Singular

D.15.2.6 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"; /////////////// //// CAREFUL: the following examples seems to be unfeasible at the moment, see remark in the paper //echo=2; /////////////// //// 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; /////////////// //// 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; ```