7.2.3.3 module operations (plural)

+

addition (concatenation of the generators and simplification) Note that "-" implicitely converts a module into a matrix; see below example.

*

right or left multiplication with number, ideal, or poly (but not `module` * `module`!)

module_expression [ int_expression , int_expression ]

is a module entry, where the first index indicates the row and the second the column

module_expressions [ int_expression ]

is a vector, where the index indicates the column (generator)

Example:

ring A=0,(x,y,z),Dp; matrix D[3][3]; D[1,2]=-z; D[1,3]=y; D[2,3]=x; // this algebra is U(so_3) def B=nc_algebra(1,D); setring B; module M = [x,y],[0,0,x*z]; module N = matrix((x+y-z)*M) - matrix(M*(x+y-z)); // no - for type module print(N); ==> -y-z,0, ==> -x+z,0, ==> 0, -x2-xy-yz-z2