1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1in dimension 7. We compute its integral closure in the ambient lattice ℤ7. The fastest way is applying the function intclToricRing to the ideal that is generated by the monomials whose exponent vectors are the generators of the cone (to compute it in the group of the monoid generated by these vectors use normalToricRing) . One can convert the vectors to monomials in the following way:
R=ZZ/37[x_1..x_7]; |
l={{1, 0, 0, 0, 0, 0, 0},
{0, 1, 0, 0, 0, 0, 0},
{0, 0, 1, 0, 0, 0, 0},
{0, 0, 0, 1, 0, 0, 0},
{0, 0, 0, 0, 1, 0, 0},
{0, 0, 0, 0, 0, 1, 0},
{1, 1, 1, 0, 0, 0, 1},
{1, 1, 0, 1, 0, 0, 1},
{1, 0, 1, 0, 1, 0, 1},
{1, 0, 0, 1, 0, 1, 1},
{1, 0, 0, 0, 1, 1, 1},
{0, 1, 1, 0, 0, 1, 1},
{0, 1, 0, 1, 1, 0, 1},
{0, 1, 0, 0, 1, 1, 1},
{0, 0, 1, 1, 1, 0, 1},
{0, 0, 1, 1, 0, 1, 1}}; |
L=for i in l list R_i |
S=intclToricRing L |
hb = flatten \ exponents \ gens S |
M=matrix l; |
d=(normaliz(M,"normalization"))#"gen" |
set entries d===set hb |
nmzFilename="rproj2"; |
intclToricRing L; |
hypes=readNmzData("sup") |
rmNmzFiles(); |
normaliz(hypes,"inequalities") |
set entries oo#"gen"===set hb |
1 1 1 -1 -1 -1 0 0 0 1 1 1 0 0 0 -1 -1 -1 0 1 1 -1 0 0 -1 0 0 1 0 1 0 -1 0 0 -1 0 1 1 0 0 0 -1 0 0 -1 0 1 1 0 -1 0 0 0 -1 1 1 0 0 -1 0 -1 0 0(this is the solution cone for a 3x3 magic square). To this end one has to choose type 5.
eq=matrix {{1, 1, 1, -1, -1, -1, 0, 0, 0}, {1, 1, 1, 0, 0, 0, -1, -1, -1}, {0, 1, 1, -1, 0, 0, -1, 0, 0}, {1, 0, 1, 0, -1, 0, 0, -1, 0}, {1, 1, 0, 0, 0, -1, 0, 0, -1}, {0, 1, 1, 0, -1, 0, 0, 0, -1}, {1, 1, 0, 0, -1, 0, -1, 0, 0}}; |
normaliz(eq,"equations") |