Singular Manual: graver4ti2

| #### D.4.33.3 graver4ti2 Procedure from library `sing4ti2.lib` (see sing4ti2_lib). Usage: graver4ti2(A[,i]); A=intmat i=int Assume: - A is a matrix with integer entries which describes the lattice as ker(A), if second argument is not present, as the left image Im(A) = {zA : z \in ZZ^k}, if second argument is a positive integer - number of variables of basering equals number of columns of A (for ker(A)) resp. of rows of A (for Im(A)) Create: temporary files sing4ti2.mat, sing4ti2.lat, sing4ti2.gra in the current directory (I/O files for communication with 4ti2) Note: input rules for 4ti2 also apply to input to this procedure hence ker(A)={x|Ax=0} and Im(A)={xA} Return: toric ideal specified by Graver basis thereof Example:
    LIB "sing4ti2.lib";
    ring r=0,(x,y,z,w),dp;
    matrix M[2][4]=0,1,2,3,3,2,1,0;
    graver4ti2(M);
    ==> _[1]=-y2+xz
    ==> _[2]=-y3+x2w
    ==> _[3]=-yz+xw
    ==> _[4]=-z2+yw
    ==> _[5]=-z3+xw2

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