On Nov 13, 7:44 pm, William Stein <wst...@gmail.com> wrote:
> On Fri, Nov 13, 2009 at 5:09 PM, kstueve <kevin.stu...@gmail.com> wrote:
>
> > To sage-dev
> > Can someone please explain to me what traits are in the context of
> > tvisual? The wiki page for it (http://www.enthought.com/traitsfrom
> > the pagehttps://svn.enthought.com/enthought/wiki/TVTKIntroduction) is
> > a dead link.
> > A google search of either vpython.org or svn.enthought.com produces
> > many results for visual, but none for tvisual. I am guessing that
> > tvisual is part of TVTK and visual part of VPython.
>
> > I see tvtk at the
> > pagehttps://svn.enthought.com/enthought/wiki/TVTKIntroduction
> > (traited vtk), and vtk athttp://mayavi.sourceforge.net/.
> >http://www.vtk.org/says that vtk is the visualization toolkit.
>
> > Jason Grout said "Since we also already have momentum for
> > incorporating mayavi.." Can someone please give me details. Is Jason
> > saying that Sage-dev is in the process of making mayavi part of Sage,
> > so it would be easy to use parts of mayavi?
>
> No. To the best of my knowledge nobody is working on including
> mayavai + vtk in Sage. VTK is quite difficult to build, to put it
> mildly.
>
> > What are the benefits of using tvtk over vpython? Vpython is faster.
> > How does Tvtk has a cleaner API?
>
> Note that tvtk and vpython don't work via a web browser. Part of the
> challenge of Sage -- and the opportunity -- is making capabilities
> available via a webpage. For that, the only options are javascript
> (=AJAX) or Java.
>
> > Does anyone have any thoughts on using OpenModelica?
>
> It's license is GPL-incompatible. However, I've been told they are in
> the process of changing their license to be GPL-compatible. I hope
> this happens.
>
>
>
> > Another question:
> > Time permitting, I would like to be able to solve symbolic physics
> > problems. Instead of just giving initial conditions and solving for
> > later values, it would be nice to say (symbolically) "it takes t
> > seconds for the ball to reach the basket, at what angle was it
> > thrown". How might you go about this? I think that this could be
> > done using a theorem prover of sorts that searches the space of
> > theorems that can be proven from a small set of axioms and givens and
> > a set of manipulation rules. Of course this is an NP-complete problem
> > that is intractable in general (think Fermat's last theorem),
>
> Fermat's last theorem has nothing to do with NP complete problems, as
> far as I know. What connection were you thinking of? I'm curious.
Automated theorem proving is NP-complete (because the boolean
satisfiability problem (which is NP-complete) reduces to finding a
proof of satisfiability (and a proof of satisfiability will exist with
length a fixed polynomial of the size of the original boolean
satisfiability problem) and proofs can be verified in time polynomial
of the length of the proof). I gave Fermat's last theorem as an
example of the difficulty of finding the correct 300 page permutation
of symbols that represents a correct proof of a statement. Perhaps it
sounded as if I was discussing trying many potential integer solutions
to x^n+y^n=z^n, which is not what I meant.
Asking a computer to find a 300 page proof of a statement like
Fermat's last theorem by search is a bad idea. I think asking a
computer to find a 5 line solution to a simple symbolic physics
problem (the sort you find in freshman physics) might be a good idea.
I am curious about how trig_simplify works. "return self.parent()
(self._maxima_().trigexpand().trigsimp())"
It doesn't seem to use search. Does anyone know if there are any
components of Sage that use search by an automated theorem prover?
http://en.wikipedia.org/wiki/Automated_theorem_proving#Decidability_of_the_problem
>
> I'm also confused as to what doing physics symbolically has to do with
> theorem provers.
Theorem proving can be attacked by doing a search of all theorems that
follow from the axioms (although it will take time exponential in the
length of the theorem). Many physics problems are presented
effectively as a set of equations. Solving a set of equations
symbolically (that is designed to be solved symbolically by a student
in several steps) can be attacked by doing a search of the equations
that follow from the original equations for one that gives the value
in question. The analogy to theorem proving is strong-you might be
searching for an equation/theorem of the form "x = _____"
As an example of the sort of problem for which I think search might be
useful (problem 83 on page 81 from Tipler Physics for Scientists for
Engineers):
"At 1/2 of it's maximum height, the speed of a projectile is 3/4 of
its initial speed. What was its launch angle?"
This is a symbolic problem that cannot be solved by plugging values
into a projectile motion equation from an equation sheet.
Is there a better way to approach such problems from a programming
point of view? I guess for this problem, you could just employ some
sort of numerical educated guess and check/Newton's method/binary
search algorithm, but such a solution does not show work or steps and
it would be easy to find a similar problem that is entirely symbolic.
Correct me if I'm wrong, but I believe that the only way to solve a
problem like this is to write down what you know and manipulate it
until you arrive at a solution (which is a search problem).
>
> > but most
> > problems given to freshman physics students are only a few steps long,
> > meaning that the tree of possible proofs is relatively small and can
> > be exhaustively searched.
> > Does Sage have the ability to symbolically simplify "sin^2(theta)+cos^2
> > (theta)" to "1"?
>
> Yes:
> sage: var('theta')
> theta
> sage: f = sin(theta)^2 + cos(theta)^2
> sage: f.trig_simplify()
> 1
>
> > For numeric problems such as "at what angle must the ball be thrown to
> > reach the basket in 2 seconds?", it might be possible to use some sort
> > of binary search to find the correct value.
>
> > Here is a link to my (very early) pre-draft of my writeup, so that you
> > can view the bibliography.
> >http://docs.google.com/View?id=df9q29vh_45dfx2wmfg
>
> > I declare Crocker's rules. http://www.sl4.org/crocker.html
>
> And I exercise it :-)
>
> William
>
>
>
>
>
> > Kevin Stueve
>
> > On Sep 23, 3:31 pm, Fernando Perez <fperez....@gmail.com> wrote:
> >> On Wed, Sep 23, 2009 at 4:41 AM, Prabhu Ramachandran
>
> >> <pra...@aero.iitb.ac.in> wrote:
> >> > Thanks Fernando. The speed issue is still true but I wouldn't blame
> >> > traits since that isn't the source of the bottleneck. I think there are
> >> > a little too many events and too many renders. I have not had the time
> >> > to profile it carefully.
>
> >> Thanks for the clarifications, Prabhu. I remembered the performance
> >> drop, but wasn't sure what all of the reasons were under the hood and
> >> I was worried I could misrepresent the issue.
>
> >> It would really be great to have vpython-like performance with the
> >> clean tvtk api! Here's to hoping it's possible :)
>
> >> Cheers,
>
> >> f
>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washingtonhttp://wstein.org
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