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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

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#202 2012-04-12 00:06:00

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

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#204 2012-04-12 00:14:31

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: PSLQ and LLL?

Now run this:

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

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#206 2012-04-12 00:27:26

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

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#208 2012-04-12 00:32:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

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#210 2012-04-12 00:57:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

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#212 2012-07-13 05:24:00

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

Offline

#214 2012-07-13 05:35:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: PSLQ and LLL?

That should be obvious.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

Offline

#216 2012-07-13 05:44:58

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

Offline

#218 2012-07-13 08:03:33

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

Offline

#220 2012-07-13 08:22:23

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

Offline

#222 2012-07-13 08:40:59

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

Offline

#224 2012-07-13 08:50:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: PSLQ and LLL?

That multiplies the vector by 10^dig.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

Offline

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