Singular

D.4.28.3 graver4ti2

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

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