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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]
See freeAlgebra (letterplace); module; vector.