) 2017 Lagu
+%%
+%% 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
+%% @defmethod @@sym complement (@var{x}, @var{y})
+%% The complement of @var{x} with @var{y} as Universe.
+%%
+%% Example:
+%% @example
+%% @group
+%% a = interval (sym (0), 10);
+%% b = interval (sym (4), 6);
+%% a - b
+%%   @result{} ans = (sym) [0, 4) ∪ (6, 10]
+%% @end group
+%% @end example
+%% @example
+%% @group
+%% complement (b, a)
+%%   @result{} ans = (sym) [0, 4) ∪ (6, 10]
+%% @end group
+%% @end example
+%%
+%% @end defmethod
+
+
+function y = complement(x, y)
+  if (nargin ~= 2)
+    print_usage ();
+  end
+  y = elementwise_op ('lambda x, y: x.complement(y)', sym (x), sym (y));
+end
+
+
+%!test
+%! R = domain ('Reals');
+%! a = interval (sym (-1), 1);
+%! b = interval (sym (-inf), -1, true, true) + interval (sym (1), inf, true, true);
+%! assert (isequal (complement (a, R), b))

inst/@sym/complexregion.m

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+%% Copyright (C) 2017 Lagu
+%%
+%% 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
+%% @defmethod @@sym complexregion (@var{x}, @var{y})
+%% Represents the Set of all Complex Numbers.
+%% It can represent a region of Complex Plane in 
+%% both the standard forms Polar and Rectangular coordinates.
+%% Where @var{x} are the interval and if @var{y} is true
+%% you will get the polar form, if is not specified or is false
+%% it will be constructed in rectangular form.
+%%
+%% Example for rectangular form:
+%% @example
+%% @group
+%% a = interval (sym (0), 2);
+%% b = interval (sym (5), 7);
+%% complexregion (a * b)
+%%   @result{} ans = (sym) @{x + y⋅ⅈ | x, y ∊ [0, 2] × [5, 7]@}
+%% @end group
+%% @end example
+%%
+%% Example for polar form:
+%% @example
+%% @group
+%% a = interval (sym (1), 2);
+%% b = interval (sym (0), sym (pi) * 2);
+%% complexregion (a * b, true)
+%%   @result{} ans = (sym) @{r⋅(ⅈ⋅sin(θ) + cos(θ)) | r, θ ∊ [1, 2] × [0, 2⋅π)@}
+%% @end group
+%% @end example
+%%
+%% @end defmethod
+
+
+function y = complexregion(x, y)
+  if (nargin > 2)
+    print_usage ();
+  elseif nargin == 1
+    y = false;
+  end
+  y = elementwise_op ('lambda x, y: ComplexRegion(x, polar=y)', sym (x), logical (y));
+end
+
+
+%% This function is tested in @sym/ainterval, @sym/binterval
+%% @sym/ispolar, @sym/psets, @sym/sets and @sym/normalizethetaset

inst/@sym/contains.m

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+%% Copyright (C) 2017 Lagu
+%%
+%% 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
+%% @defmethod @@sym contains (@var{x}, @var{y})
+%% Returns True if @var{x} is contained in @var{y} as an element.
+%%
+%% Example:
+%% @example
+%% @group
+%% a = interval (sym (0), 10);
+%% contains (5, a)
+%%   @result{} ans = (sym) True
+%% @end group
+%% @end example
+%%
+%% @end defmethod
+
+
+function y = contains(x, y)
+  if (nargin ~= 2)
+    print_usage ();
+  end
+  y = elementwise_op ('lambda x, y: x in y', sym (x), sym (y));
+end
+
+
+%!test
+%! a = interval (sym (0), 10);
+%! assert (logical (~contains (-1, a)))
+
+%!test
+%! a = interval (sym (0), 10);
+%! assert (logical (contains (5, a)))