##### 7.7.9.0. 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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