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add simplify identities #529

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56 changes: 52 additions & 4 deletions inst/@sym/simplify.m
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Original file line number Diff line number Diff line change
Expand Up @@ -19,8 +19,13 @@
%% -*- texinfo -*-
%% @documentencoding UTF-8
%% @defmethod @@sym simplify (@var{x})
%% @defmethodx @@sym simplify (@var{x}, @var{y})
%% Simplify an expression.
%%
%% @var{y} can be 'special' or 'complete'.
%% 'special' will simplify special function with identities.
%% 'complete' will replace the identities and then simplify.
%%
%% Example:
%% @example
%% @group
Expand All @@ -47,15 +52,46 @@
%% @end group
%% @end example
%%
%% When @var{y} is 'special':
%% @example
%% @group
%% syms x
%% simplify(beta(x, 1), 'special')
%% @result{} ans = (sym)
%% Γ(x)
%% ────────
%% Γ(x + 1)
%% @end group
%% @end example
%%
%% When @var{y} is 'complete':
%% @example
%% @group
%% syms x
%% simplify(beta(x, 1), 'complete')
%% @result{} ans = (sym)
%% 1
%% ─
%% x
%% @end group
%% @end example
%%
%% @seealso{@@sym/isAlways, @@sym/factor, @@sym/expand, @@sym/rewrite}
%% @end defmethod

%% Source: http://docs.sympy.org/dev/tutorial/simplification.html

function y = simplify(x)

cmd = 'return sp.simplify(*_ins),';
function y = simplify(x, y)

y = python_cmd (cmd, x);
if (nargin == 1)
y = python_cmd('return simplify(*_ins),', x);
elseif ( strcmp( y, 'special'))
y = python_cmd('return expand_func(*_ins),', x);
elseif ( strcmp( y, 'complete'))
y = python_cmd('return simplify(expand_func(*_ins)),', x);
else
print_usage ();
end

end

Expand All @@ -66,3 +102,15 @@
%! q = horner (p);
%!assert(~isequal( p - q, 0))
%!assert(isequal( simplify(p - q), 0))

%!test
%! syms x
%! A = simplify(beta(x, 1), 'special');
%! B = gamma(x)/gamma(x+1);
%! assert( isequal( A, B ))

%!test
%! syms x
%! A = simplify(beta(x, 1), 'complete');
%! B = 1/x;
%! assert( isequal( A, B ))