# Singular

#### 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; ```