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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
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