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#201 2012-04-11 23:52:34

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

You didn't wtite it like that before!Here's the new output:

{{24, 0, 0, 120, 0, 140, 0, -15, 0, -236},
{-1020, -430, -77, 188, -802, -515, -743, -339, 202, -203},
{-367, -461, -955, 317, 400, -72, 603, -923, 229, 286},
{40, 509, -464, -705, 1310, -805, -76, -647, 229, -769},
{1320, -100, 177, 585, -1344, -742, 188, 50, 8, 74},
{-436, 491, -1733, -347, -118, 380, 282, 505, -200, -28},
{419, -62, -756, -270, 1352, 97, -1105, 1090, -248, -102},
{-222, 295, 774, -878, -429, 788, -669, -966, 355, 0},
{-19, -1712, 637, -920, -43, -34, 34, 628, -199, -609}}

Last edited by anonimnystefy (2012-04-12 00:04:02)


“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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#202 2012-04-12 00:06:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

An extra character got added!

This is correct.

test[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]}]];

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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#203 2012-04-12 00:10:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

{{24, 0, 0, 120, 0, 140, 0, -15, 0},
{-1020, -430, -77, 188, -802, -515, -743, -339, 202},
{-367, -461, -955, 317, 400, -72, 603, -923, 229},
{40, 509, -464, -705, 1310, -805, -76, -647, 229},
{1320, -100, 177, 585, -1344, -742, 188, 50, 8},
{-436, 491, -1733, -347, -118, 380, 282, 505, -200},
{419, -62, -756, -270, 1352, 97, -1105, 1090, -248},
{-222, 295, 774, -878, -429, 788, -669, -966, 355},
{-19, -1712, 637, -920, -43, -34, 34, 628, -199}}

Last edited by anonimnystefy (2012-04-12 00:11:30)


“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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#204 2012-04-12 00:14:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

Now run this:


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.

Online

#205 2012-04-12 00:24:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

{{24, 0, 0, 120, 0, 140, 0, -15, 0},
{-1020, -430, -77, 188, -802, -515, -743, -339,
  202}, {-367, -461, -955, 317, 400, -72, 603, -923, 229}, {40,
  509, -464, -705, 1310, -805, -76, -647, 229}, {1320, -100, 177,
  585, -1344, -742, 188, 50, 8}, {-436, 491, -1733, -347, -118, 380,
  282, 505, -200}, {419, -62, -756, -270, 1352, 97, -1105,
  1090, -248}, {-222, 295, 774, -878, -429, 788, -669, -966,
  355}, {-19, -1712, 637, -920, -43, -34, 34, 628, -199}}


“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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#206 2012-04-12 00:27:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

What do you notice about post 203 and 205?


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.

Online

#207 2012-04-12 00:29:28

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

The first row and a part of the second are the same.


“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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#208 2012-04-12 00:32:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

Look only for rows that are exactly the same.


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.

Online

#209 2012-04-12 00:51:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

They are all the same!!!


“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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#210 2012-04-12 00:57:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

Okay, you have done something wrong:

Enter these and check rows:


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.

Online

#211 2012-07-13 05:19:25

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

bobbym wrote:

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]}]
     ];

Hi bobbym

Why are you multiplying dig by 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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#212 2012-07-13 05:24:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

A PSLQ works to some digit precision. You fit a constant that you have determined experimentally to some number of decimal places. That is an attempt to work to the precision of the constant that is being fit.


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.

Online

#213 2012-07-13 05:26:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

But why multiply dig by 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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#214 2012-07-13 05:35:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

That should be obvious.


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.

Online

#215 2012-07-13 05:37:55

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

It is not.


“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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#216 2012-07-13 05:44:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

Multiplying by that integerizes the vector that you are using. After all the PSLQ is a rational fit for a constant!


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.

Online

#217 2012-07-13 07:38:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

But what good would the number 25*10^25 possibly do to you?


“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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#218 2012-07-13 08:03:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

Each constant in the vector is turned into an integer part and a fractional part.


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.

Online

#219 2012-07-13 08:15:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

But dig is already an integer.


“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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#220 2012-07-13 08:22:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

But the constants in the vector are not!


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.

Online

#221 2012-07-13 08:37:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

I understand that. So there is no reason to multiply dig by 10^dig, only the vector.


“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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#222 2012-07-13 08:40:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

Hmmm. But I never do multiply did by 10^dig?!


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.

Online

#223 2012-07-13 08:42:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

a=Append[a,10^dig*N[l,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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#224 2012-07-13 08:50:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,091

Re: PSLQ and LLL?

That multiplies the vector by 10^dig.


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.

Online

#225 2012-07-13 08:51:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: PSLQ and LLL?

Wait, the second parameter for the function N[] is to how many digits we round down?


“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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