Home Online Manual
Top
Back: ncrepIsDefinedDim
Forward: ncrepIsRegular
FastBack:
FastForward:
Up: ncrat_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

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