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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

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#302 2012-07-14 06:33:06

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

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.

If it ain't broke, fix it until it is.

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

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

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#304 2012-07-14 08:15:41

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

Re: PSLQ and LLL?

Turns a decimal into the closest fraction.


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

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

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#306 2012-07-14 08:32:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

Re: PSLQ and LLL?

I thought maxima had a similar command.


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

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

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#308 2012-07-14 08:45:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

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.

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

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#310 2012-07-14 08:54:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

Re: PSLQ and LLL?

What real number?


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

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

Re: PSLQ and LLL?

Rationalize[2.71818]


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

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

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#314 2012-07-14 08:59:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

Re: PSLQ and LLL?

Oh boy. Are you serious?


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

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

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#316 2012-07-14 09:04:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

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.

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

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#318 2012-07-14 09:13:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

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.

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

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#320 2012-07-14 09:18:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

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.

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

Offline

#322 2012-07-14 10:39:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

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.

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

Offline

#324 2012-07-14 13:54:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,987

Re: PSLQ and LLL?

Is the rest of the program done?


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

If it ain't broke, fix it until it is.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

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

Offline

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