The problem chosen seems to be
integrate((16*x^3-42*x^2+2*x)/sqrt(-16*x^8+112*x^7-204*x^6+28*x^5-x^4+1),x)
The integrand is of the form dy/sqrt(1-y^2)
and so the integral is arcsin(y).
An algorithm to look for this kind of pattern (in general) would not be
difficult to write, although it does
On Thu, Dec 26, 2019 at 11:54 AM Brent W. Baccala wrote:
>
>
> I know the Risch algorithm fairly well.
>
> I made two screencast videos describing how to use Axiom or Sage to simplify
> one of the integrals used in the Facebook paper.
>
> Quick summary - Axiom works quite well. Sage can't do it
I know the Risch algorithm fairly well.
I made two screencast videos describing how to use Axiom or Sage to
simplify one of the integrals used in the Facebook paper.
Quick summary - Axiom works quite well. Sage can't do it in one step, but
the new function field features in Sage 9 allow the i
On Wed, Dec 18, 2019 at 6:05 PM E. Madison Bray wrote:
>
> On Wed, Dec 18, 2019 at 6:39 AM rjf wrote:
> >
> > I was trying to come up with a simple example of how this integration
> > program claim
> > was bogus. Here it is.
> >
> > Take one of your favorite prime-testing programs and generate
See, for example, Rubi, or my earlier project Tilu, for programs that
> absorbed,
in some sense learning from tables of integrals.
This is not classical machine learning, because the objects being learned
are
patterns. So the result for sin(x)dx works for sin(u)du, as a trivial
pattern
matc
On Wed, Dec 18, 2019 at 6:39 AM rjf wrote:
>
> I was trying to come up with a simple example of how this integration program
> claim
> was bogus. Here it is.
>
> Take one of your favorite prime-testing programs and generate
> a list of 10,000 Largish Primes. I don't know how large, but
> say 5
I was trying to come up with a simple example of how this integration
program claim
was bogus. Here it is.
Take one of your favorite prime-testing programs and generate
a list of 10,000 Largish Primes. I don't know how large, but
say 50 decimal digits or more.
Make 10^8 factorization problem
I was unclear. Davis disagrees with Lample and Charton in their claim of
neural nets being somehow superior to established CAS.
(And yes, the review is by Davis, not Lample.)
On Tuesday, December 17, 2019 at 4:21:07 PM UTC-8, rjf wrote:
>
> disagrees with me? or Emmanuel?
> Lample's abstract (
oops, the review is by Davis; the paper is by Lample and Charton, both of
Facebook.
On Tuesday, December 17, 2019 at 4:21:07 PM UTC-8, rjf wrote:
>
> disagrees with me? or Emmanuel?
> Lample's abstract (of the review) concluded with
>
> The claim that this outperforms Mathematica on symbolic i
disagrees with me? or Emmanuel?
Lample's abstract (of the review) concluded with
The claim that this outperforms Mathematica on symbolic integration needs
to be very much qualified.
I glanced at the full review and I don't see that I disagree with it.
Generating 80 million randomly generated e
You could e-mail the authors, now that you have names and addresses.
Maybe they'd part with source.
On Monday, December 16, 2019 at 7:39:11 AM UTC-8, Dima Pasechnik wrote:
>
>
>
> On Mon, 16 Dec 2019, 15:14 Richard_L, >
> wrote:
>
>> Apparently, someone disagrees. See Ernest Davis's posting to
I tested (some of?) the integrals from Table 7 with FriCAS, without any
(bad) surprises.
