entation 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
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The general approach for computing series in SymPy is algorithmically
misdesigned.
See:
https://github.com/sympy/sympy/issues/26957
On Thu, 22 Aug 2024 at 13:26, emanuel.c...@gmail.com
wrote:
>
> The series method of a (large) expressin doesn’t return :
>
> from sympy import * x1, x2, x3, x4, w1
It is a lot easier to use a computer algebra system than lean but the
goals are different. I was thinking about the idea of making an AI
that could talk to a theorem prover like lean. The idea would be that
you have an AI that hallucinates lots of proofs that may or may not be
correct but then you
It would be good to have this in SymPy but unfortunately it is not
implemented yet.
It is also not available in python-flint or Flint either.
On Fri, 16 Aug 2024 at 15:38, Chris Smith wrote:
>
> As far as I can tell, these matrices are not computed implicitly. You would
> have to copy the appro
automatic evaluation is a good
thing (try Add(Integer(1), Integer(-1), evaluate=False) ) in general.
BR Oscar
Den tors 8 aug. 2024 kl 12:20 skrev Rodrigo Koblitz <
rodrigokobl...@gmail.com>:
> Hi everyone,
>
> I'm new to SymPy and I'm probably missing something basic. I
For a simple case like assuming that b > -1 you can use a change of variables:
bp1 = Symbol('(b+1)', positive=True)
expr = expr.subs(b, bp1-1)
--
Oscar
On Sat, 27 Jul 2024 at 17:08, Pierre H wrote:
>
> Actually, thinking a bit more, I can get away with the assumption that
t necessarily
hold. From first principles SymPy defines x^y as being exp(log(x)*y)
where log should be understood as having a branch cut on the negative
reals so that log(x) = log(abs(x)) + I*arg(x) and arg(x) is in
(-pi,pi]. This branch cut determines when identities like (1/a)^x =
1/a^x will hold.
which topologies would be
computationally useful?
Oscar
On Sat, 27 Jul 2024 at 10:20, Robert Simione
wrote:
>
> Hello all,
> I was reading the Sympy documentation on Sets which is under the Logic
> section of the documentation, but a LOT the properties discussed like
> boundaries a
though.
Somehow getting the wrong roots then results in having four rather
than two terms in the solution. There is a bug in the
nth_linear_constant_coefficient solver handling the roots somewhere.
--
Oscar
On Sun, 21 Jul 2024 at 10:33, Tony K B wrote:
>
> got wrong answer for this ODE
ports of regressions will come just because
there was such a big gap of time between 1.12 and 1.13 meaning that
many big changes have accumulated between the releases without being
as widely tested by users and downstream libraries. I expect that
there will be several 1.13.x bugfix releases.
Osca
).removeO().as_poly(x).all_coeffs()[::-1]
Out[7]: [0, 1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880]
--
Oscar
On Tue, 9 Jul 2024 at 10:41, emanuel.c...@gmail.com
wrote:
>
> Doesn't matter :
>
> ```
> >>> from sympy import *
> >>> x=symbols("x")
&g
e.
Thanks to everyone who contributed to this release!
- Daan Koning (he/him)*
- Anton Akhmerov
- Han Wei Ang*
- anutosh491
- Isidora Araya*
- atharvParlikar*
- Oscar Benjamin
- Evandro Bernardes
- Anurag Bhat
- Francesco Bonazzi
- Augusto Borges*
- João Bravo*
- Sam Brockie
- Pontus von Brömssen
-
represent points in the
non-full-dimensional cells.
--
Oscar
On Tue, 2 Jul 2024 at 23:22, Maaz Muhammad wrote:
> Hi all! I'm a PhD student at the University of Toronto, working on
> polynomials (optimization, algorithms, and applications).
>
> As part of my work, I needed to
On Tue, 2 Jul 2024 at 17:29, Aaron Meurer wrote:
>
> On Tue, Jul 2, 2024 at 5:09 AM Oscar Benjamin
> wrote:
> >
> > On Mon, 1 Jul 2024 at 18:04, Aaron Meurer wrote:
> > >
> > > On Mon, Jul 1, 2024 at 4:38 AM Oscar Benjamin
> > >
On Tue, 2 Jul 2024 at 12:09, Oscar Benjamin wrote:
>
> If sympy uses python-flint 0.n to say 0.n+3 then python-flint can test
> older versions of sympy for as long as they are "supported" and sympy
> can just not use newer versions. Then we can say that sympy now
> accep
On Mon, 1 Jul 2024 at 18:04, Aaron Meurer wrote:
>
> On Mon, Jul 1, 2024 at 4:38 AM Oscar Benjamin
> wrote:
> >
> > I think my preference is:
> >
> > 1. Use python-flint >= 0.6.0, < 1.0 automatically.
> > 2. Don't use python-flint < 0.5.0 or &
ython-flint regardless of the version.
4. Keep future versions of python-flint compatible with SymPy 1.13
until python-flint 1.0.
5. Once SymPy 1.13 is released add a job in python-flint CI to test
against SymPy 1.13.
Does anyone have any views on this?
As far as I know this is the only outstanding
y are available.
Oscar
On Friday 28 June 2024 at 17:35:48 UTC+1 Kaj Malm wrote:
> Dear Oscar Benjamin,
>
>
> I hope this mail will find you although I do not know your personal
> address.
>
>
> I was the first doctoral student and later a colleague of Kalevi Suominen
>
Hi Anton,
I was hoping that others might express their opinions about this.
SPEC 0 seems fine to me.
Oscar
On Wed, 19 Jun 2024 at 13:35, Anton Akhmerov wrote:
>
> Thank you Oscar for taking action. Does that mean that sympy can endorse
> spec-0? Or that will it do so starting
their names contributed a
patch for the first time for this release; 100 people contributed
for the first time for this release.
Thanks to everyone who contributed to this release!
- Daan Koning (he/him)*
- Anton Akhmerov
- Han Wei Ang*
- anutosh491
- Isidora Araya*
- atharvParlikar*
- Oscar Ben
On Tue, 4 Jun 2024 at 21:10, Oscar Benjamin wrote:
>
> Personally I am in favour of going with SPEC 0 in coordination with
> the rest of the scientific Python ecosystem. I don't want to cause any
> immediate problems for Sage though so I would be reluctant to make a
> last min
em. I don't want to cause any
immediate problems for Sage though so I would be reluctant to make a
last minute decision to drop two Python versions right now for 1.13.
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/sympy/sympy/issues/26221
https://github.com/sympy/sympy/issues/26318
Some of the others I will punt on for now because the release has been
delayed long enough.
If anyone knows of anything else that should be fixed urgently in a
1.13 release then please say so either here or on GitHub.
Oscar
uld be
> great to get some pointers on how to import
> the function in the code.
The function is not part of SymPy. The code for the function is in the
issue I linked:
https://github.com/sympy/sympy/issues/26177
You would have to copy the code from there to use it.
--
Oscar
--
You rece
ool itself gives separate intervals.
See the function _find_poly_sign_univariate in
https://github.com/sympy/sympy/issues/26177
That function finds points where a univariate polynomial is nonzero
that separate all roots.
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the root lies in the interior of the interval. In other words what is
returned is a set of individual rational points and open intervals on
the real line. An open interval might be bounded by one of the
rational points but they do not intersect because the interval does
not contain its boundary.
You can pass factor as the third argument to collect like collect(rhs,
ρ, factor). Then the collected coefficients will be factored.
On Tue, 21 May 2024 at 21:27, Don Burgess wrote:
>
> Thank you very much for your helpful reply.
>
> Since I was using collect, I used the following code:
>
> ```py
I don't know enough about this topic bur there is also galgebra which
is a library that depends on SymPy:
https://galgebra.readthedocs.io/en/latest/tutorials/algebra.html
Does that do what is needed?
On Sun, 28 Apr 2024 at 09:37, 'Carsten' via sympy
wrote:
>
> HI,
>
> I almost do not follow this
Hi Jake,
I would be happy to meet (online) with you and your supervisor at some
point if that helps.
Oscar
On Tue, 12 Mar 2024 at 11:49, Jake Moss wrote:
>
> Thank you for such a detailed reply! Seems like there will be plenty for me
> to do.
>
> I'll reach out to Davi
ith SymPy development as a retired Maths
professor. Given his breadth of knowledge I had always assumed that
his background was something like this although I never thought to go
and look it up.
