On Tue, Apr 01, 2008 at 04:30:18PM +0200, Ondrej Certik wrote:
>
> On Tue, Apr 1, 2008 at 4:18 PM, Alan Bromborsky <[EMAIL PROTECTED]> wrote:
> >
> >
> > Ondrej Certik wrote:
> > > Hi Alan!
> > >
> > > On Sun, Mar 30, 2008 at 6:20 PM, Alan Bromborsky <[EMAIL PROTECTED]>
> > wrote:
> > >
> > >> If F(x,y,z,w) and x=x(t) and y=y(t) here is what I did to calculate
> > >> df/dt. Do you have a built in method to do that?
> > >>
> > >
> > > You mean dF/dt, right?
> > >
> > >
> > >> from GAsympy import *
> > >> from sympy import *
> > >>
> > >> set_main(sys.modules[__name__])
> > >>
> > >> def PDerive(f,vlst,t):
> > >> dfdt = 0
> > >> for v in vlst:
> > >> dvdt = sympy.Symbol('d'+v.__str__()+'d'+t.__str__())
> > >> dfdt += sympy.diff(f,v)*dvdt
> > >> return(dfdt)
> > >>
> > >> make_symbols('a b c x y z w t')
> > >>
> > >> f = a*x+exp(-y)*b*z*c*w**2*x
> > >>
> > >> print 'f =',f
> > >>
> > >> dfdt = PDerive(f,[x,y],t)
> > >>
> > >> print 'dfdt =',dfdt
> > >>
> > >> ## Program output
> > >> ## f = a*x + b*c*x*z*w**2*exp(-y)
> > >> ## dfdt = dxdt*(a + b*c*z*w**2*exp(-y)) - b*c*dydt*x*z*w**2*exp(-y)
Here is my proposal:
In [1]: var('a b c x y z w t')
Out[1]: (a, b, c, x, y, z, w, t)
In [2]: f = a*x + b*c*x*z*w**2*exp(-y)
In [3]: fx = Function('fx')
In [4]: fy = Function('fy')
In [5]: g=f.subs(x,fx(t)).subs(y,fy(t))
In [6]: g
Out[6]:
2 -fy(t)
a*fx(t) + b*c*z*w *ℯ *fx(t)
In [7]: g.diff(t)
Out[7]:
d 2 -fy(t) d 2 -fy(t) d
a*──(fx(t)) + b*c*z*w *ℯ *──(fx(t)) - b*c*z*w *ℯ *fx(t)*──(fy(t))
dt dt dt
By the way, have you an advice to simply factor out the df/dt?
As I adviced in my pdf-file comment its good to distinguish the
different mathematical objects. So you have solved the naming problem.
Here is my opinion about
y = f(x, y)
So y is a function of the _symbols_ x and y. These symbols represent
maybe a real number. But when you say
x(t)
you correctly mean
(*) x = fx(t)
So x is now a function of the symbol t. When you substitute x now in f
you get an new function namly
g(t, y) = f( fx(t), y )
My question is whether anybody has a better proposal for the name fx in
(*)?
By, Friedrich
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