13.8 Add Domain

The capsule part of Implementation defines functions that implement the operations exported by the domain—usually only some of the operations. In our demo in ugDomainsDemo we asked for the value of 3*q-q+q. Where do the operations *, +, and - come from? There is no definition for them in the capsule!

The Implementation part of a definition can domain:add optionally specify an add-domain to the left of an add add (for QuadraticForm, defines SquareMatrix(n,K) is the add-domain). The meaning of an add-domain is simply this: if the capsule part of the Implementation does not supply a function for an operation, FriCAS goes to the add-domain to find the function. So do *, + and - (from QuadraticForm) come from SquareMatrix(n,K)?