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#301 2012-07-15 04:30:23

anonimnystefy
Real Member

Online

Re: PSLQ and LLL?

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

Code:

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.


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#302 2012-07-15 04:33:06

bobbym
Administrator

Online

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 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.

#303 2012-07-15 04:37:08

anonimnystefy
Real Member

Online

Re: PSLQ and LLL?

What does the Rationalize do, again?


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#304 2012-07-15 06:15:41

bobbym
Administrator

Online

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 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.

#305 2012-07-15 06:28:02

anonimnystefy
Real Member

Online

Re: PSLQ and LLL?

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

Code:

ratnum(a,dig) := round(float(a)*(10^dig))/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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#306 2012-07-15 06:32:54

bobbym
Administrator

Online

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 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.

#307 2012-07-15 06:42:11

anonimnystefy
Real Member

Online

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.


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#308 2012-07-15 06:45:07

bobbym
Administrator

Online

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 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.

#309 2012-07-15 06:54:07

anonimnystefy
Real Member

Online

Re: PSLQ and LLL?

But what about a real number?


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#310 2012-07-15 06:54:25

bobbym
Administrator

Online

Re: PSLQ and LLL?

What real number?


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.

#311 2012-07-15 06:56:40

anonimnystefy
Real Member

Online

Re: PSLQ and LLL?

e for example.


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#312 2012-07-15 06:57:49

bobbym
Administrator

Online

Re: PSLQ and LLL?

Rationalize[2.71818]


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.

#313 2012-07-15 06:58:21

anonimnystefy
Real Member

Online

Re: PSLQ and LLL?

That is not e.


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#314 2012-07-15 06:59:41

bobbym
Administrator

Online

Re: PSLQ and LLL?

Oh boy. Are you serious?


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.

#315 2012-07-15 07:02:38

anonimnystefy
Real Member

Online

Re: PSLQ and LLL?

Why does your function have another parameter?


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#316 2012-07-15 07:04:18

bobbym
Administrator

Online

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 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.

#317 2012-07-15 07:05:45

anonimnystefy
Real Member

Online

Re: PSLQ and LLL?

Last edited by anonimnystefy (2012-07-15 07:05:59)


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#318 2012-07-15 07:13:16

bobbym
Administrator

Online

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 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.

#319 2012-07-15 07:14:43

anonimnystefy
Real Member

Online

Re: PSLQ and LLL?

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


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#320 2012-07-15 07:18:14

bobbym
Administrator

Online

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 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.

#321 2012-07-15 08:28:00

anonimnystefy
Real Member

Online

Re: PSLQ and LLL?

Ok, what next?


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#322 2012-07-15 08:39:31

bobbym
Administrator

Online

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 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.

#323 2012-07-15 10:15:35

anonimnystefy
Real Member

Online

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?


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#324 2012-07-15 11:54:04

bobbym
Administrator

Online

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 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.

#325 2012-07-15 12:08:48

anonimnystefy
Real Member

Online

Re: PSLQ and LLL?

No. Only up to the Lattice Reduce.


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
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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