Singular

7.8.4 ncgen

Syntax:

ncgen ( int_expression )

Type:

poly

Purpose:

returns the i-th free non-commutative generator of a free bimodule.

Note:

ncgen in bimodules is used together with the commutative gen, which encodes the component or the position in a vector.

Example:

LIB"freegb.lib"; ring r= 0,(x,y),dp; ring R = freeAlgebra(r,4,3); // R supports free bimodule up to rank 3 typeof(ncgen(2)); ==> poly vector v = [ncgen(1)*x, x*ncgen(2), y*ncgen(3)*x]; v; ==> y*ncgen(3)*x*gen(3)+ncgen(1)*x*gen(1)+x*ncgen(2)*gen(2) print(v*x); ==> [ncgen(1)*x*x,x*ncgen(2)*x,y*ncgen(3)*x*x] print(x*v); ==> [x*ncgen(1)*x,x*x*ncgen(2),x*y*ncgen(3)*x]