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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