Am Montag, 16. Dezember 2019 16:39:11 UTC+1 schrieb Dima Pasechnik:
>
>
>
> On Mon, 16 Dec 2019, 15:14 Richard_L, >
> wrote:
>
>> Apparently, someone disagrees. See Ernest Lample's posting to the arXiv:
>>
On Mon, 16 Dec 2019, 15:14 Richard_L, wrote:
> Apparently, someone disagrees. See Ernest Lample's posting to the arXiv:
> https://arxiv.org/abs/1912.05752
>
> On Friday, September 27, 2019 at 8:06:31 AM UTC-7, Dima Pasechnik wrote:
>>
>> https://openreview.net/pdf?id=S1eZYeHFDS
>>
>> I wish they
Apparently, someone disagrees. See Ernest Lample's posting to the arXiv:
https://arxiv.org/abs/1912.05752
On Friday, September 27, 2019 at 8:06:31 AM UTC-7, Dima Pasechnik wrote:
>
> https://openreview.net/pdf?id=S1eZYeHFDS
>
> I wish they had code available...
>
--
You received this message
I am not aware specifically of the methods used in FriCAS.
It is possible, I suppose, that given an expression it immediately
tries to find an appropriate differential field and begins some version
of the Risch "algorithm" (which actually fails to be an algorithm
for various reasons), and doesn't
>
>
>> Are you saying that FriCAS is the only CAS which doesn't do this?
>>
>
> AFAICT, FriCAS dos this also...
>
> I don't think so - are you sure? Neither do I not know the Risch
algorithm nor FriCAS' implementation of it too well, but I would have
thought that FriCAS doesn't do pattern mat
!
What you describe
- is doable, and
- is outright academic fraud...
I doubt somehow that the authors would be dumb enough to risk that.
"Never assign to human ill will what can be explained by human stupidity".
(Napoleon Bonaparte, IIRC).
However, I agree that using an external
Hi, Martin !
Le lundi 7 octobre 2019 11:30:17 UTC+2, Martin R a écrit :
>
>
> Here's the trick. S' will, with very high probability, be a sum. Say
>> s1+s2+s3.
>> A CAS will usually try to compute integrate(s1,x) + integrate(s2,x)+
>> integrate(s3,x).
>> That's the way integral tables work too
> Here's the trick. S' will, with very high probability, be a sum. Say
> s1+s2+s3.
> A CAS will usually try to compute integrate(s1,x) + integrate(s2,x)+
> integrate(s3,x).
> That's the way integral tables work too.
>
> Are you saying that FriCAS is the only CAS which doesn't do this?
Marti
If they were interested in a fair comparison they would use a test set from
(for example) Rubi or one of the CAS.
My guess is that they did this:
1. generate a random expression S favoring + and * in the tree.
2. differentiate S to get S'
3. "learn" the integral of S'.
Here's the trick. S' w
Le mercredi 2 octobre 2019 01:48:15 UTC+2, rjf a écrit :
>
> I think that if you read the paper you would not expect it to compete with
> a CAS
> except on its made-up artificial testset.
>
Could you amplify ?
> RJF
>
>
> On Monday, September 30, 2019 at 10:57:44 AM UTC-4, Martin R wrote:
>>
I think that if you read the paper you would not expect it to compete with
a CAS
except on its made-up artificial testset.
RJF
On Monday, September 30, 2019 at 10:57:44 AM UTC-4, Martin R wrote:
>
> Actually, I think it would be even more interesting to compare with
> FriCAS, because FriCAS has
Actually, I think it would be even more interesting to compare with FriCAS,
because FriCAS has the most complete implementation of the Risch algorithm
and does not at all rely on pattern matching.
Martin
Am Sonntag, 29. September 2019 15:00:01 UTC+2 schrieb mmarco:
>
> I would be very interest
I would be very interested in comparing their results with RUBI.
El viernes, 27 de septiembre de 2019, 21:53:00 (UTC+2), Eric Gourgoulhon
escribió:
>
> Thanks for sharing!
> This looks very promising. I hope we have it in Sage some day.
>
> Eric.
>
> Le vendredi 27 septembre 2019 17:06:31 UTC+2,
Thanks for sharing!
This looks very promising. I hope we have it in Sage some day.
Eric.
Le vendredi 27 septembre 2019 17:06:31 UTC+2, Dima Pasechnik a écrit :
>
> https://openreview.net/pdf?id=S1eZYeHFDS
>
> I wish they had code available...
>
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