Singular Manual: ncrepIsDefined

| #### 7.10.6.26 ncrepIsDefined Procedure from library `ncrat.lib` (see ncrat_lib). Usage: list l = ncrepIsDefined(q, vars, n, maxcoeff); Return: list(dim, list vars, list(A1, ..., Ak)), where: If dim > 0 then there are matrices A1, ..., Ak of size dim such that q is defined at A = (A1, ..., Ak), i.e., q.mat is invertible at A. If dim = 0 then no such point was found. Note: Test whether q.mat is invertible via evaluation at random matrix points with integer coefficients in [-maxcoeff, maxcoeff]. Stops after n tries. Use ixi-matrix in i-th try. The list vars contains the nc variables which occur in q. Example:
    LIB "ncrat.lib";
    ncInit(list("x", "y"));
    ncrat f = ncratFromString("inv(x*y-y*x)");
    ncrep q = ncrepGet(f);
    ncrepIsDefined(q, list(x, y), 5, 10);
    ==> [1]:
    ==>    2
    ==> [2]:
    ==>    [1]:
    ==>       x
    ==>    [2]:
    ==>       y
    ==> [3]:
    ==>    [1]:
    ==>       _[1,1]=0
    ==>       _[1,2]=-9
    ==>       _[2,1]=-2
    ==>       _[2,2]=7
    ==>    [2]:
    ==>       _[1,1]=8
    ==>       _[1,2]=-9
    ==>       _[2,1]=-4
    ==>       _[2,2]=-2
    ncrat g = ncratFromString("inv(x-x)");
    ncrep r = ncrepGet(g);
    ncrepIsDefined(r, list(x), 5, 10);
    ==> [1]:
    ==>    0
    ==> [2]:
    ==>    [1]:
    ==>       x
    ==> [3]:
    ==>    empty list

User manual for Singular version 4.4.1, 2025, generated by texi2html.