PSLQ and LLL?

bobbym · 2012-04-11 03:00:42

Nothing, if it is working. But built in functions are faster and use less memory.

anonimnystefy · 2012-04-11 03:06:44

Ok,I'm gonna try both.I think there is a time measuring function in Maxima.Let me see if I can use it somehow.

bobbym · 2012-04-11 03:09:36

It will you be your code so use whichever one you like, we have several more lines to translate.

bobbym · 2012-04-11 03:12:58

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]}]*)
   a];

Use the addrow function to replace the append.

anonimnystefy · 2012-04-11 03:16:12

Hi bobbym

Should the function append it on the right or down?

bobbym · 2012-04-11 03:29:33

On top of the identity matrix. Addrow is the maxima command to do that.

anonimnystefy · 2012-04-11 03:41:51

Ok.I found the Transpose.What is Rationalize?

bobbym · 2012-04-11 05:54:52

Maxima has a rationalize command.

anonimnystefy · 2012-04-11 05:59:36

Ok.Let's go step by step.

What is what in here: 10^dig*N[l, dig]

bobbym · 2012-04-11 06:05:03

The parameter of the function call pslq(l,dig). l is basis vector and dig is the number of digits.

anonimnystefy · 2012-04-11 06:08:45

And what is N[l,dig]?

bobbym · 2012-04-11 06:10:41

That is mathematica taking the list of constants and turning them into floating point numbers.

bobbym · 2012-04-11 06:15:28

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]}]*)
   a];

The lattice reduce command that is the problem.

anonimnystefy · 2012-04-11 06:17:18

hi bobbym

How does one append a vector length 2 to a square matrix of arbitrary size?

bobbym · 2012-04-11 06:22:57

The vector is 1 x n and the matrix is n x n.

anonimnystefy · 2012-04-11 06:51:09

What is that vector? I am confused.

How does the vector look like? And how would that translate to Maxima?

bobbym · 2012-04-11 06:55:47

The vector is inputted by the user it contains the constants and the value to be fit.

anonimnystefy · 2012-04-11 06:57:34

hi bobbym

And 'dig' is the number of digits of what?

bobbym · 2012-04-11 06:59:41

For the PSLQ you have your constants, like 5, pi, sqrt(3), e and you have the value you want to determine to some amount of digits.

anonimnystefy · 2012-04-11 07:01:11

Oh,ok.

So what is multiplied by 10^dig?

bobbym · 2012-04-11 07:10:23

The vector of constants and the number.

That is easy, the problem is there does not seem to be a lattice reduce. This is the heart of the algorithm.

anonimnystefy · 2012-04-11 07:12:33

See if this helps:

http://www.math.utexas.edu/pipermail/ma … 15235.html

bobbym · 2012-04-11 07:21:13

Yes, I have already been looking at that. It is written in Lisp, which I have entirely forgotten. The chances of getting that to work are one in ten thousand.

anonimnystefy · 2012-04-11 07:22:54

But,if we don't get to the lattice reduce part,there is no point in being able to do the lattice reduce part.

bobbym · 2012-04-11 07:26:56

All the rest of my function is simple almost cosmetic. I could get around all of it one way or another. The lattice reduce is the actual algorithm.

Math Is Fun Forum

#126 2012-04-11 03:00:42

Re: PSLQ and LLL?

#127 2012-04-11 03:06:44

Re: PSLQ and LLL?

#128 2012-04-11 03:09:36

Re: PSLQ and LLL?

#129 2012-04-11 03:12:58

Re: PSLQ and LLL?

#130 2012-04-11 03:16:12

Re: PSLQ and LLL?

#131 2012-04-11 03:29:33

Re: PSLQ and LLL?

#132 2012-04-11 03:41:51

Re: PSLQ and LLL?

#133 2012-04-11 05:54:52

Re: PSLQ and LLL?

#134 2012-04-11 05:59:36

Re: PSLQ and LLL?

#135 2012-04-11 06:05:03

Re: PSLQ and LLL?

#136 2012-04-11 06:08:45

Re: PSLQ and LLL?

#137 2012-04-11 06:10:41

Re: PSLQ and LLL?

#138 2012-04-11 06:15:28

Re: PSLQ and LLL?

#139 2012-04-11 06:17:18

Re: PSLQ and LLL?

#140 2012-04-11 06:22:57

Re: PSLQ and LLL?

#141 2012-04-11 06:51:09

Re: PSLQ and LLL?

#142 2012-04-11 06:55:47

Re: PSLQ and LLL?

#143 2012-04-11 06:57:34

Re: PSLQ and LLL?

#144 2012-04-11 06:59:41

Re: PSLQ and LLL?

#145 2012-04-11 07:01:11

Re: PSLQ and LLL?

#146 2012-04-11 07:10:23

Re: PSLQ and LLL?

#147 2012-04-11 07:12:33

Re: PSLQ and LLL?

#148 2012-04-11 07:21:13

Re: PSLQ and LLL?

#149 2012-04-11 07:22:54

Re: PSLQ and LLL?

#150 2012-04-11 07:26:56

Re: PSLQ and LLL?

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