Singular Manual: maxZeros

| #### D.5.8.5 maxZeros Procedure from library `orbitparam.lib` (see orbitparam_lib). Usage: maxZeros(L,v); L list, v matrix. Assume: L is a list of strictly upper triangular n x n matrices of same size. The vector space <L> genererated by the elements of L should be closed under the Lie bracket. v is matrix of constants of size n x 1. The basering has at least size(L) variables. However we will only use tangentGens(L,v)[1] many of them. Return: matrix of constants over the basering giving an element in the orbit of v under the action of exp(<L>) with (at least) as many zeros as the dimension of the orbit. Theory: We apply `parametrizeOrbit` to obtain a parametrization of the orbit according to the theorem of Chevalley-Rosenlicht. By determining the parameters from bottom to top we find an element in the orbit with (at least) as many zeros as the dimension of the orbit. Example:
    LIB "orbitparam.lib";
    ring R = 0,(x),dp;
    matrix L1[3][3] = 0,1,0, 0,0,0, 0,0,0;
    matrix L2[3][3] = 0,0,1, 0,0,0, 0,0,0;
    matrix L3[3][3] = 0,1,1, 0,0,1, 0,0,0;
    list L = L1,L2,L3;
    matrix v[3][1] = 1,2,3;
    maxZeros(L,v);
    ==> _[1,1]=0
    ==> _[2,1]=0
    ==> _[3,1]=3
    ring R1 = 0,(x),dp;
    matrix L1[4][4] = 0,1,0,0, 0,0,0,0, 0,0,0,1, 0,0,0,0;
    matrix L2[4][4] = 0,0,1,0, 0,0,0,1, 0,0,0,0, 0,0,0,0;
    list L = L1,L2;
    matrix v[4][1] = 1,2,3,4;
    maxZeros(L,v);
    ==> _[1,1]=-1/2
    ==> _[2,1]=0
    ==> _[3,1]=0
    ==> _[4,1]=4

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