#### D.13.1.5 groebnerFanP

Procedure from library `polymake.lib` (see polymake_lib).

Usage:
  groebnerFanP(f); f poly

Return:
  list, the ith entry of L[1] contains information about the ith cone in the Groebner fan dual to the ith vertex in the Newton polytope of the f
  L[1][i][1] = integer matrix representing the inequalities which describe the cone
  L[1][i][2] = a list which contains the inequalities represented by L[1][i][1] as a list of strings
  L[1][i][3] = an interger matrix whose rows are the extreme rays of the cone
  L[2] = is an integer matrix whose rows span the linearity space of the fan, i.e. the linear space which is contained
  in each cone
  L[3] = the Newton polytope of f in the format of the procedure newtonPolytopeP
  L[4] = integer matrix where each row represents the exponent vector of one monomial occuring in the input polynomial

Note:
  - if you have already computed the Newton polytope of f then you might want to use the procedure normalFanL instead in order to avoid doing costly computation twice
  - the procedure calls for its computation polymake by Ewgenij Gawrilow, TU Berlin and Michael Joswig, so it only works if polymake is installed; see http://www.math.tu-berlin.de/polymake/

Example:

    LIB "polymake.lib";
    ring r=0,(x,y,z),dp;
    matrix M[4][1]=1,x,y,z;
    poly f=y3+x2+xy+2xz+yz+z2+1;
    // the Newton polytope of f is
    list gf=groebnerFanP(f);
    // the exponent vectors of f are ordered as follows
    gf[4];
    // the first cone of the groebner fan has the inequalities
    gf[1][1][1];
    // as a string they look like
    gf[1][1][2];
    // and it has the extreme rays
    print(gf[1][1][3]);
    // the linearity space is spanned by
    print(gf[2]);
    // the vertices of the Newton polytope are:
    gf[3][1];
    // its dimension is
    gf[3][2];
    // np[3] contains information how the vertices are connected to each other,
    // e.g. the 1st vertex is connected to the 2nd, 3rd and 4th vertex
    gf[3][3][1];

User manual for Singular version 4-0-3, 2016, generated by texi2html.