up previous next
IsTree5

checks if a facet complex is a tree

Syntax
IsTree5(L: LIST): [BOOL,LIST ]
IsTree5(L: LIST, "NOOPT"): [BOOL,LIST]
IsTree5(L: LIST, "OPT"): [BOOL,LIST]
IsTree5(L: LIST, "CS_NOOPT"): [BOOL,LIST]
IsTree5(L: LIST, "CS_OPT"): [BOOL,LIST]

Description
This function return whether the facet complex described by the list L of square free power products is a tree, plus a list which:

- is empty if L is a tree

- contains three elements of a cycle of L if L is not a tree.

Four options NOOPT,OPT,CS_NOOPT,CS_OPT are available as second argument, specifying different algorithms; the default is CS_OPT. For a full description of the algorithms we refer to the paper M. Caboara, S. Faridi e P. Selinger, Simplicial cycles and the computation of symplicial trees. Accepted for publication on the Journal of Symbolic Computation (2006).

Example
  Use R ::= Q[x,y,z,t];
  D := [xy, yz, zt, tx];
  IsTree5(D);
[FALSE, [xy, xt, yt]]
-------------------------------
  IsTree5([xy, yz, zt]);
[TRUE, [ ]]
-------------------------------