Singular Manual: secondaryPolytope

| #### D.13.4.2 secondaryPolytope Procedure from library `polymake.lib` (see polymake_lib). Usage: secondaryPolytope(polygon[,#]); list polygon, list # Assume: - polygon is a list of integer vectors of the same size representing the affine coordinates of lattice points - if the triangulations of the corresponding polygon have already been computed with the procedure triangulations then these can be given as a second (optional) argument in order to avoid doing this computation again Purpose: the procedure considers the marked polytope given as the convex hull of the lattice points and with these lattice points as markings; it then computes the lattice points of the secondary polytope given by this marked polytope which correspond to the triangulations computed by the procedure triangulations Return: list, say L, such that: L[1] = intmat, each row gives the affine coordinates of a lattice point in the secondary polytope given by the marked polytope corresponding to polygon L[2] = the list of corresponding triangulations Note: if the triangluations are not handed over as optional argument the procedure calls for its computation of these triangulations the program points2triangs from the program topcom by Joerg Rambau, Universitaet Bayreuth; it therefore is necessary that this program is installed in order to use this procedure; see http://www.rambau.wm.uni-bayreuth.de/TOPCOM/); Example:
    LIB "polymake.lib";
    // the lattice points of the unit square in the plane
    list polygon=intvec(0,0),intvec(0,1),intvec(1,0),intvec(1,1);
    // the secondary polytope of this lattice point configuration is computed
    list secpoly=secondaryPolytope(polygon);
    // the points in the secondary polytope
    print(secpoly[1]);
    // the corresponding triangulations
    secpoly[2];

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