Singular Manual: ncdetection

| ##### 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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