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D.15.1.6 autX

Procedure from library autgradalg.lib (see autgradalg_lib).

Usage:
autX(RL, w, TOR); RL: ideal, w: intvec, TOR: optional list of integers.

Purpose:
compute generators for the hopf algebra O(Aut(X))
of the Mori dream space X given by Cox(X) := basering/RL and the ample class w.

Assume:
there is no torsion.

Return:
a ring. Also exports an ideal Iexported.

Example:
 
LIB "autgradalg.lib";
/////////////
// PP2
//  intmat Q[1][4] =
//    1,1,1,1;
//
//  ring R = 0,T(1..ncols(Q)),dp;
//
//  // attach degree matrix Q to R:
//  setBaseMultigrading(Q);
//  ideal I = 0;
//  intvec w0 = 1;
//
//  def RR = autX(I, w0);
//  setring RR;
//  Iexported;
//
//  basering;
//  dim(std(Iexported));
//
//  kill RR, Q, R;
//
//  quit;
//  /////////////
//  // example 3.14 from the paper
//  intmat Q[3][5] =
//    1,1,1,1,1,
//    1,-1,0,0,1,
//    1,1,1,0,0;
//
//  list TOR = 2;
//  ring R = 0,T(1..5),dp;
//
//  // attach degree matrix Q to R:
//  setBaseMultigrading(Q);
//
//  ideal I = T(1)*T(2) + T(3)^2 + T(4)^2;
//  list TOR = 2;
//
//  intvec w0 = 2,1,0;
//  def RR = autX(I, w0, TOR);
//  setring RR;
//
//  kill RR, Q, R;