Oscar
On Sun, 10 Mar 2024 at 16:59, Jason Moore wrote:
>
> Hi Oscar,
>
> That is very sad to
ut the status of the existing
> integrations of Flint and recommendations from Oscar Benjamin's blog posts.
That would be fantastic.
> I've seen that SymPy is now able to use Flint as the ground type for dense
> univariate polynomials from PR #25722. Is there a similar PR for
vi to share
their thoughts and memories here.
Oscar
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To view
s of
SymPy should I try to support within my package that has SymPy as a
dependency" because I am not sure what the benefit would be of
supporting more than 1 version of SymPy.
Is there a reason that someone would need to combine a newer version
of your package with an older version of SymPy?
ith. There is no way to put version constraints on
optional dependencies in pip/PyPI land.
Oscar
On Sun, 10 Mar 2024 at 14:24, Anton Akhmerov wrote:
>
> Hi all,
>
> There is now SPEC 0, a SciPy-community-wide standard for versions of
> different packages that developers should aim
You don't need to worry about those errors. They are not related to
the changes in your PR and any PR can be merged even if those tests
fail. It looks like those same errors are showing on all PRs right
now.
The errors that you see are in the numpy nightly test job. This is a
job that runs the sym
True
In [54]: is_root_of_unity(sqrt(5))
Out[54]: False
Oscar
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T
We should just remove slotscheck from CI. It isn't useful enough to
justify any CI maintenance burden.
--
Oscar
On Tue, 13 Feb 2024 at 13:20, Shishir Kushwaha
wrote:
>
> I have opened a PR which potentially fixes the issue , however the warnign
> about the deprecated modules
that it is easy for someone else to read
your comment and then confirm that it should be closed.
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ting the code and opening
the PR without doing that checking leaves all of the work to the
reviewer. Anyone else could review it though by doing that checking.
--
Oscar
On Tue, 6 Feb 2024 at 07:59, Jason Moore wrote:
>
> Note that we get lots of PRs at this time because we require GSoC app
review old issues then I suggest using the issue labels to focus on
a particular area of the code base like "integrals" or "solvers" etc.
This sort of work is actually much more helpful to the project than
opening pull requests for "easy to fix" issues.
--
Oscar
On Fri, 2 Feb 2024 at 22:36, Aaron Meurer wrote:
>
> On Fri, Feb 2, 2024 at 3:28 PM Oscar Benjamin
> wrote:
> >
> > Without making python-flint a hard dependency there is no way to
> > specify what versions should be acceptable in an install so I think
> > th
It's hard to tell from a screenshot. Do you have a link to the PR?
On Fri, 2 Feb 2024 at 17:36, Shishir Kushwaha
wrote:
>
> Do I need to add my details everytime to thee .mailmap file when making a PR
> , I did it in my first PR as mentioned in the documentation but when creating
> a new comitt
On Fri, 2 Feb 2024 at 21:52, Aaron Meurer wrote:
>
> On Fri, Feb 2, 2024 at 9:41 AM Oscar Benjamin
> wrote:
> >
> > I think that probably the right way to do this is just for SymPy to
> > use python-flint by default if it is installed but with an almost
> > exact
on constraint. The environment variable could
still be used to override the version check but the default if no
environment variable is set should just be to use python-flint but
only the expected 0.6.x versions.
Does anyone have any thoughts on how exactly to do this?
--
Oscar
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many other features in Flint not yet exposed in
python-flint. Contributions are welcome from anyone who would like to
see more added!
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is worse than useless:
we waste people's time by even suggesting that it is a reasonable
project.
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to
project should not be listed.
We should not roll anything over from previous years automatically in
the way that is currently done either in terms of the list of mentors
or the list of projects.
--
Oscar
On Wed, 24 Jan 2024 at 22:40, Aaron Meurer wrote:
>
> Hi Oscar.
>
> I agree wi
me ago by people who are no
longer around and likely have no intention of mentoring any projects
or updating the ideas page.
Oscar
On Wed, 24 Jan 2024 at 18:49, Aaron Meurer wrote:
>
> It is time again for us to apply to Google to be a GSoC mentoring org.
>
> I need help updating the G
much interpreter
overhead in both cases that the real underlying operation does not
really take a majority of the runtime. I think that probably tends to shift
what data structures seem fastest in the context of SymPy when compared to
implementations of the same operations in other languages.
