Singular

  fan f;                              // ambient dim 0, no cones, lineality
                                      // space = ambient space
  fan f = emptyFan(int n);            // ambient dim = n, no cones,
                                      // symmetry subgroup = <e>
  fan f = n;                          // synonymous convenience method for
                                      // 'fan f = emptyFan(n)'
  fan f = emptyFan(
                 optional intmat G);  // symmetry group generated by rows of
                                      // G; ambient dim = number of columns
                                      // of G
            // Here a row r = r_1, ...r_n represents the permutation
            // which takes i to r_i. SINGULAR will check for the validity
            // of the provided rows, i.e. whether {r_1,...,r_n} = {1,...,n}
  fan f = fullFan(int n);             // ambient dim = n, the fan consists of
                                      // one cone which equals the ambient
                                      // space, symmetry subgroup = <e>
  fan f = fullFan(
                 optional intmat G);  // symmetry group generated by rows of
                                      // G; ambient dim = number of columns
                                      // of G; the fan consists of one cone
                                      // which equals the ambient space