Re: Rational exponent

[Kevin Acres <research@research-systems.com>]

I've added a small example for an exponent of -1. Ideally I need to 
accept any rational exponent here without SER/POL clashes.

Kevin.

On 2024-01-31 23:59, Kevin Acres wrote:
> I have a function that I would like to use with rational exponents.
> Currently it only works with integral exponents.
>
> I'm struggling a little and any help is welcomed.
>
> Kevin.
>
> /*
>  * z : Integer input 0..2^n-1
>  * p : irreducible polynomial of degree n
>  * n : output is in binary format 0..2^n-1
>  * e : exponent
> */
> fn2(z,p,n,e) = {
>     my(s,t=vector(n)~,k,a);
>
>     if(z==0, return(t~););
>     k = Pol(binary(z))^e;
>     a = lift(Mod(k, p));
>     s=Vecrev(a);
>     s *= denominator(s);
>     s %= 2;
>     for(i=1,#s,
>         t[i]=s[i];
>     );
>     t~;
> };

A short example for an exponent of -1. Ideally I need to be able to use 
rational exponents instead of -1.

    for(i = 1, 10,
        r = fn2(i-1, poly, e, -1);
        print([i, poly, e, -1, r]);
    );

[1, x^6 + x^4 + x^3 + 1, 6, -1, [0, 0, 0, 0, 0, 0]]
[2, x^6 + x^4 + x^3 + 1, 6, -1, [1, 0, 0, 0, 0, 0]]
[3, x^6 + x^4 + x^3 + 1, 6, -1, [0, 0, 1, 1, 0, 1]]
[4, x^6 + x^4 + x^3 + 1, 6, -1, [1, 1, 1, 0, 1, 1]]
[5, x^6 + x^4 + x^3 + 1, 6, -1, [0, 1, 1, 0, 1, 0]]
[6, x^6 + x^4 + x^3 + 1, 6, -1, [1, 1, 1, 0, 1, 1]]
[7, x^6 + x^4 + x^3 + 1, 6, -1, [1, 1, 1, 0, 1, 1]]
[8, x^6 + x^4 + x^3 + 1, 6, -1, [1, 0, 1, 1, 1, 1]]
[9, x^6 + x^4 + x^3 + 1, 6, -1, [1, 1, 0, 1, 0, 0]]
[10, x^6 + x^4 + x^3 + 1, 6, -1, [1, 1, 1, 0, 1, 1]]