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8 Tope posets

8.1 Operations

8.1-1 TopePoset

Returns: A TopePoset object

Constructs the tope poset of the oriented matroid OM with respect to the base tope BTope (given as sign vector).

gap> O:=OM([[1,0],[0,1]]); Ts:=OMCovectors(O)[1]; T:=Ts[1];
<OrientedMatroid: 2 elements, rank 2>
[ [ -1, -1 ], [ 1, 1 ], [ -1, 1 ], [ 1, -1 ] ]
[ -1, -1 ]
gap> TP:=TopePoset(O,T);
<TopePoset with 3 topes>

8.2 Attributes

8.2-1 TPGroundSet

Returns: A list of lists.

The ground set of the tope poset TP. It is a list of list, recording the separating elements of the given tope from the base tope.

gap> TPGroundSet(TP);
[ [ [  ] ], [ [ 1 ], [ 2 ] ], [ [ 1, 2 ] ] ]

8.2-2 TPBaseTope

Returns: A sign vector.

Returns the bast tope of the tope poset TP.

gap> TPBaseTope(TP);
[ -1, -1 ]

8.2-3 TPRankPoly

Returns: A polynomial.

Returns the rank generating polynomial of the tope poset TP.

gap> TPRankPoly(TP);
t^2+2*t+1

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