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7.2.3.3 module operations (plural)
+
- addition (concatenation of the generators and simplification) Note that "-" implicitly 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
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