-
than working on the polys GCD code though. There are some 300
open issues with the polys tag if you are interested specifically in
polynomials:
https://github.com/sympy/sympy/issues?q=is%3Aissue+is%3Aopen+label%3Apolys+
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that are labelled as "easy to fix"
(although that label is not always accurate).
Oscar
On Sat, 13 Jan 2024 at 12:06, 'Shishir Kushwaha 5-Yr IDD: Mathematical
Sci.s, IIT(BHU)' via sympy wrote:
>
> My greetings to all the respected contributors and admins .
>
> I am S
I think what you mean here is more like "variables" rather than
"symbols". You might want to try using Spyder which can show you the
values of all of the Python variables you have defined.
On Thu, 7 Dec 2023 at 17:16, Mario Lemelin wrote:
>
> If I had one functionality to have in Sympy, it would
On Mon, 6 Nov 2023 at 11:46, Oscar Benjamin wrote:
>
> I don't anticipate any changes to the LLL code between now and the
> 1.13 release except that I might try to add the lll method to Matrix
> so that it is not necessary to convert to DomainMatrix explicitly.
I jus
On Mon, 6 Nov 2023 at 03:22, T-Rex wrote:
>
> Thanks @oscar! I didn't think I would get a reply from the blog's owner :-)
>
> Re setting of the environment variable SYMPY_GROUND_TYPES=flint: (1) Would
> that be in conflict with other parts of sympy/numpy/scipy?
ent variable SYMPY_GROUND_TYPES=flint then the
DomainMatrix.lll method will automatically use Flint which is a lot
faster for this operation.
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also very likely that there will be some work soon on supporting
Flint's generic ring types in python-flint.
There are many other features in Flint not yet exposed in
python-flint. Contributions are welcome from anyone who would like to
see more added!
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Oscar
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hould include some
meaningful text in the message.
Oscar
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To view this discus
⎬ ∪ ⎨2⋅n⋅π + ─ │ n ∊ ℤ⎬
⎩ 6 │ ⎭ ⎩6 │ ⎭
The problem is that solveset solves this in an overly complicated way
using complex numbers even if the domain is reals. Then a small
rounding error makes it look like the solutions are not real.
--
Oscar
On Thu, 5 Oct 2023 at 16
On Sun, 10 Sept 2023 at 16:37, David Bailey wrote:
>
> On 07/09/2023 00:07, Oscar Benjamin wrote:
> > Hi all,
> >
> > I have a new blog post following the last one:
> > https://oscarbenjamin.github.io/blog/czi/post2.html
> >
> > This one discusses SymPy&
On Thu, 7 Sept 2023 at 11:14, wrote:
>
> Dear Oscar,
>
> While 99% is way above my head (I studied engineering 40+ years ago), it is
> fascinating reading!
> I had no idea, how much 'math' was in sympy.
>
> In your post you write:
>
> if gmpy2 is instal
Hi all,
I have a new blog post following the last one:
https://oscarbenjamin.github.io/blog/czi/post2.html
This one discusses SymPy's polynomial system, improvements that can be
made and in particular how to make use of python-flint to speed up
polynomial operations in SymPy.
--
Oscar
--
at is not confusing. Many users are already
confused about the distinction between Python types like int and SymPy
types like Integer and then also things like NumPy arrays etc so
adding multiple types of SymPy expression risks confounding that.
--
Oscar
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rithm within the algebra subsystem rather than
the symbolic subsystem.
Possibly the limiting factor for SymPy implementing heurisch in the
ideal way right now is support for symbolic algebraic extensions like
Q(x)[sqrt(x)] within the domain system although polys.agca has
FiniteMonogenicExtension that cou
spam for me a lot of the time).
I don't understand what you are asking or suggesting but feel free to
explain in more detail.
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linear equations. Is exact vs approximate the main
distinction here between what hyint does and what heurisch does?
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On Fri, 25 Aug 2023 at 18:38, Ralf Schlatterbeck wrote:
>
> Hello Oscar,
> First, thanks for the very quick answer!
>
> On Fri, Aug 25, 2023 at 03:19:31PM +0100, Oscar Benjamin wrote:
> > >
> > > Trying to solve this with the 'LU' solver produces a real
te much more quickly than GJ.
