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#26 2014-04-22 23:48:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

 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.
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.

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#27 2014-04-22 23:53:36

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,174
Website

Re: How does Randall do these?

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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#28 2014-04-22 23:56:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

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.
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.

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#29 2014-04-23 00:33:45

ShivamS
Member
Registered: 2011-02-07
Posts: 3,365

Re: How does Randall do these?

Agnishom wrote:

Can you teach me that?

You need some linear algebra.

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#30 2014-04-23 00:42:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

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.
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.

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#31 2014-04-23 02:16:29

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,174
Website

Re: How does Randall do these?

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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#32 2014-04-23 02:32:47

ShivamS
Member
Registered: 2011-02-07
Posts: 3,365

Re: How does Randall do these?

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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#33 2014-04-23 03:51:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

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.
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.

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#34 2014-04-23 07:13:23

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

Re: How does Randall do these?

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

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#35 2014-04-23 07:23:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

If I know Randall, he is 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.

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#36 2014-04-23 10:08:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

Re: How does Randall do these?

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

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#37 2014-04-23 10:28:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

Can you come up with more digits easily to test?


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.

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#38 2014-04-23 11:18:14

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

Re: How does Randall do these?

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

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#39 2014-04-23 11:24:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

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.
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.

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#40 2014-04-23 13:12:02

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

Re: How does Randall do these?

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


“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

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#41 2014-04-23 13:18:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

The top row is the exact answer!


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.

Offline

#42 2014-04-23 13:21:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

Re: How does Randall do these?

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


“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

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#43 2014-04-23 13:22:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

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.
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.

Offline

#44 2014-04-23 13:27:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,801

Re: How does Randall do these?

Hm?


“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

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#45 2014-04-23 13:29:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

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.
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.

Offline

#46 2014-04-23 14:19:05

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,174
Website

Re: How does Randall do these?

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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#47 2014-04-23 14:23:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

One of the mightiest sites on the web.


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.

Offline

#48 2014-04-26 19:13:44

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: How does Randall do these?

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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#49 2014-04-26 20:33:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,367

Re: How does Randall do these?

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.
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.

Offline

#50 2014-04-26 21:49:59

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: How does Randall do these?

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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