Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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## Topic review (newest first)

gAr
2011-03-19 21:37:57

Hi bobbym,

Yes, may be.

bobbym
2011-03-19 21:29:26

Hi gAr;

It might pop up as a problem some day.

gAr
2011-03-19 21:24:34

Thanks bobbym, this much is sufficient for my understanding.
This is very interesting, I'll play around it.

bobbym
2011-03-19 21:15:40

That is correct.

All that the command did was recognize 1.5707963267948966192313216916397514420985846996876 as π/2.

I am out of examples.

gAr
2011-03-19 21:09:40

Hi bobbym,

Okay.
And the answer is pi/2.

bobbym
2011-03-19 20:50:33

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.

gAr
2011-03-19 20:37:46

Perhaps pslq is more appropriate for real numbers.

Does your algorithm give all the possible values for integers?

bobbym
2011-03-19 20:30:38

I got another solution different than that.

a = 1
b = 3
c = 8

gAr
2011-03-19 20:25:31

Yes, I get
Relation:  0 =
+  4.* 141
+  1.* 95
+  4.* -40
+  1.* -499
I need to force it to check for every possible solution!

bobbym
2011-03-19 20:10:36

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?

gAr
2011-03-19 19:05:41

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

gAr
2011-03-19 18:59:32

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.

bobbym
2011-03-19 18:40:11

Or I can give you mine and we can start translating it. That would make compatibility between our answers.

gAr
2011-03-19 18:38:11

Hi bobbym,

I went there when you first mentioned about PSLQ. I'll read again and see if I can get something.

bobbym
2011-03-19 18:30:25

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