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#26 2011-03-19 16:32:29
- gAr
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Re: Experimental mathematics
Hi bobbym,
I entered this: pslq([92,1,5,10,25])
and output is [0, 0, -1, -2, 1]
I don't know what I'm missing!
"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."
#27 2011-03-19 16:40:04
- bobbym
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Re: Experimental mathematics
Hi;
That answer is right but it is not very useful. It says:
0*92 = 0*1 - 1*5 - 2*10 + 1 * 25
Maybe if you enter the values as floating point? [92.00000000000000000, 1.000000000000000000, 5.0000000000000000, 10.000000000000000, 25.000000000000000]
Adjust the number of zeros to match your precision.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#28 2011-03-19 17:35:38
- gAr
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Re: Experimental mathematics
Hi bobbym,
Still no fruit.
I think it's not problem with precision, still looking around.
"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."
#29 2011-03-19 17:49:28
- bobbym
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Re: Experimental mathematics
Hi gAr;
Continue working with it. It may be that the algorithm I am using is the best. I am just looking at a site where his pslq blows up for some inputs while mine keeps on going.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#30 2011-03-19 17:59:56
- gAr
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Re: Experimental mathematics
Ok. This one stops after one solution. Does not continue to search other solutions.
Looking for way to control that.
"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."
#31 2011-03-19 18:04:24
- bobbym
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Re: Experimental mathematics
Hi gAr;
Are you saying that you got a solution?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#32 2011-03-19 18:08:01
- gAr
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Re: Experimental mathematics
Hi bobbym,
I mean the vector which is not useful here.
"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."
#33 2011-03-19 18:30:25
- bobbym
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Re: Experimental mathematics
Hi gAr;
At the bottom of this page is a Sage implementation ( I think ) of the PSLQ. It is very similar to mine. Check it out and see what you think.
http://trac.sagemath.org/sage_trac/ticket/853
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#34 2011-03-19 18:38:11
- gAr
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Re: Experimental mathematics
Hi bobbym,
I went there when you first mentioned about PSLQ. I'll read again and see if I can get something.
"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."
#35 2011-03-19 18:40:11
- bobbym
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Re: Experimental mathematics
Or I can give you mine and we can start translating it. That would make compatibility between our answers.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#36 2011-03-19 18:59:32
- gAr
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Re: Experimental mathematics
That's okay with me.
I found this link useful from the sagetrac page: http://crd.lbl.gov/~dhbailey/mpdist/
But got a runtime error when running mathtool.
"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."
#37 2011-03-19 19:05:41
- gAr
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Re: Experimental mathematics
I should have run mathinit before that. Now it's ok.
pslq[92,1,5,10,25]
PSLQM1 integer relation detection: n = 5
Iteration 0 MP initialization
Iteration 0 Start MP iterations
Iteration 3 itermp: Small value in y = 0.000000D 0
Iteration 3 Relation detected
Min, max of y = 0.000000D 0 1.041723D -2
Max. bound = 1.017072D 0
Index of relation = 1 Norm = 4.000000D 0 Residual = 0.000000D 0
CPU times:
0.00 0.00
Relation: 0 =
+ 1.* 92
+ -2.* 1
+ -1.* 5
+ -1.* 10
+ -3.* 25
"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."
#38 2011-03-19 20:10:36
- bobbym
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Re: Experimental mathematics
Very good! I think you understand computers. You have to play with them, and then force them to do what you want.
That shows that we can solve some diophantine equations with the PSLQ.
Supposing we need to find one integer solution to
95 c - 40 b -499 a = 141
We would just PSLQ this vector [ 141, 95, - 40, -499]
What do you get?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#39 2011-03-19 20:25:31
- gAr
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Re: Experimental mathematics
Yes, I get
Relation: 0 =
+ 4.* 141
+ 1.* 95
+ 4.* -40
+ 1.* -499
I need to force it to check for every possible solution!
"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."
#40 2011-03-19 20:30:38
- bobbym
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Re: Experimental mathematics
I got another solution different than that.
a = 1
b = 3
c = 8
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#41 2011-03-19 20:37:46
- gAr
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Re: Experimental mathematics
Perhaps pslq is more appropriate for real numbers.
Does your algorithm give all the possible values for integers?
"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."
#42 2011-03-19 20:50:33
- bobbym
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Re: Experimental mathematics
No, I never figured out how to coax it to get more of them. In some cases in the solution of equations when you have one solution you can get others by using some math at that point.
This one came up a while back
Some of the packages could do it immediately. It takes a human a very long time.
Using the methods of experimental math:
We compute it to 50 places
1.5707963267948966192313216916397514420985846996876
Then PSLQ it.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#43 2011-03-19 21:09:40
- gAr
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Re: Experimental mathematics
Hi bobbym,
Okay.
And the answer is pi/2.
"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."
#44 2011-03-19 21:15:40
- bobbym
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Re: Experimental mathematics
That is correct.
All that the command did was recognize 1.5707963267948966192313216916397514420985846996876 as π/2.
I am out of examples.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#45 2011-03-19 21:24:34
- gAr
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Re: Experimental mathematics
Thanks bobbym, this much is sufficient for my understanding.
This is very interesting, I'll play around it.
"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."
#46 2011-03-19 21:29:26
- bobbym
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Re: Experimental mathematics
Hi gAr;
It might pop up as a problem some day.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#47 2011-03-19 21:37:57
- gAr
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Re: Experimental mathematics
Hi bobbym,
Yes, may be.
"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."