CoCoA:IsTree5

IsTree5

checks if a facet complex is a

tree

Description

This function is implemented in CoCoALib (requires an active CoCoAServer).

This function tests 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 by

M. Caboara, S. Faridi, and P. Selinger, Simplicial cycles and

the computation of simplicial trees, Journal of Symbolic Computation, vol.42/1-2, pp.77-88 (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, [ ]]
-------------------------------

Syntax

IsTree5(L: LIST): [BOOL,LIST ]
IsTree5(L: LIST, <quotes>NOOPT</quotes>): [BOOL,LIST]
IsTree5(L: LIST, <quotes>OPT</quotes>): [BOOL,LIST]
IsTree5(L: LIST, <quotes>CS_NOOPT</quotes>): [BOOL,LIST]
IsTree5(L: LIST, <quotes>CS_OPT</quotes>): [BOOL,LIST]

   <type>cocoaserver</type>

Introduction to CoCoAServer