| #### 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);
    ==> Evaluating Commandline Options ...
    ==> ... done.
    ==> 0
    ==> 0
    // the points in the secondary polytope
    print(secpoly[1]);
    ==>      1     2     2     1
    ==>      2     1     1     2
    // the corresponding triangulations
    secpoly[2];
    ==> [1]:
    ==>    [1]:
    ==>       1,2,3
    ==>    [2]:
    ==>       2,3,4
    ==> [2]:
    ==>    [1]:
    ==>       1,3,4
    ==>    [2]:
    ==>       1,2,4

User manual for Singular version 4.4.0, 2024, generated by texi2html.