Singular Manual: ncrepIsDefinedDim

| #### 7.10.6.25 ncrepIsDefinedDim Procedure from library `ncrat.lib` (see ncrat_lib). Usage: list l = ncrepIsDefinedDim(q, N, vars, n, maxcoeff); Return: list(k, list vars, list(A1, ..., Ak)), where: If k = N then there are matrices A1, ..., Ak of size N such that q is defined at A = (A1, ..., Ak), i.e., q.mat is invertible at A. If k = 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 square matrices of dimension N. 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);
    ncrepIsDefinedDim(q, 1, list(x, y), 10, 100);
    ==> [1]:
    ==>    0
    ==> [2]:
    ==>    [1]:
    ==>       x
    ==>    [2]:
    ==>       y
    ==> [3]:
    ==>    empty list
    ncrepIsDefinedDim(q, 2, list(x, y), 10, 100);
    ==> [1]:
    ==>    2
    ==> [2]:
    ==>    [1]:
    ==>       x
    ==>    [2]:
    ==>       y
    ==> [3]:
    ==>    [1]:
    ==>       _[1,1]=-55
    ==>       _[1,2]=-24
    ==>       _[2,1]=39
    ==>       _[2,2]=-17
    ==>    [2]:
    ==>       _[1,1]=36
    ==>       _[1,2]=-58
    ==>       _[2,1]=-13
    ==>       _[2,2]=-55

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