Vinzent Steinberg wrote:
> On Mar 27, 4:55 pm, Ondrej Certik <ond...@certik.cz> wrote:
>
>> On Fri, Mar 27, 2009 at 8:34 AM, Vinzent Steinberg
>>
>> <vinzent.steinb...@googlemail.com> wrote:
>>
>>
>>> This is strange, because just constructing such an expression triggers
>>> this trivial simplification:
>>>
>>>>>> (cos(x)**3)**(2/3)*cos(y)**2 - (cos(x)**3)**(5/3)*cos(y)**2 + \
>>>>>>
>>> ... 3*cos(x)**3*cos(y)**2 + cos(x)**2*cos(y)**2*tan(x)**2 + \
>>> ... cos(x)**5*cos(y)**2*tan(x)**4
>>> cos(y)**2 + 2*cos(x)**3*cos(y)**2 + cos(x)**2*cos(y)**2*tan(x)**2 + cos
>>> (x)**5*cos(y)**2*tan(x)**4
>>>
>> What is strange on this?
>>
>> O.
>>
>
> That it doesn't simplify for Alan:
>
> Alan Bromborsky wrote:
>
>> Here is a trigsimp problem, although the problem is not really in trigsimp.
>>
>
>
>> Run this code:
>>
>
>
>> from sympy import *
>> x = Symbol('x')
>> y = Symbol('y')
>> s = sin(x)
>> c = cos(x)
>> S = sin(y)
>> C = cos(y)
>> e = (1-S**2)*(1+c)*(s**2+c**2)+C**2*(1-s**2)*c**3+C**2*(1-c**2)*c**3
>> e = expand(e)
>> print e
>> print trigsimp(e,deep=True,recursive=True)
>>
>
>
>> and get:
>>
>
>
>> sin(x)**2*cos(x) - sin(x)**2*sin(y)**2*cos(x) + cos(x)**2 + sin(x)**2 -
>> cos(x)**2*sin(y)**2 -
>> cos(x)**3*sin(y)**2 - cos(x)**5*cos(y)**2 - sin(x)**2*sin(y)**2 +
>> 2*cos(x)**3*cos(y)**2 -
>> cos(x)**3*cos(y)**2*sin(x)**2 + cos(x)**3
>>
>
>
>> (cos(x)**3)**(2/3)*cos(y)**2 - (cos(x)**3)**(5/3)*cos(y)**2 +
>> 3*cos(x)**3*cos(y)**2 +
>> cos(x)**2*cos(y)**2*tan(x)**2 + cos(x)**5*cos(y)**2*tan(x)**4
>>
>
>
>> The problem is expressions of the form: (cos(x)**3)**(5/3)
>> which probably prevent trigsimp from further simplification. Is their
>> any simple way to insure3
>> that (cos(x)**3)**(5/3) would be replaced by cos(x)**5!
>>
>
> Vinzent
> >
>
>
If you modify trigsimp here is another problem. For this code:
from sympy import *
x = Symbol('x')
y = Symbol('y')
e = cos(x)*tan(x)
print e
print trigsimp(e)
The result is:
cos(x)*tan(x)
cos(x)*tan(x)
Maybe there should be an option in trigsimp "not" to replace
sin(x)/cos(x) with tan(x) and cos(x)/sin(x)
with cot(x) ?
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