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7.5.8.0. ncdetection
Procedure from library involut.lib (see involut_lib).
- Usage:
- ncdetection();
- Return:
- ideal, representing an involution map
- Purpose:
- compute classical involutions (i.e. acting rather on operators than on variables) for some particular noncommutative algebras
- Assume:
- the procedure is aimed at non-commutative algebras with differential, shift or advance operators arising in Control Theory.
It has to be executed in a ring.
Example:
| | LIB "involut.lib";
ring R = 0,(x,y,z,D(1..3)),dp;
matrix D[6][6];
D[1,4]=1; D[2,5]=1; D[3,6]=1;
def r = nc_algebra(1,D); setring r;
ncdetection();
==> _[1]=x
==> _[2]=y
==> _[3]=z
==> _[4]=-D(1)
==> _[5]=-D(2)
==> _[6]=-D(3)
kill r, R;
//----------------------------------------
ring R=0,(x,S),dp;
def r = nc_algebra(1,-S); setring r;
ncdetection();
==> _[1]=-x
==> _[2]=S
kill r, R;
//----------------------------------------
ring R=0,(x,D(1),S),dp;
matrix D[3][3];
D[1,2]=1; D[1,3]=-S;
def r = nc_algebra(1,D); setring r;
ncdetection();
==> _[1]=-x
==> _[2]=D(1)
==> _[3]=S
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