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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
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