symbolicPolyhedron -- computes the symbolic polyhedron for a monomial ideal.

Synopsis

Usage:

symbolicPolyhedron(I)
Inputs:
- I, an ideal,
Outputs:
- a convex polyhedron,

Description

The symbolic polyhedron associated to a monomial ideal $I$ is defined in the paper "Symbolic Powers of Monomial Ideals" by S. M. Cooper, R. J. D. Embree, H. T. Ha, A. H. Hoefel. The symbolic polyhedron contains the exponent vector of any monomial in $I^n$ scaled by $1/n$.

This function uses the Polyhedra package and returns an object of type Polyhedron.

i1 : R = QQ[x,y,z];

i2 : I = ideal(x*y,y*z,x*z);

o2 : Ideal of R

i3 : symbolicPolyhedron(I)

o3 = Polyhedron{...1...}

o3 : Polyhedron

Ways to use symbolicPolyhedron :

symbolicPolyhedron(Ideal)
symbolicPolyhedron(MonomialIdeal)

symbolicPolyhedron -- computes the symbolic polyhedron for a monomial ideal.

Synopsis

Description

See also

Ways to use symbolicPolyhedron :

For the programmer