Specifically, a function space formalism, that unifies the representation of geometry and physical attributes, is proposed along with an algebra that operates on elements in those spaces.
Essentially, the computer algebra system operates by taking the input expression entered by the user and successively applies to it a series of transformation rules until the result no longer changes (see the section Term Rewriting in this article for more details).
In particular, functions operating on the real part of the algebra are considered.
The Relational Algebra defined by (Codd 1970; Codd 1991) allows to operate on, process and analyze a set of relations.
Use algebra to work out y.
Pair algebra of partitions and differential geometric tools are involved for transformation of the operating and operated subsystems respectively.
And we are inclined to classify proving a theorem in algebra, testing a hypothesis in physics and constructing an argument in philosophy as exercises of the capacity to operate with knowledge of truths.
These expressions work much like basic algebra.
A subalgebra of an algebra is a set of elements of the algebra closed under the operations of the algebra.
Another general algebraic notion which applies to Boolean algebras is the notion of a free algebra.