Installing gmpy2 can help with timings for DomainMatrix in some cases
(although probably does not make much difference in this example). In
future it will be possible to speed this up a lot using python-flint.
Specifically python-flint will provide fast multiplication and gcd f
On Sat, 19 Aug 2023 at 22:52, David Bailey wrote:
>
> On 16/08/2023 16:13, Oscar Benjamin wrote:
> > Hi all,
> >
> > I have written a blog post about recent work on SymPy and what I think
> > should be future development plans:
> >
> > https://o
high level what
I think should be done going forwards. Subsequent posts will describe
specific components in more detail.
Oscar
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t out (and explain it to everyone) then I am sure
that we can put it to good use!
Oscar
On Wed, 5 Jul 2023 at 17:36, Aaron Meurer wrote:
>
> Hi everyone.
>
> As many of you may know, I work at Quansight, a company that works
> with and funds a lot of open source work in the Python ecosys
way to fix it depends on how your local clone is
set up as well as how you use git (I am not sure how many contributors
actually use git from the command line now that various editors can do
it for you).
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re of
groups 1 and 4 when it comes up.
In any case main is becoming widely used and if it is going to be
standard practice in some sense then I think it makes sense to follow
that.
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To
On Mon, 3 Jul 2023 at 00:16, David Bailey wrote:
>
> On 02/07/2023 23:44, Oscar Benjamin wrote:
> > On Sun, 2 Jul 2023 at 23:06, David Bailey wrote:
> >> Dear Group,
> >>
> >> If I want to enter m+1/2, I define m as a symbol and write:
> >>
versions of SymPy Live would reinterpret 1/3 as
rational division in a similar way but that does not seem to be true
of the current version (maybe that was missed in the move to pyodide):
https://live.sympy.org/
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nd exactly what you are asking for but if you have a
sequence a0, a1, a2, ... and the generating function is
f(x) = a0 + a1*x + a2*x**2 + ...
Then if you have a formula f_expr for f(x) you can find a formula for ai with
f_expr.diff(x, i).subs(x, 0)/factorial(i)
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;> a = i**(-2*i), (-i)**(-2*i), ((-sqrt(3) - i)/2)**(-2*i), ((sqrt(3) -
>>> i)/2)**(-2*i)
>>> [ai.rewrite(exp) for ai in a]
[exp(pi), exp(-pi), exp(-5*pi/3), exp(-pi/3)]
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On Thu, 11 May 2023 at 19:46, David Bailey wrote:
>
> Many thanks Oscar for this release!
>
> Since it has been some time since 1.11 (or indeed 1.12rc1) was released,
> I guess there were some deep and messy problems to be resolved!
>
> It installed for me and runs my code.
&
e for this release; 42 people contributed
for the first time for this release.
Thanks to everyone who contributed to this release!
- Jyn Spring 琴春*
- anutosh491
- Ayush Aryan*
- Blair Azzopardi
- Stefan Behnle*
- Oscar Benjamin
- Evandro Bernardes*
- Anurag Bhat
- Francesco Bonazzi
- Sam Brockie*
- P
There is now SymPy Beta:
https://sympy-beta.vercel.app/
I'm not sure that we want to work on improving SymPy Gamma (rather
than improving SymPy Beta instead).
--
Oscar
On Tue, 4 Apr 2023 at 19:53, Tilo RC wrote:
>
> Hi Aman. I am another GSoC applicant and I wanted to let you know
On Tue, 4 Apr 2023 at 08:33, Aaron Meurer wrote:
>
> On Sun, Apr 2, 2023 at 10:29 AM Oscar Benjamin
> wrote:
> >
> >
> > I have figured out though a way that I could automate updates for
> > requirements.txt files using the create-pull-request action and
> &g
On Sun, 2 Apr 2023 at 02:19, Aaron Meurer wrote:
>
> On Sat, Apr 1, 2023 at 5:04 AM Oscar Benjamin
> wrote:
> >
> > On Sat, 1 Apr 2023 at 06:36, Aaron Meurer wrote:
> > >
> > > On Fri, Mar 31, 2023 at 10:33 PM Jason Moore wrote:
> > > >
>
h and open a PR.
I think that making a full bot to do this is a bunch of work though so
it is better if there is a ready made action that we can use.
My suggestion is just that we try using dependabot for some things and
see how it pans out.
