PARI's commands

[science_man_88]

eg. primorial = prime factorial || primorial (well dah) || multiplication of primes upto n || multiplication of the first n primes

is there a way to equate 2 names to a function one to mean the other. if so should be easy

oh wait I could do this:

primorial(n)= a=1;for(p=1,n,if(isprime(p),a=a*p));return(a)

prime_factorial(n)=primorial(n)

multiplication_of_primes_upto(n) = primorial(n)

then all these are equal and the code should be able to put the words into a function name and figure it out regardless.

they all work as planned I tested them.

[CRGreathouse]

Right. Actually I'd just code the first and let the AI (#1) figure out that they're all the same.

[science_man_88]

Originally Posted by CRGreathouse

Right. Actually I'd just code the first and let the AI (#1) figure out that they're all the same.

I'm not sure how to do this in AI yet (I do have a uncle in robotics teaching last I checked wonder if someone like that would help) maybe I should have learned KPL lol

AI is artificial intellegence but it seems like AI is also automatically inferred

[CRGreathouse]

I meant to also say: your method of defining function synonyms is good. (It avoids duplication, which is bad.)

Another possibility would be literally

prime_factorial=primorial

that is, setting the variable prime_factorial equal to the value of primorial, which is itself a 'function-object'. (Pari calls this a "closure".)

Originally Posted by science_man_88

I'm not sure how to do this in AI yet maybe I should have learned KPL lol

AI is artificial intellegence but it seems like AI is also automatically inferred

I meant it in the sense of artificial intelligence. The essential problem is deciding what the human wants and that's a classic strong-AI task.

[science_man_88]

yeah the equals is good see what i was thinking is:

if someone said:

"multiplication of primes upto"

it would replace " " with "_" and get a function name it can look for.

[science_man_88]

think the hard part then is:

1)size of the database
2)printing the code the function uses not the function itself(unless it makes it part of their database first).

[CRGreathouse]

Fortunately you can print functions (as closures) in the development version, which I'm sure you downloaded rather than the old 'stable' version.

foo(n)={
  if(n%7 == 4,
    print(n" is a foo");
    1
  ,
    print(n" is not a foo");
    0
  )
};
print(foo)

[science_man_88]

Reading GPRC: /cygdrive/c/Program Files/PARI/.gprc ...Done.

GP/PARI CALCULATOR Version 2.4.2 (development CHANGES-1.1971)
i686 running cygwin (ix86/GMP-4.2.1 kernel) 32-bit version
compiled: Dec 23 2007, gcc-3.4.4 (cygming special, gdc 0.12, using dmd 0.125)
(readline v5.2 enabled, extended help enabled)

Copyright (C) 2000-2006 The PARI Group

PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY
WARRANTY WHATSOEVER.

looks like it to me.

how is this like prime_factorial=primorial ? this seems to print the code of foo but doesn't equate it to another function but I think I know what you mean. This is getting less complicated by the minute, (though the database might get quite big and that's a mountain to climb).

[3.14159]

Originally Posted by CRGreathouse

But I thought you were looking at strong pseudoprimes, not Fermat pseudoprimes. In that case "Average case error estimates for the strong probable prime test" is probably more appropriate, though I don't remember if they define an analogue for P(x).

Well, I did manage to get the complete false witness sequence for 2701. It is pseudoprime to 486 bases. That means, it will be registered as composite 82% of the time.

[CRGreathouse]

Originally Posted by 3.14159

Well, I did manage to get the complete false witness sequence for 2701. It is pseudoprime to 486 bases. That means, it will be registered as composite 82% of the time.

isSPRP(n,b=2)={
	my(s=valuation(n-1,2),d=n>>s);
	n=Mod(b,n)^d;
	if(n==1,return(1));
	while(s--,
		if(n==-1,return(1));
		n=n^2
	);
	n==-1
};
ratioSlow(n)={
	1.-sum(b=1,n-1,isSPRP(n,b))/(n-1)
};
star(n)={
	n--;n>>valuation(n,2)
};
ratio(n)={
	my(f=factor(n)[,1],nu=valuation(f[1]-1,2),nn=star(n));
	for(i=2,#f,nu=min(nu,valuation(f[i]-1,2)););
	1.-(1+(2^(#f*nu)-1)/(2^#f-1))*prod(i=1,#f,gcd(nn,star(f[i])))/(n-1)
};

>ratio(2701)
time = 31 ms.
%1 = 0.8200000000000000000000000000

>ratioSlow(10^6+1)
time = 34,071 ms.
%2 = 0.9962500000000000000000000000
>ratio(10^6+1)
time = 0 ms.
%3 = 0.9962500000000000000000000000

[3.14159]

Ah, thanks. Although, I do have it perform trial division for isSPRP, up to 10⁶. isPRP does not perform trial division.


Also: Define star(n) (I haven't defined it already.)