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B.2.0.4 ncdetection
Procedure from library involution.lib (see involution_lib).
- Usage:
- ncdetection(r), r a ring
- Return:
- ideal, presenting an involution map on a noncommutative algebra r
- Note:
- returns optimized involutions for some classical noncomm algebras,
arising in the Control Theory, namely algebras with
differential, shift or advance operators
Example:
| LIB "involution.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;
ncalgebra(1,D);
ncdetection(r);
==> _[1]=x
==> _[2]=y
==> _[3]=z
==> _[4]=-D(1)
==> _[5]=-D(2)
==> _[6]=-D(3)
kill r;
//----------------------------------------
ring r=0,(x,S),dp;
ncalgebra(1,-S);
ncdetection(r);
==> _[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;
ncalgebra(1,D);
ncdetection(r);
==> _[1]=-x
==> _[2]=D(1)
==> _[3]=S
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