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rush in a fix because of broken CI).
Does anyone have any views on enabling dependabot on the SymPy repo
(or some similar alternative)?
--
Oscar
On Tue, 28 Mar 2023 at 22:53, Aaron Meurer wrote:
>
> That's what I was worried about too. If the bot pushes a commit, then the PR
> auth
n consider implementing another algorithm
depending on how much time there is left.
Oscar
On Fri, 31 Mar 2023 at 10:27, ABHISHEK PATIDAR <2311abhip...@gmail.com> wrote:
>
> Hi there,
>
> I'm Abhishek Patidar. I am interested in working on the Improving Polynomial
> GCDs
and add the commit, but it is
>> the author's choice to do so.
I don't think anything exists that works like that. Of course if the
fixes can be applied automatically then you could just run pre-commit
to apply them locally.
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There already is mathics which is a Wolfram Language interpreter that
is based on SymPy. It would seem a bit odd to create a new one.
On Fri, 24 Mar 2023 at 19:48, Aaron Meurer wrote:
>
> I believe the primary function of this project is to make it easier to
> integrate the RUBI integrator into S
recommended me, however they seem like undoable at the moment.
Take a look at the issues with the polys tag:
https://github.com/sympy/sympy/issues?q=is%3Aissue+is%3Aopen+label%3Apolys
This issue for example needs someone to understand the possibilities
and improve the documentation:
https://git
23. I looked in to the
> resources to provided for the project and I'm now looking for a mentor to
> disuss / validate different ideas. Any help is welcome.
Hi Mohit,
Feel free to discuss ideas around this project here on the mailing list.
Oscar
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test/
Integrating that improved plotting module back into SymPy would make a
great project. There are some (I think small) difficulties in doing
this in a way that is backwards compatible so it needs a bit of work:
https://github.com/sympy/sympy/issues/23036
--
Oscar
>
> I would appre
On Fri, 17 Mar 2023 at 20:39, Aaron Meurer wrote:
>
> On Sun, Mar 12, 2023 at 3:04 PM Atahan Haznedar
> wrote:
> >
> > Hello Oscar,
> >
> > Sorry for the late reply, after seeing the post you have made, I can pretty
> > much can say that I am really e
ng 琴春*
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- P
e systems polynomial equations.
--
Oscar
On Sat, 4 Mar 2023 at 07:01, Atahan Haznedar wrote:
>
> Hello everyone, I am Atahan Haznedar from Turkey. Even though Turkish is my
> native language, I am fluent with English. I am a third year Mathematics
> undergraduate in Bogazici University in I
this works.
> Learn why evalf(5) works. The documentation at
> https://docs.sympy.org/latest/modules/evalf.html
> doesn't make it clear to me what the possible arguments are and what they
> mean.
> Find documentation for sorted and key=degree.
> I searched for sympy degree and fou
It should be possible to set order=None with init_printing and that
does work for the pretty printer but not for string printing (i.e.
print(expr) or str(expr)).
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Oscar
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On Fri, 3 Mar 2023 at 23:29, Oscar Benjamin wrote:
>
> On Fri, 3 Mar 2023 at 21:32, David Bailey wrote:
> >
> > Oscar,
> >
> > The release of SymPy 1.12 seemed to be very close, but nothing has
> > happened!
> >
> > It doesn't really
On Fri, 3 Mar 2023 at 21:32, David Bailey wrote:
>
> Oscar,
>
> The release of SymPy 1.12 seemed to be very close, but nothing has
> happened!
>
> It doesn't really matter to me, but it would be interesting to explore
> whatever is new.
Hi David,
I should hav
alculus with big-O objects is still questionable but SymPy currently
has the behaviour you expect for integration and differentiation.
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Oscar
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ckle.dump(varX, f)
> f.close()
> The error is "Can't pickle q1: attribute lookup q1 on __main__ failed"
You need to call the variable the same name as the function:
q1 = Function('q1')
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Oscar
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On Thu, 26 Jan 2023 at 20:28, David Bailey wrote:
>
> On 26/01/2023 12:56, Oscar Benjamin wrote:
> > I've opened an issue to track releasing SymPy 1.12:
> > https://github.com/sympy/sympy/issues/24601
> >
> I went ahead and installed what I thought would
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