This also by Hongbo Li(Lee) ?
https://www.issac-conference.org/2017/assets/tutorial_slides/Li.pdf
On 8/23/24 9:12 PM, Sangyub Lee wrote:
I had a few discussions after Christopher Smith's comments, which I
believe could be useful to share:
* The Area Method uses constructive geometry, so it might be
beneficial to provide a tool that can draw actual diagrams, in
addition to solving the geometry problems (for example, the
ability to draw random points, lines, circles).
* There were discussions between myself and others regarding the
choice between the Wu Method and the Area Method. However, this
ultimately led to the conclusion that the Area Method should be
used due to the poor performance of sparse multivariate
polynomials at that time. (Intuitively, we considered using
separate x and y symbols for every point in the geometry.)
* Maybe things have improved by 2024, but I'm not 100% sure.
Nonetheless, the performance of sparse multivariate polynomials
could clearly contribute to improvements in SymPy as well.
* I also note that the performance of the 'cancel' function and
algebraic number operations could be improved. I believe that many
of the datasets from the book on the Area Method could also be
useful for providing test cases for these issues. Some geometry
problems took dozens of seconds to compute or were not feasible to
implement due to performance bottlenecks with algebraic numbers.
* I note that the debate between using geometry invariants (like the
Area Method) and polynomials (like the Wu Method or Gröbner basis)
has not yet been concluded. The problem is that geometric
identities lead to very inefficient representations of polynomials
(think of writing a matrix determinant for every triangle, which
is obviously inefficient). This has motivated the use of a
symbolic system that represents the determinant expression
directly and efficiently.
* I believe that research on this topic was advanced by people like
Hongbo Lee (Invariant Algebras and Geometry Reasoning), but I
haven't fully read his work yet. It could offer improvements.
* I also note that the Area Method could potentially be implemented
with Galgebra due to its relevance, but I previously skipped this
because Galgebra was more focused on geometric analysis (such as
computing derivatives), which was not relevant to the topic.
However, I think suggestions from the Galgebra community could be
valuable here.
* I also had access to a full version of the Area Method (including
Pythagorean identities) from my previous employer. While it may
not be possible to share the code, it's fairly easy to figure out
from the original paper I cited.
On Saturday, August 24, 2024 at 1:30:18 AM UTC+2 [email protected] wrote:
Area method: https://github.com/sympy/sympy/issues/22160
Angle method: https://github.com/sympy/sympy/issues/22644
/c
On Friday, August 23, 2024 at 6:24:36 PM UTC-5 Oscar wrote:
On Fri, 23 Aug 2024 at 23:29, Sangyub Lee <[email protected]>
wrote:
>
> To be more productive, SymPy itself can enhance its geometry
capabilities by incorporating Wu's method or a deductive
database approach,
> which are useful in addressing geometric challenges.
> I’ve also shared the implementation of the Area method with
SymPy, which can be searched.
I know that you have said that this can be searched but can
you share
a link to what you are referring to?
I think that would be useful to others reading this.
--
Oscar
--
You received this message because you are subscribed to the Google
Groups "sympy" group.
To unsubscribe from this group and stop receiving emails from it, send
an email to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/sympy/0d3d94ac-b3f9-48b1-bbea-512ce4ce1f22n%40googlegroups.com
<https://groups.google.com/d/msgid/sympy/0d3d94ac-b3f9-48b1-bbea-512ce4ce1f22n%40googlegroups.com?utm_medium=email&utm_source=footer>.
--
You received this message because you are subscribed to the Google Groups
"sympy" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/sympy/e0a3c604-b1ed-4349-a0ce-ad42cce03e1a%40gmail.com.
