+1
On Nov 13, 2008, at 8:48 PM, Ondrej Certik wrote:
>
> The simplifications were already implemented for cosh(), so this
> patch fixes it
> for sinh() and tanh() as well.
> ---
> sympy/functions/elementary/hyperbolic.py | 28 +++++++++++
> ++++++--
> .../functions/elementary/tests/test_hyperbolic.py | 10 ++++++-
> 2 files changed, 34 insertions(+), 4 deletions(-)
>
> diff --git a/sympy/functions/elementary/hyperbolic.py b/sympy/
> functions/elementary/hyperbolic.py
> index fe9b0db..ebb29ec 100644
> --- a/sympy/functions/elementary/hyperbolic.py
> +++ b/sympy/functions/elementary/hyperbolic.py
> @@ -52,6 +52,17 @@ class sinh(Function):
> if coeff.is_negative:
> return -cls(-arg)
>
> + if isinstance(arg, asinh):
> + return arg.args[0]
> +
> + if isinstance(arg, acosh):
> + x = arg.args[0]
> + return sqrt(x-1) * sqrt(x+1)
> +
> + if isinstance(arg, atanh):
> + x = arg.args[0]
> + return x/sqrt(1-x**2)
> +
> @staticmethod
> @cacheit
> def taylor_term(n, x, *previous_terms):
> @@ -152,12 +163,12 @@ class cosh(Function):
> if coeff.is_negative:
> return cls(-arg)
>
> - if isinstance(arg, acosh):
> - return arg.args[0]
> -
> if isinstance(arg, asinh):
> return sqrt(1+arg.args[0]**2)
>
> + if isinstance(arg, acosh):
> + return arg.args[0]
> +
> if isinstance(arg, atanh):
> return 1/sqrt(1-arg.args[0]**2)
>
> @@ -261,6 +272,17 @@ class tanh(Function):
> if coeff.is_negative:
> return -cls(-arg)
>
> + if isinstance(arg, asinh):
> + x = arg.args[0]
> + return x/sqrt(1+x**2)
> +
> + if isinstance(arg, acosh):
> + x = arg.args[0]
> + return sqrt(x-1) * sqrt(x+1) / x
> +
> + if isinstance(arg, atanh):
> + return arg.args[0]
> +
> @staticmethod
> @cacheit
> def taylor_term(n, x, *previous_terms):
> diff --git a/sympy/functions/elementary/tests/test_hyperbolic.py b/
> sympy/functions/elementary/tests/test_hyperbolic.py
> index 1d5c7eb..e42df20 100644
> --- a/sympy/functions/elementary/tests/test_hyperbolic.py
> +++ b/sympy/functions/elementary/tests/test_hyperbolic.py
> @@ -306,9 +306,17 @@ def test_acoth():
>
> def test_simplifications():
> x = Symbol('x')
> - assert cosh(acosh(x)) == x
> + assert sinh(asinh(x)) == x
> + assert sinh(acosh(x)) == sqrt(x-1) * sqrt(x+1)
> + assert sinh(atanh(x)) == x/sqrt(1-x**2)
> +
> assert cosh(asinh(x)) == sqrt(1+x**2)
> + assert cosh(acosh(x)) == x
> assert cosh(atanh(x)) == 1/sqrt(1-x**2)
>
> + assert tanh(asinh(x)) == x/sqrt(1+x**2)
> + assert tanh(acosh(x)) == sqrt(x-1) * sqrt(x+1) / x
> + assert tanh(atanh(x)) == x
> +
> def test_issue1037():
> assert cosh(asinh(Integer(3)/2)) == sqrt(Integer(13)/4)
> --
> 1.5.6.5
>
>
> >
--------------------
Fabian Seoane
http://fseoane.net
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