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7.5.3.0. 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 noncommutative algebras with differential, shift or advance operators arising in Control Theory. It has to be executed in the 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;
nc_algebra(1,D);
==> //   characteristic : 0
==> //   number of vars : 6
==> //        block   1 : ordering dp
==> //                  : names    x y z D(1) D(2) D(3) 
==> //        block   2 : ordering C
==> //   noncommutative relations: ...
ncdetection();
==> _[1]=x
==> _[2]=y
==> _[3]=z
==> _[4]=D(1)
==> _[5]=D(2)
==> _[6]=D(3)
kill r;
//----------------------------------------
ring r=0,(x,S),dp;
nc_algebra(1,-S);
==> //   characteristic : 0
==> //   number of vars : 2
==> //        block   1 : ordering dp
==> //                  : names    x S 
==> //        block   2 : ordering C
==> //   noncommutative relations: ...
ncdetection();
==> _[1]=x
==> _[2]=S
kill r;
//----------------------------------------
ring r=0,(x,D(1),S),dp;
matrix D[3][3];
D[1,2]=1;  D[1,3]=-S;
nc_algebra(1,D);
==> //   characteristic : 0
==> //   number of vars : 3
==> //        block   1 : ordering dp
==> //                  : names    x D(1) S 
==> //        block   2 : ordering C
==> //   noncommutative relations: ...
ncdetection();
==> _[1]=x
==> _[2]=D(1)
==> _[3]=S


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