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#376 2013-03-30 14:12:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

Okay, I am sorry if I gave you that impression. I have been reading everything you said and have not intentionally put anything other than what I think in my replies. My apology if I seemed argumentative, I was not trying to be.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#377 2013-03-30 14:15:32

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

No, no. There is really no need to apologize. Maybe tomorrow, when I log on with the laptop, I will have a better chance of explaining what I want.

You do not seem argumentative. Just a bit stubborn. But, then again, I am no better.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#378 2013-03-30 14:28:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

Not stubborn, passionate about numerical methods.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#379 2013-03-30 14:29:16

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

Well, I did not attack it as a numerical method.

But let's leave that for tomorrow.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#380 2013-03-31 10:17:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

Hmmm, it is tomorrow and I do not see ole anonimnystefy here.

So, I will argue with myself:

bobbym: I think the PSLQ is great.

bobbym: It sure is, it was voted one of the top 10 algorithms of the 20th century.

bobbym: I did not know that...

bobbym: Possibly it was voted number one.

bobbym: I will tell anonimnystefy when I see him.

bobbym: You do that, he might listen to you.

more to follow...


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#381 2013-03-31 10:30:42

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

You have not been here whole day while I was on the laptop.

Anyway, I think you have the wrong idea. I have nothibg against PSLQ. I am kust saying that it is not a method for solving integrals, because it is always paired up with some way of numerical integration.

On the other hand, I do think that contour integration is a method for solving integrals, because to solve an integral with it you do not need anything besides it submethods.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Online

#382 2013-03-31 10:32:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

That is you must admit a strange distinction about why one is and why another one is not.

Let me say that coupled together PSLQ and numerical integration will do a heck of a lot more integrals than contour integration.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#383 2013-03-31 10:36:47

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

It is not strange. Look at it this way: contour integration is a method for solving integrals, but solely finding the residues isn't.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#384 2013-03-31 10:41:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

contour integration is a method for solving integrals, but solely finding the residues isn't

Numerical integration is a method for solving integrals but using the PSLQ isn't.

Sounds the same as your post!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#385 2013-03-31 10:58:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

There you go!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#386 2013-03-31 11:01:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

But using both is a powerful method to solve definite integrals.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#387 2013-03-31 11:03:10

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

That is true.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Online

#388 2013-03-31 11:06:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

So did you do one with your PSLQ?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#389 2013-03-31 11:10:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

I haven't yet. I explored the world of Mathematica.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Online

#390 2013-03-31 11:11:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

How did you do that?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#391 2013-03-31 11:20:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

Well, I searched for different things.

I found an implementation of a random walk, for example.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Online

#392 2013-03-31 11:24:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

A random walk can be done in M extremely easily. You use the accumulate function.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#393 2013-03-31 11:26:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

I think he used NestList.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Online

#394 2013-03-31 11:27:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

M has a 1000 ways to do everything and that is its greatest strength and its biggest weakness.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#395 2013-03-31 11:33:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

Why is it a weakness?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Online

#396 2013-03-31 11:41:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

The learning curve is not very steep for ordinary humans like myself.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#397 2013-03-31 11:47:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

Hm. I'm not sure if that is a weakness on M's side or the user side.

Anyway, have you ran a simulation for the first two parts of the rat problem?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Online

#398 2013-03-31 12:03:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

Yes, and it is not getting Agnishom's answer for c) so I would like to check it again before showing it.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#399 2013-03-31 12:11:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,820

Re: PSLQ and LLL?

Why not post it anyway? If there is an error somewhere, there are better chances of spotting it.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Online

#400 2013-03-31 12:17:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,508

Re: PSLQ and LLL?

When 2 answers do not agree that worries me a lot. Just a wee bit more tabasco!

Of course the user is weak, it is up to the package to help him out. Not everyone is a Newton or reptile spawned. Anyway 6000 commands and 500 added on each new release can be daunting.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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