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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

```
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]}]
];
```

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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Then?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

Try one:

`pslq[{-16.69947371922907049618724347541020677037,1, \[Pi], \[Pi]^2, \[Pi]^3, \[Pi]^4, \[Pi]^5, \[Pi]^6, \[Pi]^7}, 25]`

and then

`pslq[{-16.6994737192290704961872434007314678413017917428814446693080866964921,1, \[Pi], \[Pi]^2, \[Pi]^3, \[Pi]^4, \[Pi]^5, \[Pi]^6, \[Pi]^7},50]`

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

Agnishom wrote:

Can you teach me that?

You need some linear algebra.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

Also, he could use numerical analysis and a good grasp of M commands.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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What is linear algebra like?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

One of my friends describe it as "The hand wavy stuff."

It deals with potentially any aspect of maths that is algebraic, so involves operations of addition and multiplication, and such that these operations are linear. Something earns the title linear if it has to do with lines, planes and so on. Such things can be given by equations that are linear in the sense of they only involve x,y etc and NOT x^2, y^2 or higher powers.

It is a vast subject, and it is very easy to learn, hard to describe because there is so much of it. Generally it deals with: vectors, vector spaces, linear maps (matrices), solving linear equations in more than one unknown. It might go on to talk about determinants, eigenvectors, eigenspaces.

It is practical, and has a very elegant theoretical aspect as well, but not difficult.

*Last edited by ShivamS (2014-04-23 02:33:00)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

Did you try the example yet?

Also, you should keep in mind that some results are misleading.

When Randall says that the 4th root of 9^2 + 19^2/22 is pi he is of course incorrect!

Here is the correct use of M.

`NSolve[x^4 == N[Solve[x^4 == 9^2 + 19^2/22]], WorkingPrecision -> 25]`

`N[Pi, 25]`

Pi is a transcendental number that means it is not a root of a non-zero polynomial equation with rational (or integer) coefficients.

**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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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

If you had read the comic in post #1 you would know that he does not mean that seriously.

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

If I know Randall, he is 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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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Well, then you don't.

I have a question about PSLQ, how would you get what 10.34159265358979 is with it?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

Can you come up with more digits easily to test?

**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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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Well, that is the one I had in mind, but, what does PSLQ actually give out for that?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

It would depend on what your basis vector was.

`pslq[{10.341592653589792, 1, \[Pi], \[Pi]^2, \[Pi]^3, \[Pi]^4}, 10]`

See the top row.

**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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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Hm, it seems to get worse to more arguments it has.

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

The top row is the exact answer!

**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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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Yes, yes, that's okay. What I'm saying is that it gets worse at finding the relations the more constants I add.

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

Again, that depends.Maple and the ISC have solved the problem succesfully I have not.

**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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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Hm?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

Do not be like a mathematician, Do not worry about the times the algorithm does not get there. Rejoice in the fact that it often does!

**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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Who is the ISC?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

One of the mightiest sites on the web.

**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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Try one:

`pslq[{-16.69947371922907049618724347541020677037,1, \[Pi], \[Pi]^2, \[Pi]^3, \[Pi]^4, \[Pi]^5, \[Pi]^6, \[Pi]^7}, 25]`

and then

`pslq[{-16.6994737192290704961872434007314678413017917428814446693080866964921,1, \[Pi], \[Pi]^2, \[Pi]^3, \[Pi]^4, \[Pi]^5, \[Pi]^6, \[Pi]^7},50]`

What is that number supposed to be, there's some mismatch.

16.69947371922907049618724347541020677037

16.6994737192290704961872434007314678413017917428814446693080866964921

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,832

Probably to higher precision.

That is the integral in

http://www.mathisfunforum.com/viewtopic.php?id=15243

since it is an approximation each version of M gives a different answer although the pslq still gets there!

**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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Ah, okay!

Thanks for reminding that, I had almost lost touch with the pslq.

This is the higher precision output by D. H. Bailey's "experimental mathematician's toolkit": -16.69947371922907049618724340073146784130179174288144470245664281170485

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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