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3.2 bracket

Syntax:
bracket ( poly_expression p, poly_expression q )
Type:
poly
Purpose:
Computes the Lie bracket [p,q]=pq-qp of the first polynomial with the second. Uses special routines, based on the Leibniz rule.
Example:
 
ring r=(0,Q),(x,y,z),Dp;
minpoly=Q^4+Q^2+1;
matrix C[3][3];
matrix D[3][3];
C[1,2]=Q2;    C[1,3]=1/Q2;  C[2,3]=Q2;
D[1,2]=-Q*z;  D[1,3]=1/Q*y; D[2,3]=-Q*x; 
ncalgebra(C,D);  // this is a quantum deformation of U(so_3).
poly p=Q^4*x2+y2+Q^4*z2+Q*(1-Q^4)*x*y*z; // this is the central element  
p=p^3; // it is still central
poly q=(x+Q*y+Q^2*z)^4;  // take some big noncentral element
size(q); // check how many monomials are in q
==> 28
bracket(p,q); // check p*q=q*p
==> 0


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            User manual for Singular version 2-1-99, August 2004, generated by texi2html.