# CASA Function: neighborhoodTree

Checks whether a given object is a neighborhood tree.

### Calling Sequence:

• b := `type/neighborhoodTree`(l)
• b := type(l,neighborhoodTree)

### Parameters:

l : list(list)
• a list of lists

### Result:

b : boolean
• Either true or false, depending on whether the list of lists is a neighborhood tree or not.

### Description:

• This function checks whether a given object is a neighborhood tree or not.
• A neighborhood tree is defined recursively. First of all, the empty list is a neighborhood tree. A list l of lists is a neighborhood tree if, first of al, the lists l[i] in l contain six elements. The first element is a nonnegative integer; the second, third and fourth elements are coordinates of a point in a projective plane. The fifth element is a set of transformations. The sixth element l[i][6] again is a neighborhood tree. And if, secondly, this definition ends; i.e. for every 1 <= i <= nops(l) we have a certain k[i] such that l[i][6][6]..[6] = [] with k[i] levels.

### Examples:

> A := mkImplAlgSet([y^6-x^3+x^4+x^6],[x,y]);

> G := neighbGraph(A);

> type(G,neighborhoodTree);