\\% Basic manipulations of vectors.
\\ Author: Ralf Stephan, (reformatted by Joerg Arndt)
\\ online at http://www.jjj.de/pari/
\\ version: 2010-April-02 (18:00)


ggf(v)=
{ /* Guess generating function for supplied vector of integers */
/* Example: ggf(vector(10,j,fibonacci(j)^2)) ==> (-x + 1)/(x^3 - 2*x^2 - 2*x + 1) */

    local(l,m,p,q,B);
    l = length(v);
    B = floor(l/2);
    if ( B<4,  return(0) );
    m = matrix(B, B, x, y, v[x-y+B+1]);
    q = qflll(m, 4)[1];
    if ( length(q)==0,  return(0) );
\\    p = sum(k=1, B, x^(k-1)*q[k,1]);
    p = sum(k=1, B, 'x^(k-1)*q[k,1]);
\\    q = Pol( Pol( vector(l, n, v[l-n+1]) )*p + O(x^(B+1)) );
    q = Pol( Pol( vector(l, n, v[l-n+1]) )*p + O('x^(B+1)) );
    if ( polcoeff(p,0)<0,  q=-q; p=-p);
    q = q/p;
\\    p = Ser(q+O(x^(l+1)));
    p = Ser(q+O('x^(l+1)));
    for (m=1, l, if( polcoeff(p,m-1)!=v[m],  return(0)) );
    return(q);
} /* ------- */

\\ qflll(x,{flag=0}): LLL reduction of the vectors forming the matrix x
\\ (gives the unimodular transformation matrix).
\\ flag is optional, and can be
\\ 0: default,
\\ 1: lllint algorithm for integer matrices,
\\ 2: lllintpartial algorithm for integer matrices,
\\ 3: lllrat for rational matrices,
\\ 4: lllkerim giving the kernel and the LLL reduced image,
\\ 5: lllkerimgen same but if the matrix has polynomial coefficients,
\\ 7: lll1, old version of qflll,
\\ 8: lllgen, same as qflll when the coefficients are polynomials,
\\ 9: lllint algorithm for integer matrices using content.

\\ ==== end of file ====