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7.10.6.27 ncrepIsRegular

Procedure from library ncrat.lib (see ncrat_lib).

Usage:
list l = ncrepIsRegular(q, vars, n, maxcoeff);

Return:
list(k, list vars, list(a1, ..., ak)), where:
If k = 1 then there are scalars (1x1-matrices) a1, ..., ak 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 integers in [-maxcoeff, maxcoeff].
Stops after n tries. 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);
ncrepIsRegular(q, list(x, y), 10, 100);
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       x
==>    [2]:
==>       y
==> [3]:
==>    empty list
ncrat g = ncratFromString("inv(1+x*y-y*x)");
ncrep r = ncrepGet(g);
ncrepIsRegular(r, list(x, y), 10, 100);
==> [1]:
==>    1
==> [2]:
==>    [1]:
==>       x
==>    [2]:
==>       y
==> [3]:
==>    [1]:
==>       _[1,1]=-55
==>    [2]:
==>       _[1,1]=-24


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