PARI's commands

[science_man_88]

I know that:
2x+1 single mersennes when x is the previous single mersenne
2x^2+4x+1 double mersennes when x is the previous double mersenne

I know the relation of the exponents of a triple mersenne as they are the double mersennes but does anyone know of a general form other than (2^y+1)*(2^x-1) for triple, quadruple, quintuple, etc. mersennes ? edit: sorry wrong thread for some reason I thought this was the theory of mersenne primes thread

[science_man_88]

does anyone know why they haven't merged Pol and Polrev ? I could see a newer version with {n=1} being a switch where n=1 makes it Pol and -1 makes it Polrev, though I guess that's because I'm trying to make my own version that does something like both.

[CRGreathouse]

Originally Posted by science_man_88

does anyone know why they haven't merged Pol and Polrev ?

Why would they?

[science_man_88]

Originally Posted by CRGreathouse

Why would they?

I was just thinking that it would reduce the number of functions, but I can't make anything that quick my best attempt involved parsum:

Pols(t,v='x,{n=1})=if(n==1,parsum(w=1,#t-1,t[w]*v^(#t-w),t[#t]),parsum(w=2,#t,t[w]*v^(#t-(#t-w+1)),t[1]))

edit: which is about 1200 times as slow for a vector of length 10000

[science_man_88]

parmatrix(m,n,{X},{Y},{expr=0})={
a=matrix(m,n,x,y,0);
parfor(x=1,n,
        parvector(m,y,
                      a[x,y]=eval(expr)
                      )
        )
     ;a
}

I was trying to make a parallel function for matrices ( in case it might ever be useful)

[CRGreathouse]

You forgot my().

[science_man_88]

Originally Posted by CRGreathouse

You forgot my().

It doesn't fully work as written even with my, what am I missing?

[CRGreathouse]

I would do

parmatrix(m,n,expr=(a,b)->0)={
  my(a=matrix(m,n));
  parfor(x=1,m,
    for(y=1,n,
      a[x,y]=expr(x,y)
    )
  );
  a
};

with the understanding that the third argument needs to be given as a closure:

f(x,y)=x^2+sigma(y);
parmatrix(5, 5, f) \\ user function called by name
parmatrix(4, 6, gcd) \\ built-in function called by name
parmatrix(4, 4, (x,y) -> x+y) \\ anonymous function

You can't define a function in gp with a true expr argument (you'd need to use the PARI library directly in C).

[science_man_88]

Originally Posted by CRGreathouse

I would do

parmatrix(m,n,expr=(a,b)->0)={
  my(a=matrix(m,n));
  parfor(x=1,m,
    for(y=1,n,
      a[x,y]=expr(x,y)
    )
  );
  a
};

with the understanding that the third argument needs to be given as a closure:

f(x,y)=x^2+sigma(y);
parmatrix(5, 5, f) \\ user function called by name
parmatrix(4, 6, gcd) \\ built-in function called by name
parmatrix(4, 4, (x,y) -> x+y) \\ anonymous function

You can't define a function in gp with a true expr argument (you'd need to use the PARI library directly in C).

Okay, Thanks for the code and hint. One further question what function won't return all 0's from the matrix default of 0's ?

[CRGreathouse]

Originally Posted by science_man_88

One further question what function won't return all 0's from the matrix default of 0's ?

I don't know what you mean. I gave three examples of functions that don't return all 0s.

[science_man_88]

Originally Posted by CRGreathouse

I don't know what you mean. I gave three examples of functions that don't return all 0s.

I tried every one of those and got back 0's:

(11:48) gp > parmatrix(m,n,expr=(a,b)->0)={
  my(a=matrix(m,n));
  parfor(x=1,m,
    for(y=1,n,
      a[x,y]=expr(x,y)
    )
  );
  a
};
(12:12) gp > f(x,y)=x^2+sigma(y);
(12:13) gp > parmatrix(5, 5, f)
%67 =
[0 0 0 0 0]

[0 0 0 0 0]

[0 0 0 0 0]

[0 0 0 0 0]

[0 0 0 0 0]

(12:13) gp > parmatrix(4, 6, gcd)
%68 =
[0 0 0 0 0 0]

[0 0 0 0 0 0]

[0 0 0 0 0 0]

[0 0 0 0 0 0]

(12:13) gp > parmatrix(4, 4, (x,y) -> x+y)
%69 =
[0 0 0 0]

[0 0 0 0]

[0 0 0 0]

[0 0 0 0]