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#201 2012-04-12 21:52:34

anonimnystefy
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Re: PSLQ and LLL?

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

Code:

{{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 22:04:02)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#202 2012-04-12 22:06:00

bobbym

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Re: PSLQ and LLL?

This is correct.

Code:

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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#203 2012-04-12 22:10:37

anonimnystefy
Real Member

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Re: PSLQ and LLL?

Code:

{{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 22:11:30)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#204 2012-04-12 22:14:31

bobbym

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Re: PSLQ and LLL?

Now run this:

In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#205 2012-04-12 22:24:53

anonimnystefy
Real Member

Offline

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}}

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#206 2012-04-12 22:27:26

bobbym

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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#207 2012-04-12 22:29:28

anonimnystefy
Real Member

Offline

Re: PSLQ and LLL?

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#208 2012-04-12 22:32:13

bobbym

Offline

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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#209 2012-04-12 22:51:44

anonimnystefy
Real Member

Offline

Re: PSLQ and LLL?

They are all the same!!!

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#210 2012-04-12 22:57:35

bobbym

Offline

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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#211 2012-07-14 03:19:25

anonimnystefy
Real Member

Offline

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?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#212 2012-07-14 03:24:00

bobbym

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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#213 2012-07-14 03:26:22

anonimnystefy
Real Member

Offline

Re: PSLQ and LLL?

But why multiply dig by 10^dig?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#214 2012-07-14 03:35:10

bobbym

Offline

Re: PSLQ and LLL?

That should be obvious.

In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#215 2012-07-14 03:37:55

anonimnystefy
Real Member

Offline

Re: PSLQ and LLL?

It is not.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#216 2012-07-14 03:44:58

bobbym

Offline

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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#217 2012-07-14 05:38:12

anonimnystefy
Real Member

Offline

Re: PSLQ and LLL?

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#218 2012-07-14 06:03:33

bobbym

Offline

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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#219 2012-07-14 06:15:53

anonimnystefy
Real Member

Offline

Re: PSLQ and LLL?

But dig is already an integer.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#220 2012-07-14 06:22:23

bobbym

Offline

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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#221 2012-07-14 06:37:12

anonimnystefy
Real Member

Offline

Re: PSLQ and LLL?

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#222 2012-07-14 06:40:59

bobbym

Offline

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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#223 2012-07-14 06:42:53

anonimnystefy
Real Member

Offline

Re: PSLQ and LLL?

a=Append[a,10^dig*N[l,dig]];

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#224 2012-07-14 06:50:06

bobbym

Offline

Re: PSLQ and LLL?

That multiplies the vector by 10^dig.

In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

#225 2012-07-14 06:51:12

anonimnystefy
Real Member

Offline

Re: PSLQ and LLL?

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón