13.11 Short Forms¶
In FriCAS, a domain could be defined using only an add-domain and no capsule. Although we talk about rational numbers as quotients of integers, there is no type RationalNumber in FriCAS. To create such a type, you could compile the following short-form definition:
RationalNumber() == Fraction(Integer)
The Exports part of this definition is missing and is taken to be equivalent to that of Fraction(Integer). Because of the add-domain philosophy, you get precisely what you want. The effect is to create a little stub of a domain. When a user asks to add two rational numbers, FriCAS would ask RationalNumber for a function implementing this +. Since the domain has no capsule, the domain then immediately sends its request to Fraction (Integer).
The short form definition for domains is used to define such domains as MultivariatePolynomial: MultivariatePolynomial
MultivariatePolynomial(vl: List Symbol, R: Ring) == SparseMultivariatePolynomial(R, OrderedVariableList vl)