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#301 2012-07-14 06:30:23

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

I am quoting here for the sake of easier access tome.

pslq[l_,dig_]:=Module[{a},
     a=IdentityMatrix[Length[l]];
     a=Append[a,10^dig*N[l,dig]];
     a=Transpose[a];
     a=Rationalize[a,10^-dig];
     a=LatticeReduce[a];
     Take[a,All,{1,Length[l]}]
     ];

I will now do the next lines. Then we will have to find a Lattice Reduce function for Maxima.


“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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#302 2012-07-14 06:33:06

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

Okay, work on them, I have to do a chore be back soon.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#303 2012-07-14 06:37:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

What does the Rationalize do, again?


“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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#304 2012-07-14 08:15:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

Turns a decimal into the closest fraction.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#305 2012-07-14 08:28:02

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

I figured that out and tried writing a Maxima function, but it is not working:

ratnum(a,dig) := round(float(a)*(10^dig))/10^dig;

“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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#306 2012-07-14 08:32:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

I thought maxima had a similar command.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#307 2012-07-14 08:42:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

It doesn't. Or at least I don't know about it. My function returns good number for rationals but not reals.


“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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#308 2012-07-14 08:45:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

Hold on, I am installing the newest Geogebra. I will see what I can find.

Rationalize[.123456] yields


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#309 2012-07-14 08:54:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

But what about a real number?


“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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#310 2012-07-14 08:54:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

What real number?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#311 2012-07-14 08:56:40

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

e 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

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#312 2012-07-14 08:57:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

Rationalize[2.71818]


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#313 2012-07-14 08:58:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

That is not e.


“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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#314 2012-07-14 08:59:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

Oh boy. Are you serious?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#315 2012-07-14 09:02:38

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

Why does your function have another parameter?


“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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#316 2012-07-14 09:04:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

One thing at a time. We need to stop right here.


What is e, I mean the symbol e? What can you tell me about it? Give me everything you got, it is important.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#317 2012-07-14 09:05:45

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

Last edited by anonimnystefy (2012-07-14 09:05:59)


“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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#318 2012-07-14 09:13:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

Nope!

e is the symbol for that. It was invented by Euler. e stands for

That little symbol has an infinite amount of digits. It represents a transcendental number. What does that mean?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#319 2012-07-14 09:14:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

It is not a root of an equation with rational coefficients?


“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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#320 2012-07-14 09:18:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

No, not exactly what we need here.

A transcendental number has some properties.

1) It is irrational ( can't be expressed in the reduced form a / b, where a,b are integers)

2) It is not the root of any polynomial (loose definition, you know the type of poly I mean).

So now asking M or M or M or M to evaluate
Rationalize[e] is just plumb kaboobly doo.

By rule 1 it is impossible. We can rationalize a truncated decimal approximation of e. Same thing with π. Those symbols are compact representations of something else.

It is wise that you skeddadled out of the forum because I feel a rant coming on.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#321 2012-07-14 10:28:00

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

Ok, what next?


“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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#322 2012-07-14 10:39:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

I gave you the Rationalize command. So what is next?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#323 2012-07-14 12:15:35

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

Arghh, the troubling Lattice Reduce. We will need to find a way to do it in Maxima. Is there a code for tthe Lattice Reduce function?


“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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#324 2012-07-14 13:54:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,882

Re: PSLQ and LLL?

Is the rest of the program done?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#325 2012-07-14 14:08:48

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,605

Re: PSLQ and LLL?

No. Only up to the Lattice Reduce.


“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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