Hi Alec,
Am Freitag, den 09.04.2010, 16:52 -0700 schrieb Alec Mihailovs:
> For example,
>
> var('t R_u c')
> map(function,('R_b', 'psi', 'm_z'))
> r = R_b(t)*sin(psi(t))
> z = R_b(t)*cos(psi(t))+m_z(t)
> Dr, Dz = r.diff(t), z.diff(t)
> v=vector([Dr,Dz]) * vector([cos(psi(t)),sin(psi(t))])
> w=v.simplify_trig()
> w.substitute_function(m_z,lambda t:-sqrt(R_b(t)^2-R_u^2))
>
> 2*sin(psi(t))*cos(psi(t))*D[0](R_b)(t) -
> sin(psi(t))*R_b(t)*D[0](R_b)(t)/sqrt(-R_u^2 + R_b(t)^2) -
> (2*sin(psi(t))^2*R_b(t) - R_b(t))*D[0](psi)(t)
>
> Alec Mihailovs
thanks for your solution, of course it works well. Besides it's a nice
lesson in typing economics in Sage :-)
I tried to understand my mistake and I realised that I have difficulties
to distinguish between symbolic expressions and functions and when to
use either. In the tutorial there is a section "Some Common Issues with
Functions" which states several possibilities to define a "function".
But I am lost if I have to decide which to use in an special example:
If I type
sage: f = function('f')
sage: type(f)
<class 'sage.symbolic.function_factory.NewSymbolicFunction'>
sage: var('x')
x
sage: type(f(x))
<type 'sage.symbolic.expression.Expression'>
ok, no surprise. But
sage: g = function('g', x)
sage: type(g)
<type 'sage.symbolic.expression.Expression'>
sage: type(g(x))
<type 'sage.symbolic.expression.Expression'>
sage: h1 = sin(f(x))
sage: type(h1)
<type 'sage.symbolic.expression.Expression'>
sage: h2 = lambda t: sin(f(t))
sage: type(h2)
<type 'function'>
sage: h1.diff(x)
cos(f(x))*D[0](f)(x)
sage: h2.diff(x)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call
last)
/home/ecki/<ipython console> in <module>()
AttributeError: 'function' object has no attribute 'diff'
What's the difference between f and g? Why can I differentiate a
symbolic expression, but not a function? As a mathematician I expected
the other way :-( The tutorial states that S(x) = sin(x) defines a
"callable symbolic expression". But I get
sage: S(x) = sin(x)
sage: type(S)
<type 'sage.symbolic.expression.Expression'>
sage: type(S(x))
<type 'sage.symbolic.expression.Expression'>
Is there a difference between a "callable symbolic expression" and a
"symbolic expression"? Why can I type
sage: S.diff()
x |--> cos(x)
but
sage: sin.diff()
---------------------------------------------------------------------------
AttributeError ...
Is there any more comprehensive description of the different types of
functions and symbolic expressions and when to use them? Of course, I
can go the hard tour and dig into the source, or I play around until I
get the "right feeling", but I wonder if there is an easier way.
Thanks in advance
Eckhard
My system:
Dell Optiplex GX620, Intel Pentium 630, 1GB RAM
:~$ uname -a
Linux Adler 2.6.24-27-generic #1 SMP Fri Mar 12 00:52:19 UTC 2010 x86_64
GNU/Linux
:~$ lsb_release -d
Description: Ubuntu 8.04.4 LTS
up to date
:~$ sage --version
| Sage Version 4.3.3, Release Date: 2010-02-21 |
installed tar ball:
sage-4.3.3-linux-64bit-ubuntu_8.04.4_lts-x86_64-Linux.tar.gz
--
Dr. Eckhard Kosin
Services in Mathematics and Simulation
mailto:[email protected]
http://www.mathematik-service-kosin.de
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