PARI's commands - Page 135

CRGreathouse · 2010-09-21, 23:09

Quote:

Originally Posted by 3.14159

Next: How to fake SIQS data?

Of course it's trivial to fake them at present since you're not asking for any data...

I don't know of an easy way at present, but let me think on it.

3.14159 · 2010-10-04, 02:56

Quote:

Originally Posted by CRGreathouse

Of course it's trivial to fake them at present since you're not asking for any data...

I don't know of an easy way at present, but let me think on it.

You have any ideas? Anything at all?

CRGreathouse · 2010-10-04, 12:03

Quote:

Originally Posted by 3.14159

You have any ideas? Anything at all?

Yes -- but I'd prefer not to share until I get a working version.

3.14159 · 2010-10-04, 21:23

Quote:

Originally Posted by CRGreathouse

Yes -- but I'd prefer not to share until I get a working version.

Well, you can notify me full speed ahead whenever you have those ideas.

CRGreathouse · 2010-10-04, 22:25

Quote:

Originally Posted by 3.14159

Well, you can notify me full speed ahead whenever you have those ideas.

I have the ideas now, but haven't worked through the math needed to implement them yet. I'll also need to find a system with a fast GCD -- I think GMP 5 has Moller's improvements coded in, so maybe that.

science_man_88 · 2010-10-10, 16:41

Code:

(13:30) gp > U(x,P,Q)= v=vector(x+1,n,0);v[1]=0;v[2]=1;for(y=3,x+1,v[y]=P*v[y-1]-Q*v[y-2]);print(v);
(13:33) gp > V(x,P,Q)= v=vector(x+1,n,0);v[1]=2;v[2]=P;for(y=3,x+1,v[y]=P*v[y-1]-Q*v[y-2]);print(v);

I deleted the tests of the stuff i pasted to save room. like them CRG and is there ever a third kind ? I know Mersenne numbers are U(P,Q) for P=3 Q=2 for this type but the V aren't quite the exponents I was wondering if we could ever make more kinds so that one may be a list of the exponents.

CRGreathouse · 2010-10-10, 17:34

Yes, I like them, but I'd like it better with ";v" instead of ";print(v);". Always return, never print! With the return version you can do fun stuff like isprime(U(7,3,2)).

These are (homogeneous linear) recurrence relations (with constant coefficients); there are many more possibilities.

science_man_88 · 2010-10-10, 18:13

one thing I don't like is Wikipedia doesn't list it under lucas sequences I have a account just I forgot it all lol. maybe if someone remembers they can edit it lol.

CRGreathouse · 2010-10-10, 22:43

What is "it"?

science_man_88 · 2010-10-10, 22:56

Quote:

Originally Posted by CRGreathouse

What is "it"?

Mersenne numbers it doesn't list them as a famous example in http://en.wikipedia.org/wiki/Lucas_sequence but they are P=3 Q=2

CRGreathouse · 2010-10-10, 23:23

That's hard because some definitions require them to have a prime exponent, in which case they're not recurrence relations.

2010-10-10, 16:41	#1480
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶·131 Posts	thought I'd put this here. Code: (13:30) gp > U(x,P,Q)= v=vector(x+1,n,0);v[1]=0;v[2]=1;for(y=3,x+1,v[y]=Pv[y-1]-Qv[y-2]);print(v); (13:33) gp > V(x,P,Q)= v=vector(x+1,n,0);v[1]=2;v[2]=P;for(y=3,x+1,v[y]=Pv[y-1]-Qv[y-2]);print(v); I deleted the tests of the stuff i pasted to save room. like them CRG and is there ever a third kind ? I know Mersenne numbers are U(P,Q) for P=3 Q=2 for this type but the V aren't quite the exponents I was wondering if we could ever make more kinds so that one may be a list of the exponents.

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2010-10-10, 17:34	#1481
CRGreathouse Aug 2006 3·1,993 Posts	Yes, I like them, but I'd like it better with ";v" instead of ";print(v);". Always return, never print! With the return version you can do fun stuff like isprime(U(7,3,2)). These are (homogeneous linear) recurrence relations (with constant coefficients); there are many more possibilities.

2010-10-10, 18:13	#1482
science_man_88 "Forget I exist" Jul 2009 Dumbassville 10000011000000₂ Posts	one thing I don't like is Wikipedia doesn't list it under lucas sequences I have a account just I forgot it all lol. maybe if someone remembers they can edit it lol.

2010-10-10, 22:43	#1483
CRGreathouse Aug 2006 1011101011011₂ Posts	What is "it"?

2010-10-10, 23:23	#1485
CRGreathouse Aug 2006 3·1,993 Posts	That's hard because some definitions require them to have a prime exponent, in which case they're not recurrence relations.