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B.1.0.2 centralizer
Procedure from library center.lib (see center_lib).
- Usage:
- centralizer(F, MaxDeg[, N]); poly F, int MaxDeg, int N
- Return:
- ideal generated by found elements
- Note:
- computes the 'minimal' set of elements of centralizer(F).
Since in general algorithms knows nothing about the number and degrees of
desired polynomials one have to specify any kind of termination condition:
1. MaxDeg - maximal degree of desired elements or/and
2. n - the minimal number of desired elements to find.
Example:
| LIB "center.lib";
ring a=0,(x,y,z),dp;
matrix D[3][3]=0;
D[1,2]=-z;
D[1,3]=2*x;
D[2,3]=-2*y;
ncalgebra(1,D); // this is U(sl_2)
poly f = 4*x*y+z^2-2*z; // central polynomial
f;
==> 4xy+z2-2z
ideal c = centralizer(f, 2); // find all elements of degree <= 2 which lies in centralizer of f
c;
==> c[1]=z
==> c[2]=y
==> c[3]=x
inCentralizer(c, f);
==> 1
ideal cc = centralizer(f, -1, 2 ); // find at least first two non trivial elements of the centralizer of f
cc;
==> cc[1]=z
==> cc[2]=y
==> cc[3]=x
inCentralizer(cc, f);
==> 1
poly g = z^2-2*z; // any polynomial
g; "";
==> z2-2z
==>
c = centralizer(g, 2); // find all elements of degree <= 2 which lies in centralizer of g
c; "";
==> c[1]=z
==> c[2]=xy
==>
inCentralizer(c, g);
==> 1
cc = centralizer(g, -1, 2 ); // find at least first two non trivial elements of the centralizer of g
cc; "";
==> cc[1]=z
==> cc[2]=xy
==>
inCentralizer(cc, g);
==> 1
| center, inCentralizer
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