So far we have used Fortran90s operator overload capacity to include the ability to add, subtract, multiply, and divide sep_type's.
| Operator | Usage |
| Addition | C = A + B |
| Subtraction | C = A - B |
| Multiply | C = A * B |
| Divide | C = A / B |
Each operation checks that the dimensionality of the two spaces conform, add performs the desired operation. The traces are looped over, if both input traces are associated with zero trace, an output is not allocated at the given location, otherwise the give operation is performed and the output is stored in the associated output location.