Top
Back: findAuto
Forward: involution
FastBack: freegb_lib
FastForward: gkdim_lib
Up: involut_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document
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


Top Back: findAuto Forward: involution FastBack: freegb_lib FastForward: gkdim_lib Up: involut_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4-0-3, 2016, generated by texi2html.