Singular

D.4.26.1 markov4ti2

Usage:

markov4ti2(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 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:

files sing4ti2.mat, sing4ti2.lat, sing4ti2.mar 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 Markov basis thereof

LIB "sing4ti2.lib";
ring r=0,(x,y,z),dp;
matrix M[2][3]=0,1,2,2,1,0;
markov4ti2(M);
==> _[1]=-y2+xz
matrix N[1][3]=1,2,1;
markov4ti2(N,1);
==> _[1]=xy2z-1
==> _[2]=xy2z-1