Derivative without Simplification

[Michi S]

Hello!

Is there a way to turn off the automatic simplification by calculating the derivative of a function? For example

t = sym.symbols('t')
sym.Derivative( (sin(t)+exp(t))**3 , t ).doit()

gives:
(exp(t) + sin(t))**2*(3*exp(t) + 3*cos(t))

I need the result without any simplifications (in order to detect the inner derivative for further calculations)

Should be:
(exp(t) + sin(t))**2*3*(exp(t) + cos(t))

[Michi S]

factor(sym.Derivative( (sin(t)+exp(t))**3 , t ).doit())

works, but it would still be nice if someone could tell me, if there is way to turn the simplification of ;)

[Richard Fateman]

I don't understand why you need it, but you could write your own differentiation program

without simplification in about 1/2 page of code.

http://dl.acm.org/citation.cfm?id=307341&CFID=796040025&CFTOKEN=79612797

[Christophe Bal]

Hello.

Have you try factorization ?

Christophe BAL

Enseignant de mathématiques en Lycée et développeur Python amateur

---

French teacher of math in a high school and amateur Python developer

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[Aaron Meurer]

Unfortunately, distribution of numbers across additions is done
automatically, so disabling it is not easy. Using factor() here is
your best solution.

Aaron Meurer

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[Michi S]

Thanks for the answers! For the purpose of my master thesis I am trying to optimize the simulaion of helicopter dynamics. These dynamics are pretty complicated, which leads to huge equations for most states. In order to speed up the calculation I need to detect functions that where already evaluated. The inner derivative that is produced due to the chain rule is such a function, that I need to detect.

factor() works only for the first derivative unfortunately. In the second and higher derivatives it does not factorize the inner derivates anymore:

t = sym.symbols('t')

diff( (sin(t)+exp(t))**5 , t )
>> (exp(t) + sin(t))**4*(5*exp(t) + 5*cos(t))

factor(diff( (sin(t)+exp(t))**5 , t ))
>> 5*(exp(t) + sin(t))**4*(exp(t) + cos(t))

factor(diff( (sin(t)+exp(t))**5 , t, t ))
>> 5*(exp(t) + sin(t))**3*(5*exp(2*t) + 8*exp(t)*cos(t) - sin(t)**2 + 4*cos(t)**2)


I think, writing my own differentiation programm will be a little bit to hard to solve my issue. Is there no other way besides factor() and wiriting my own programm?


Thank for your help!

Am Mittwoch, 1. Juni 2016 15:34:28 UTC+2 schrieb Michi S:

[Aaron Meurer]

On Tue, Jun 7, 2016 at 8:58 AM, Michi S <misc...@gmail.com> wrote:
>
> Thanks for the answers! For the purpose of my master thesis I am trying to
> optimize the simulaion of helicopter dynamics. These dynamics are pretty
> complicated, which leads to huge equations for most states. In order to
> speed up the calculation I need to detect functions that where already
> evaluated. The inner derivative that is produced due to the chain rule is
> such a function, that I need to detect.
>
> factor() works only for the first derivative unfortunately. In the second
> and higher derivatives it does not factorize the inner derivates anymore:
>
> t = sym.symbols('t')
> diff( (sin(t)+exp(t))**5 , t )
>>> (exp(t) + sin(t))**4*(5*exp(t) + 5*cos(t))
>
> factor(diff( (sin(t)+exp(t))**5 , t ))
>>> 5*(exp(t) + sin(t))**4*(exp(t) + cos(t))
>
> factor(diff( (sin(t)+exp(t))**5 , t, t ))
>>> 5*(exp(t) + sin(t))**3*(5*exp(2*t) + 8*exp(t)*cos(t) - sin(t)**2 +
>>> 4*cos(t)**2)

What output were you expecting here? I don't think the second factor
can be factorized. Note however that it can be simplified slightly if
you call trigsimp() on it.

Aaron Meurer

>
>
> I think, writing my own differentiation programm will be a little bit to
> hard to solve my issue. Is there no other way besides factor() and wiriting
> my own programm?
>
>
> Thank for your help!
>
>
> Am Mittwoch, 1. Juni 2016 15:34:28 UTC+2 schrieb Michi S:
>>
>> Hello!
>>
>> Is there a way to turn off the automatic simplification by calculating the
>> derivative of a function? For example
>>
>> t = sym.symbols('t')
>> sym.Derivative( (sin(t)+exp(t))**3 , t ).doit()
>>
>> gives:
>> (exp(t) + sin(t))**2*(3*exp(t) + 3*cos(t))
>>
>> I need the result without any simplifications (in order to detect the
>> inner derivative for further calculations)
>>
>> Should be:
>> (exp(t) + sin(t))**2*3*(exp(t) + cos(t))
>

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[Alan Bromborsky]

You might want to look at "New Foundations for Classical Mechanics" by David Hestenes and the rigid body rotor description of equations of motion.

http://www.amazon.com/Foundations-Classical-Mechanics-Fundamental-Theories/dp/0792353021

Should be in your school library.

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[Richard Fateman]

I think you are merely trying to find common subexpressions to speed up evaluation.

There are lots of ways to do that.

The simplest is to precompute sin(t), cos(t), exp(t) or whatever non-elementary

functions are involved.  Then you can also consider using horner's rule  or

something like factor.  But there should be a common-subexpression extraction

program around, no?

RJF

[Aaron Meurer]

Yep.  It's called cse().

Aaron Meurer 

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[Jason Moore]

You may also be interested in PyDy which generates optimized C code from symbolic equations of motion. It uses cse under the hood for some of the optimizations. PyDy directly works with the EoMs that are formed from sympy.physics.mechanics.

Jason
moorepants.info
+01 530-601-9791

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